Science, Art and Nature in Medieval and Modern Thought

SCIENCE, ART AND NATURE l IN MEDIEVAL AND MODERN THOUGHT SID-EREVS N V N C I VS MAGNA, L O N G E Q V E ADM1RAB1LIA S...

Author: A. C. Crombie

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SCIENCE, ART AND NATURE l IN MEDIEVAL AND MODERN THOUGHT

SID-EREVS N V N C I VS

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V E N E T I I S , Apud Thomam Baglionum. M DC X. Superiorum Permiffu, & Privilegio. Galileo Galilei, Sidereus mincius (1610): title page. This little book marks a turning-point in Galileo's life. Here he published his first telescopic discoveries, notably of the mountainous surface of the Moon and the satellites of Jupiter, which he named the Medicean stars after the Grand Duke of Tuscany. Here also he showed a serious commitment to the Gopernican system.

SCIENCE, ART AND NATURE IN MEDIEVAL AND MODERN THOUGHT

A.C. CROMBIE

THE HAMBLEDON PRESS LONDON

AND

RIO GRANDE

Published by Hambledon Press 1996 102 Gloucester Avenue, London NW1 8HX (UK) PO Box 102, Rio Grande, Ohio 45674 (USA) ISBN 1 85285 067 1 © Alistair Cameron Crombie 1996 A description of this book is available from the British Library and from the Library of Congress

Printed on acid-free paper and bound in Great Britain by Cambridge University Press

Contents

Acknowledgements Illustrations Preface Further Bibliography of A.C. Crombie 1 Designed in the Mind: Western visions of Science, Nature and Humankind 2 The Western Experience of Scientific Objectivity 3 Historical Perceptions of Medieval Science 4 Robert Grosseteste (c. 1168-1253) 5 Roger Bacon (c. 1219-1292) [with J.D. North] 6 Infinite Power and the Laws of Nature: A Medieval Speculation 7 Experimental Science and the Rational Artist in Early Modern Europe 8 Mathematics and Platonism in the Sixteenth-Century Italian Universities and in Jesuit Educational Policy 9 Sources of Galileo Galilei's Early Natural Philosophy 10 The Jesuits and Galileo's Ideas of Science and of Nature [with A. Carugo] 11 Galileo and the Art of Rhetoric [with A. Carugo] 12 Galileo Galilei: A Philosophical Symbol 13 Alexandre Koyré and Great Britain: Galileo and Mersenne 14 Marin Mersenne and the Origins of Language 15 Le Corps à la Renaissance: Theories of Perceiver and Perceived in Hearing 16 Expectation, Modelling and Assent in the History of Optics: i, Alhazen and the Medieval Tradition; ii, Kepler and Descartes 17 Contingent Expectation and Uncertain Choice: Historical Contexts of Arguments from Probabilities 18 P.-L. Moreau de Maupertuis, F.R.S. (1698-1759): Précurseur du Transformisme 19 The Public and Private Faces of Charles Darwin 20 The Language of Science

vii ix xi xiii

1 13 31 39 51 67 89 115 149 165 231 257 263 275 291 301 357 407 429 439

vi

Science, Art and Nature in Medieval and Modern Thought

21 Some Historical Questions about Disease 22 Historians and the Scientific Revolution 23 The Origins of Western Science

443 451 465

Appendix to Chapter 10: 479 (a) Sources and Dates of Galileos Writings [with A. Carugo] (b) Pietro Redondi, Galileo eretico (Torino, 1983) [with A. Carugo] (c) Mario Biagioli, Galileo, Courtier (Chicago, 1993) Corrections to Science, Optics and Music in Medieval and Early Modern Thought (1990) 495 Index 497

Acknowledgements

The articles reprinted here first appeared in the following places and are reprinted by kind permission of the original publishers. 1

History of Science, xxvi (1988), pp. 1-12.

2

Proceedings of the 3rd International Humanistic Symposium 1975: The Case of Objectivity (Athenai: Hellenistic Society for Humanistic Studies, 1977), pp. 428-55.

3

In Italian in Federico II e le Scienze: Proceedings of the International Seminar on Frederick II and the Mediterranean World (1990), a cura di A. Paravicini Bagliani (Palermo: Sellerio, 1995).

4

Dictionary of Scientific Biography, ed. C.C. Gillispie, v (New York: Charles Scriber's Sons, 1972), pp. 548-54.

5

Ibid., i (1970), pp. 377-85.

6

L'infinito nella scienza, a cura di G. Toraldo di Francia (Roma: Enciclopedia Italiana, 1987), pp. 223-43.

7

Daedalus, cxv (1986), pp. 49-74.

8

Prismata: Naturwissenschaftsgeschichtliche Studien: Festchrift fur Willy Hartner, hrsg. Y. Maeyama aund W.G. Salzer (Wiesbaden: Franz Steiner Verlag GmbH, 1977), pp. 63-94.

9

Reason, Experiment and Mysticism in the Scientific Revolution, ed. M.L. Righini Bonelli and W.R. Shea (New York: Science History Publications, 1975), pp. 157-75.

10 Annali dell' Istituto e Museo di Storia della Scienza di Firenze, viii.2 (1983), pp. 1-68. 11 Nouvelles de la république des lettres (1988) ii, pp. 7-31. 12 Actes du VIIle Congrés International d'Histoire des Sciences (Florence, 1956), pp. 1089-95.

viii


13 The Renaissance of a History: Proceedings of the International Conference Alexandre Koyré, Paris, 1986, ed. P Redondi: History and Technology, iv (London, 1987), pp. 81-92. 14 In French in Nature, histoire, société: Essais en hommage à Jacques Roger, éd. C. Blanckaert, J.-L. Fischer, R. Rey (Paris: Editions Klincksieck, 1995); Appendix: The Times Literary Supplement, 2 October 1992, p. 23. 15 Le Corps à la Renaissance: Actes du XXXe Colloque de Tours 1987, sous la direction de J. Céard, M.M. Fontaine, J.-C. Margolin (Paris: Aux Amateurs de Livres, 1990), pp. 379-87. 16 Studies in History and Philosophy of Science, xxi (1990), pp. 605-32, xxii (1991), pp. 89-115. 17 The Rational Arts of Living, ed. A.C. Crombie and N.G. Siraisi, Smith College Studies in History, vol. 50 (Northampton, Mass., 1987), pp. 53101; first version published in French in Médecine et Probabilités: Actes de la Journée d'Etudes du 15 December 1979, éd. A. Fagot (Paris: I'Université Paris-Val de Marne, 1982). 18 Revue de synthèse, lxxviii (1957), pp. 35-56. 19 First published as 'Darwin's Scientific Method' in Actes du IXe Congrès International d'Histoire des Sciences, Barcelona-Madrid 1959 (Barcelona/ Paris, 1960), pp. 354-62; reprinted in The Listener (London: B.B.C., November 1959). 20 Presented at the Forum de la communication scientifique et technique: Quelles langues pour la science?, organise a l'initiative du Ministère de la Francophonie; published in French in Alliage: Culture - Science Technique, no. 4 (Eté, 1990), pp. 39-42. 21 Sida: Epidémies et sociétés, 20 et 21 juin 1987, éd. C. Mérieux (Lyon, 1987), pp. 115-21. 22 Physis, xi (1969), pp. 167-80. 23 Metascience, n.s.ii (1993), pp. 1-16.

Illustrations

Galileo Galilei, Sidereus nuncius (1610): title page

ii

Figure illustrating Roger Bacon's fifth rule

56

Galileo Galilei, from // Saggiatore (1623) : frontispiece

88

The beginning of Galileo's autograph Disputationes

152

Autograph page of Galileo's Tractatio de Caelo

154

Watermark showing a backward-looking lamb

157

Diagram of the Copernican system, with the Sun in the centre, from Galileo's Dialogo (1632)

164

Pope Urban VIII facing Galileo

165

Galileo Galilei by Mario Leoni (1624)

230

Galileo Galilei, Dialogo (1632): title page

256

Vincenzo Galilei, Dialogo della musica antica (1581): title page

274

Rene Descartes, by an unknown artist

300

Euclid: the geometry of vision

302

Euclidian vision: from Robert Fludd, Utriusque cosmi. . . historia: Microcosmus (Oppenheim, 1618)

303

The anatomy of the eye (1572)

306

Diagram of the eye, from Roger Bacon, Opus Majus

307

Light rays and the eye, from Roger Bacon, Opus Majus

312

Alberti's grid (1435)

318

A painting of a cross-section of the visual pyramid: from Fludd (1618)

318

x


Leonardo da Vinci, Codex Atlanticus, f. 337, illustrating his comparison of the eye with a camera obscura

321

Leonardo da Vinci, Codex D, f. 3v

322

Observing a solar eclipse in a camera obscura (1545)

323

Kepler, Ad Vitellionem paralipomena (Frankfurt, 1604), after Plater, De corporis humani structura et usu (Basel, 1583)

333

Descartes, La dioptrique (Leiden, 1637), illustrating Kepler's ocular dioptrics

337

Kepler, Ad Vitellionem paralipomena (Frankfurt, 1604), vol. 3, prop, xxiii

340

Scheiner, Rosa ursina (Bracciani, 1630), comparing the eye and a camera obscura with a lens system, and the effects on each of using further lenses

346

Descartes, La dioptrique (Leiden, 1637), illustrating the transmission of light

351

Scheiner, Oculus (Oeniponti, 1619), showing the structure of the eye

353

Preface

This second volume of essays forms a coherent set of studies like the first volume Science, Optics and Music in Medieval and Early Modern Thought published in 1990. Both volumes complement my books Augustine to Galileo: Medieval and Early Modern Science and Robert Grosseteste and the Origins of Experimental Science 1100-1700 and lead into my Styles of Scientific Thinking in the European Tradition: The History of Argument and Explanation Especially in the Mathematical and Biomedical Sciences and Arts (3 volumes, published by Gerald Duckworth & Co. Ltd, London, 1994), and forthcoming Galileo's Arguments and Disputes in Natural Philosophy (with the collaboration of Adriano Carugo), and Marin Mersenne: Science, Music and Language. The history of Western science is the history of a vision and an argument, initiated by the ancient Greeks in their search for principles at once of nature and of argument itself. This scientific vision, explored and controlled by argument, and the diversification of both vision and argument by scientific experience and by interaction with the wider contexts of intellectual culture, constitute the long history of European scientific thought. Underlying that development have been specific commitments to conceptions of nature and of science with its intellectual and moral assumptions, accompanied by a recurrent critique. Their diversification has generated a series of different styles of scientific thinking and of making theoretical and practical decisions. These styles are described and analysed in the opening chapter and exemplified in more detail in those that follow. These deal with scientific objectivity, the historiography of medieval science, Robert Grosseteste and Roger Bacon (Chapter 5 in collaboration with John North), the medieval conception of laws of nature, and the historical relation between rational design in scientific experimentation and in the arts exemplified especially by perspective painting. After a chapter on the place of mathematics in sixteenthcentury Italian universities and in Jesuit educational policy, there are five substantial studies of Galileo and his ideals of scientific demonstration and experimentation, of his use of rhetoric, and of his reputation. Two of them, Chapters 10 and 11, were written in collaboration with my colleague Adriano Carugo. Central to them are our discoveries of the use by Galileo of works by Jesuit philosophers at the Collegio Romano or associated therewith, which

xii


have thrown an entirely new and very influential light on Galileo's intellectual biography. These chapters contain the original and authentic account of these discoveries. Next come studies of Mersenne and the origins of language, and of the role of hypothetical modelling in the investigation of hearing and more particularly of vision, with a detailed analysis of the theories and researches of Alhazen, Kepler and Descartes. These complement and bring up to date my long monograph on the subject (1967) republished in Science, Optics and Music. There is a further substantial analysis of historical contexts of arguments from probabilities, from the qualitative treatment found in ancient medicine, ethics and law, through the quantification of probabilities initiated with insurance and commerce in fifteenth-century Italy, given mathematical elegance especially by Pascal, Huygens and Leibniz, developed further in the fields of demography and economics, and applied to a form of evolution by natural selection in the eighteenth century by Maupertuis and finally in crucial detail by Darwin. Concluding chapters deal with scientific language, conceptions of disease, and the historiography of science. Some of the papers included in this volume (chs. 3,10 appendix (a), 14, 20) have not been published in English before. The others have been left as they were first printed except for minor corrections. Thus they record stages in the process of discovery and interpretation, as in the chapters on Galileo, especially when dealing with problems of dating, many of them still unsolved. They have been reprinted with continuous pagination, with footnotes at the bottom of the page, and with appropriate revision of internal references. Immediately relevant further bibliography has been added as required at the ends of chapters. An extensive bibliography for the whole subject is included in my Styles of Scientific Thinking. Additions to my own publications, beyond those included in the bibliography of my writings in Science, Optics and Music, are listed below. Finally, once again it is a pleasure to thank all those who provided the occasions for these papers, in Belagio, Athens, Erice, Rome, Cambridge, Mass., Capri, Florence, Paris, Tours, Smith College, Barcelona and Annecy. A.C. Crombie 30 November 1994 Trinity College, Oxford

Further Bibliography of A.C. Crombie

Acknowledgements should have been made in Science, Optics and Music to the bibliography published in The Light of Nature: Essays in the History and Philosophy of Science Presented to A.C. Crombie, ed. J.D. North and J.J. Roche. Dordrecht, Martinus Nijhoff Publishers, 1985. (a) Books on the History of Science

1992

Stili di pensiero scientifico agli inizi dell' Europa moderna. Napoli, Bibliopolis. Spanish translation by J.L. Barona, Valencia, 1994.

1994

Styles of Scientific Thinking in the European Tradition: The History of Argument and Explanation Especially in the Mathematical and Biomedical Sciences and Arts, 3 vols. London, Gerald Duckworth & Co. Ltd., 1994. (b) Papers on the History of Science

1990

'Le corps a la Renaissance: Theories of Perceiver and Perceived in Hearing' in Le Corps a la Renaissance: Actes du xxxe Colloque de Tours 1987, sous la direction de J. Céard, M.M. Fontaine, J.-C. Margolin. Paris, Aux Amateurs de Livres, pp. 379-87. 'Expectation and Assent in Seventeenth-Century Scientific Argument: Galileo and Others' (Banfi Lecture, 1989), Istituto Antonio Banfi Annali, iii (1989-90), pp. 11-54 'La Langue maternelle de la science', Alliage: Culture - Science Technique, no. 4 (Eté, 1990), pp. 39-42. Review of E. Grant and J.E. Murdoch (ed.), Mathematics and its Applications to Science and Natural Philosophy in the Middle Ages (Cambridge, 1987) in English Historical Review, cv (1990), pp. 1007-8.

1990/91 'Expectation, Modelling and Assent in the History of Optics, i: Alhazen and the Medieval Tradition; ii: Kepler and Descartes',

xiv

Science, Art and Nature in Medieval and Modern Thought Studies in History and Philosophy of Science, xxi (1990), pp. 605-32, xxii (1991), pp. 89-115

1992

Review of Nicolas-Claude Fabri de Peiresc, Lettres à Claude Saumaise et à son entourage (1620-1637), éd. Agnes Bresson. Firenze, Leo S. Olschki, 1992, Times Literary Supplement, 2 October 1992, p. 23.

1993

The Origins of Western Science', Metascience, n.s. ii, pp. 1-16. Presentation of Lessico filosofico dei secoli xvii e xviii, Sezione latina, a cura di Marta Fattori con la collaborazione di M.L. Bianchi, fasc.i (Roma, 1992) at the Warburg Institute, London, 3 May 1993, in Nouvelles de la Republique des Lettres, (1993)-ii, 102-4.

1994

Reviews of Elspeth Whitney, Paradise Restored: The Mechanical Arts from Antiquity through the Thirteenth Century (Philadelphia: American Philosophical Society, Transactions lxxx.1, 1990) and Georges Minois, L'Eglise et la Science: Histoire d'un malentendu. De Saint Augustine a Galilee (Paris, 1990) in English Historical Review, cix (1994), pp. 136-8; and of Guiseppe Olmi, L'inventario del mondo: Catalogazione della natura a luoghi delsapere nella prima etá moderna (Bologna, 1992) in Journal of the History of Collections, forthcoming. 'The Greek Origins of European Scientific Styles', Ad familiares: The journal of the Friends of Classics, vii (1994), pp. xii-xiv. 'The History of European Science', New European: European Business Review, xciv (1994), pp. ii-v. 'Historical Perceptions of Medieval Science' in Federico II e le Scienze: Proceedings of the International Seminar on Frederick II and the Mediterranean World, a cura di A. Paravicini Bagliani. Palermo, Sellerio, pp. 15-24. 'Marin Mersenne et les origines du langage' in Nature, histoire, société: Essais en hommage a Jacques Roger, prés. par C. Blanckaert, J.-L. Fischer, J. Rey. Paris, Editions Klincksieck, pp. 35-46.

1995

'Boundaries of normality' in Malatia i cultura: Seminari d'Estudis sobre la Ciència, ed. J.L. Barona (Valencia, 1995), pp. 11-17. 'Per una antropologia històrica del saber científic', interview by Marc Borràs in Mètode: Revista de difusió de la investigació de la Universitat de València, ix (1995), pp. 14-17. 'Commitments and Styles of European Scientific Thinking' in History of Science, xxiii (1995), pp. 225-38.

'Univers' (with J.D. North) in Les caractères originaux de I'Occident medieval, éd. J. Le Goff, J.-C. Schmitt. Paris, Librairie Arthème Fayard, forthcoming.

Bibliography

xv

"Philosophical Commitments and Scientific Progress" in The Idea of Progress (Academia Europea conference 1994), forthcoming. (c) Editorships Editor, 1949-54 of The British Journal for the Philosophy of Science. Joint founder and editor of History of Science: A Review of Literature, Research and Teaching, Cambridge, W. Heffer and Sons, 1962-72; Science History Publications 1973- . (d) Scientific Papers Papers on (i) interspecific competition (an experimental and mathematical analysis on some aspects of ecology and natural selection) and (ii) the physiology of the chemical sense-organs in insects. 1941

On Oviposition, Olfactory Conditioning and Host Selection in Rhizopertha dominica Fab. (Insecta, coleoptera)', Journal of Experimental Biology, 18, pp. 62-79.

1942

'The Effect of Crowding upon the Oviposition of Grain-Infesting Insects',/. Exp. Biol., 19, pp. 311-40.

1943

'The Effect of Crowding upon the Natality of Grain-Infesting Insects', Proceedings of the Zoological Society of London, A, 113, pp. 77-98.

1944

'On Intraspecific and Interspecific Competition in Larvae of Graminivorous Insects', 7. Exp. BioL, 20, pp. 135-51. 'On the Measurement and Modification of the Olfactory Responses of Blow-Flies', /. Exp. BioL, 20, pp. 159-66. 'Sensillae of the Adults and larvae of the Beetle Rhizopertha dominica Fab. (Bostrichidae)', Proceedings of the Royal Entomological Society of London A, 19, pp. 131-2.

1945

'On Competition between Different Species of Graminivorous Insects', Proceedings of the Royal Society, B, 132, pp. 362-95.

1946

'Further Experiments on Insect Competition', Proc. Roy. Soc., B, 133, pp. 76-109.

1947

'The Behaviour of Wireworms in Response to Chemical Stimulation' [with W.H. Thorpe, R. Hill and J.H. Darrah], /. Exp. BioL, 23, pp. 234-66. 'The Chemoreceptors of the Wire worm (Agriotes spp.) and the Relation of Activity to Chemical Composition' [with J.H. Darrah], J. Exp. Biol. 24, pp. 95-109. 'Interspecific Competition', Journal of Animal Ecology, 16, pp. 44-73.

In nature's infinite book of secrecy A little I can read. (Shakespeare, Antony and Cleopatra i.l 1)

1 Designed in the Mind: Western Visions of Science, Nature and Humankind When we speak today of natural science we mean a specific vision created within Western culture, at once of knowledge and of the object of that knowledge, a vision at once of natural science and of nature.1 We may trace the characteristically Western tradition of rational science and philosophy to the commitment of the ancient Greeks, for whatever reason, to the decision of questions by argument and evidence, as distinct from custom, edict, authority, revelation, rule-of-thumb, on some other principle or practice. They developed thereby the notion of a problem as distinct from a doctrine, and the consequent habit of envisaging thought and action in all situations as the perception and solving of problems. By deciding at the same time that among many possible worlds as envisaged in other cultures, the one world that existed was a world of exclusively self-consistent and discoverable rational causality, the Greek philosophers, mathematicians and medical men committed their scientific successors exclusively to this effective direction of thinking. They closed for Western scientific vision the elsewhere open questions of what kind of world people found themselves inhabiting and so of what methods they should use to explore and explain and control it. They introduced in this way the conception of a rational scientific system, a system in which formal reasoning matched natural causation, so that natural events must follow exactly from scientific principles, just as logical and mathematical conclusions must follow from their premises. Thus they introduced, in parallel with their conception of causal demonstration, the equally fundamental conception of formal proof. From these two conceptions all the essential character and style of Western philosophy, mathematics and natural science have followed. The exclusive rationality so defined supplied the presuppositions and came to supply the methods of reasoning alike in purely formal discourse and in the experiential exploration of nature. Hence it offered rational control of subjectmatters of all kinds, from mathematical to material, from ideas to things. A similar characteristic style is evident over the whole range of Western intellectual and practical enterprise. We have then in Western scientific culture, as an object of study to which we its students at the same time inextricably belong, a highly intellectualized and integrated whole, designed in

2


the mind like a work of art, not all at once but over many generations of interaction between creative thinking and testing, between programmes and their realization or modification or rejection. But if we insist upon the cultural specificity of the Western scientific tradition in its origins and initial development, and upon its enduring identity in diffusion to other cultures, we do not have to look far below the surface of scientific inquiry and its immediate results to see that the whole historical process has gone on in a context of intellectual and moral commitments, expectations, dispositions and memories that have varied greatly with different periods, societies and also individuals. These have affected both the problems perceived and the solutions found acceptable, and also the evaluations of desirable or undesirable ends and their motivations. The whole historical experience of scientific thinking is an invitation to treat the history of science, both in its development in the West and in its complex diffusion through other cultures, as a kind of comparative historical anthropology of thought. An historical anthropology of science must be concerned before all with people and their vision. The scientific movement offers an invitation to examine the,identity of natural science within an intellectual culture, to distinguishrihat from the identities of other intellectual and practical activities in the arts, scholarship, philosophy, law, government, commerce and so on, and to relate them all in a taxonomy of styles. It is an invitation to analyse the various elements that make up an intellectual style in the study and treatment of nature: conceptions of nature and of science, methods of scientific inquiry and demonstration diversified according to the subject-matter, evaluations of scientific goals with consequent motivations, and intellectual and moral commitments and expectations generating attitudes to innovation and change. The scientific thinking found in a particular period or society or individual gets its vision and style from different but closely related intellectual or moral commitments or dispositions. We may distinguish three. (1) First there have been conceptions of nature within the general scheme of existence and of its knowability to man. These in turn have been conditioned by language. The original Greek commitment entailed the replacement of conceptions of nature as an arbitrary sociological order maintained by personified agents, found in all ancient cosmologies and cosmogonies, with the conception of an inevitable order established by an exclusive natural causality. In the succession competing for dominance in subsequent Western thought, nature has been conceived as a product of divine economy or art with appropriate characteristics of simplicity and harmony, as a consequence of atomic chance, as a causal continuum, as a workshop of active substantial powers, as a passive system of mechanisms, as an evolutionary generation of novelty, as a manifestation of probabilities.

Western Visions of Science, Nature and Humankind

3

Any language itself embodies a theory of meaning, a logic, a classification of experience in names, a conception of both perceiver and perceived and their relation, and of relations in space and time. Philology can be an indispensable guide to theoretical ideas and real actions. The expression of a system of science in a language may not entail an immediate critique of the fundamental structure of that language, yet its vocabulary and syntax may have to be modified to provide for the conceptual and technical precision required by the science developing within it. Thus a new terminology had to be devised in medieval and early modern Latin to accommodate the new kinematic and dynamic conceptions, especially of functions, of instantaneous change and of rates of change, which could scarcely be expressed in the classical logic and syntax of subject and predicate. Terminology may have had to be revised to detach its specific scientific meaning from its source in common but inadequate or misleading analogies. "The word current", wrote Michael Faraday,2 "is so expressive in common language that when applied in the consideration of electrical phenomena, we can hardly divest it sufficiently of its meaning, or prevent our minds from being prejudiced by it". For the same reason he replaced "pole", inconveniently suggesting attraction, with the neutral "electrode", in a new terminology devised with the aid of William Whewell to fit the precise context of electro-chemistry. John Tyndall3 in his attractive account of Faraday as a discoverer exemplified a familiar historical process when he described how, in this new science, "prompted by certain analogies we ascribe electrical phenomena to the action of a peculiar fluid, sometimes flowing, sometimes at rest. Such conceptions have their advantages and their disadvantages; they afford peaceful lodging to the intellect for a time, but they also circumscribe it, and by-and-by, when the mind has grown too large for its lodging, it often finds difficulty in breaking down the walls of what has become its prison instead of its home." Thus a radically new technical language may be made up, precisely symbolized as first for mathematics and music and later for many other sciences and arts. The result may be a special language fundamentally different in intention from that implicit in the common language of the society from which it originated, but still a language that may be learned and understood in any society and may convey to it objectively communicable knowledge. Must science in different linguistic cultures always acquire differences of logical form, and must the grammatical structure of a language always impose its ontological presuppositions on the science developing within it? While the technical language of science has often been developed partly to escape from just such impositions, philology can be an accurate guide to implicit or explicit intellectual commitments of this kind and to their changes. The West learnt from the Greeks to look for causal continuity in events both physical and moral, and this has structured its natural and moral philosophy

4


alike and its whole tradition of dramatic literature and music since Antiquity. Japanese thinking, now in exemplary possession of Western science and music, seems traditionally by contrast to have accepted events in their individual existential discontinuity, impressionistically unrelated to before and after, with no general abstract term for nature, but each thing the subject of personal knowledge and companionship, not of mastery either by thought or action. The whole question might throw an interesting light in our philosophical anthropology upon a question central to the whole Western debate: that of distinguishing the argument giving rational control of subject-matter from an implication of the existence of entities appearing in the language used, or, more generally, that of distinguishing a rational structure of nature from that of the organizing human mind. (2) A second kind of intellectual commitment affecting scientific style has been to a conception of science and of the organization of scientific inquiry. Two different traditions of scientific organization and method began in Antiquity. The dominant Greek mathematicians saw as their goal the reduction of every scientific field to the axiomatic model of their most powerful intellectual invention, geometry. At once alternative and complementary to this was the much older medical and technological practice of exploring and recording by piecemeal observation, measurement and trial. The medieval and early modern experimental natural philosophers combined both traditions, to transform the geometrical pattern by an increasing preoccupation with quantitative experimental analysis of causal connections and functional relations. Yet a different pattern came from intellectual satisfaction in mathematical harmonies rather than causal processes. Other modes of intellectual organization assimilated analysis for scientific investigation to that for artistic construction, or looked for probabilities or for genetic origins and derivations. All generated scientific systems made up of theories and laws and statements of observations, providing particular explanations and solutions of problems within the framework of a general conception of nature and science, along with scientific methods diversified by the diversity both of general commitments and of particular subject-matters of varying complexity. The commitments of a period or group or individual to general beliefs about nature and about science, combined with the technical possibilities available, have regulated the problems seen, the questions put to nature, and the acceptability of both questions and answers. Such commitments have directed research towards certain types of problem and towards certain types of discovery and explanation, but away from others. They have both guided inquiry and supplied its ultimate irreducible explanatory principles. By taking us beneath the surface of immediate scientific results, they help us to identify the conceptual and technical conditions, frontiers and horizons making certain discoveries possible and explanations acceptable to a generation or group, but


5

others not, and the same not to others. More specifically a discovery or a theory or even a presentation of research may open fresh horizons but at the same time close others hitherto held possible. Dominant intellectual commitments have made certain kinds of question appear cogent and given certain kinds of explanation their power to convince, and excluded others. They established, in anticipation of any particular research, the kind of world that was supposed to exist and the appropriate methods of inquiry. Such beliefs, taken from the more general intellectual context of natural science, have regulated the expectations both of questions and of answers, the form of theories and the kinds of explanatory entities taken into them, and the acceptability of the explanations they offered. They established in advance the kind of explanation that would give satisfaction when the supposedly discoverable had been discovered. They have been challenged not usually by observation, but by re-examining the metaphysics or theology or other general beliefs assumed. In this process the cogency of such worlds might change from generation to generation as each nevertheless added to enduringly valid scientific knowledge. (3) A third kind of intellectual and moral commitment has concerned what could and should be done. This in its diverse modes has followed from diverse evaluations of the nature and purpose of existence and hence of right human action. It has been linked with dispositions generating an habitual response to events, both internally within scientific thinking itself, and externally in the responses of society: dispositions to expect to master or to be mastered by or simply to contemplate events, to change or to resist change, to anticipate innovation or conservation, to be ready or not to reject theories and to rethink accepted beliefs and to alter habits. Such dispositions have been both psychological and social. They may be specified by habitual styles and methods both of opposition and of acceptance. They may characterize a society over the whole range of its intellectual and moral behaviour, of which its natural science is simply a part. The primary focus, for example, of medieval and early modern Christian as of Islamic culture and society on the teaching and preservation of theological truth could scarcely fail to condition all human inquiries. Sensitive implications of natural philosophical and metaphysical questions and doctrines placed the whole of intellectual life within the political framework and control of a moral cosmology.The medieval Christian theological hierarchy of dignity within that cosmology, as also Islamic attitudes to the visual representation of natural objects, took that control as far as aesthetic style. Given the dual source of human knowledge in the divine gifts of true reason and of undeniable revelation, the whole enterprise made an urgent issue then of error, of the possibility of error in good faith, of the attitude to be taken to

6


unpersuadable infidels and irredeemable heretics, of the commitments and expectations of disagreement as well as agreement. In all this, and in the whole scientific movement considered in the context of society and of communication, persuasion has been as important as proof. The use of persuasive arguments to reinforce or to create the power of ideas to convince, especially when the ideas were new and the audience uncertain or unsympathetic, has been well understood by some of the greatest scientific innovators. Galileo and Descartes were both masters of the current rhetorical techniques of persuasion. Galileo devoted at least as much energy to trying to establish the identity of natural science within contemporary intellectual culture as to solving particular physical problems. He conducted all his controversies at two levels: one was concerned with the particular physical problem in question; the other was concerned with an eloquent advocacy of his conception of natural science as an enterprise in solving problems and finding scientific explanations distinct from the philosophical or theological exegesis of authorities and texts, from a literary exercise, from a commercial or legal negotiation, from magic, and so on. His test of a general explanation was its ability to incorporate the solution of particular problems. Descartes argued likewise at two levels, and this indeed was a general necessity in a period when the intellectual identity of the contemporary scientific movement was still open to misunderstanding by the learned world at large and when its methods and accepted styles of reasoning were still to some extent being established. Again, Charles Lyell, himself a lawyer, set out like a skilful lawyer to present his uniformitarian conception of geology as the only acceptable one and to discredit its hitherto accepted catastrophic rival. Charles Darwin similarly set out his argument in the Origin of species for evolution by natural selection like a legal brief: marshalling the evidence, demolishing rival explanations, proposing his own solution, raising difficulties against it, meeting them one by one, and finally concluding that his was the only plausible and acceptable explanation that could account for all the various categories of fact that had to be considered. By presenting his arguments in the wake of the statistical analysis of human economics which provided the persuasive analogy, Darwin was able to establish at one and the same time his scientific explanation by natural selection and a statistical conception of the economy of nature which belief in providential design had hitherto made widely unacceptable in biology. Persuasion has obviously been aimed at the diffusion of scientific ideas, both at the sophisticated level of the scientific community and also among the general public. Change in ideas has come about more easily in some scientific situations, periods and societies than in others. It has been easier to reject particular theories within an accepted system of general doctrine than to take the drastic step of rejecting the whole doctrine. The disposition to change, which has been


7

so marked a characteristic of the whole modern history of the West, became within the same culture an essential part of the scientific movement over a period when innovation and improvement were also becoming the intellectual habit in art, theology, philosophy, law, government, commerce and many other activities. It was a matter of individual as well as collective behaviour: Kepler, for example, contrasts notably with some of his contemporaries and opponents in controversy by his readiness to sacrifice a favourite theory to contrary evidence. The conscious cultivation and reward of a disposition towards innovation began in Western society perhaps first in the technical arts and philosophy, but it has been transmitted elsewhere mainly with Western commerce and science. A comprehensive historical inquiry into the sciences and arts mediating man's experience of nature as perceiver and knower and agent would include questions at different levels, in part given by nature, in part made by man. These correspond to the three kinds of commitment. Thus at the level of nature there is historical ecology: the reconstruction of the physical and biomedical environment and of what people made of it. The sources and problems of historical ecology, both human and physical, range from those of archaeology and palaeopathology to those of the history of climate, technology, medicine, agriculture, travel and art. Historical problems at all levels require scientific and linguistic knowledge to control the view of any present recorded through the eyes and language of those who saw it. They may require also historical knowledge of religion and of artistic style, economic theory, and other analytical disciplines. At all levels comparative historical studies of the intellectual and social commitments, dispositions and habits, and of the material conditions, that might make scientific activity and its practical applications intellectually or socially or materially easy for one society, but difficult or impossible for another, have an immediate relevance for the diverse cultures brought into contact with the science, medicine, technology and commerce of our contemporary world. It is only comparatively recently, and only in highly industrialized societies, that science and technology have risen to a dominant position among the vastly various concerns and interests that throughout history have moved men to thought and action. What have been the numbers, social position, education, occupations, institutions, private and public habits, motives, opportunities, persuasions and means of communication of the individuals taking part in scientific activities in different periods and societies? What critical audience has there been to be convinced by, use, transmit, develop, revise or reject their arguments? Where scientific and analogous inquiries have interested only a scattered minority, what opportunities have existed for establishing agreement on principles and methods, or even continuity between generations? How, for example, were these maintained in the ancient Mediterranean, or in China or

8


India? In comparison, what intellectual or moral or practical commitments motivated the teaching and learned institutions of medieval Islam and of medieval and early modern Christendom, and came in the last to establish effective conditions of education and research for an explicit scientific community? How have the conditions for science and for technology differed? What intellectual needs or habits or intentions or social pressures have there been within different philosophical or scientific or technical groups to bring about a consensus of opinion in favour of innovation or of conservation? How have scientific ideas and activities been located within the values of society at large? What has been the intellectual or moral or practical value given to science in different societies, within a range of interests so divergent as those indicated, for example, by a predominant concern with a theological scheme of human responsibility and destiny, by the cultivation of the arts or of literary learning or of logic and philosophy, by the pressures and expediencies of politics, by the needs of war, trade, industry, transport or medicine? What has been the appeal of pure intellectual curiosity and philosophical satisfaction, of a religious search for God in nature, of a desire for intellectual or moral or social or political reform, of utility in the senses either of the material improvement of the human condition or of industrial or commercial or political or military power or gain? What social or commercial or political interests have promoted or resisted scientific research and technical innovation, and the diffusion and application of ideas, discoveries and inventions? To what extent does innovation breed innovation? What was the costeffectiveness of the inventions described in histories of technology, who used them, and with what consequences? It would be relevant to compare the criteria of evidence and decision used in science or in medical diagnosis and prognosis with those used in commerce and industry, in law courts, and in choice of policies by governments. Relevant also are mentalities indicated by philosophical and social programmes and responses in relation to their social, economic and sometimes military context. So too are the intellectual and social responses of society at large to making man an object of scientific inquiry and treatment. Likewise what external pressures and internal dispositions have operated in the intellectual and practical responses of one culture to another, of Islam to Greek thought, of medieval Western Christendom to Islam and to farther Asia, of early modern Europe to China and Japan and India and the New World, of Japan in its early history to China and in the sixteenth and nineteenth centuries to the West, of China throughout its history to any other culture, of the so-called developing countries now to the industrially developed? The essence of effective scientific thinking has been the advancement of knowledge through the identification of soluble problems. What have been the


9

sources of new intellectual perceptions? How have the intellectual commitments or dispositions or habits or the technical potentialities of an individual or a group or period either promoted or discouraged creative discovery and technical invention? How have these interacted with the conditions for intellectual change or conservation in the philosophical, technical, social and materal ambience of science? To what extent has the internal logic of science taken over from features of this ambience, accidental analogies, or suggestions for new hypotheses or styles of thinking? What has been the part played in the initiation of progress by breaches of conceptual frontiers leading to asking new questions, seeing new problems, accepting new criteria of valid demonstration and cogent, satisfactory explanation? Scientific thinking has commonly progressed through periods of critical analysis bringing novel forms of speculation about the discoverable in nature in anticipation of technical inquiry. Obvious examples are the critique of the Aristotelian doctrine of qualities and causation preceding the new science of motion established from Galileo to Newton, the atomic speculations preceding the quantitative atomic theory promoted by John Dalton, and the evolutionary speculations preceding the scientific organization of the evidence and theory finally achieved by Charles Darwin. The older conceptions were discarded and the new first entertained by rethinking; but the new ideas became established as scientific knowledge only by technical scientific research. Only after that were their speculative precursors given a retrospective scientific significance. Of the essence of the Western scientific tradition, and of the evidence for its history, have been the self-conscious assessments of its presuppositions, performance and prospects that have continued through many changes of context from Archytas and Aristotle down to the latest disputes among scientists, philosophers and historians. The critical historiography of science has been an integral part of the scientific movement itself. Such assessments both of current science and of the history of science have had various purposes. Those made in medieval and early modern Europe aimed usually to monitor the identity and intellectual orientation of the contemporary scientific movement and to define its methods and criteria of acceptability of questions and answers. They were made during a long period when increasing scientific experience, historical scholarship, and awareness of other contemporary cultures enabled Europeans to measure their own scientific orientations and potentialities against those of diverse earlier and contemporary societies. The range of modern assessments points to the range of sources for an interpretation. The radical variations in contemporary assessments and their changes with time and context and individual disposition provide unique and indispensable primary evidence in historically taking the measure of the intellectual and technical and moral equipment available in any scientific situation. An habitual search during this period at once for the best form of

10


science, and for its best ancient model, projected the earlier into the contemporary tradition but with extended power. Through the variations of the scientific movement there has run a consistency of development in conceptions of explanation and method. The growth of particular scientific knowledge has carried in its wake a growth of general understanding of scientific thinking and its varieties. This consistency clarifies the historical variety of accepted explanations and methods diversified by intellectual commitments and subject-matters. Both in the perception and solution of problems within the theoretical and technical possibilities available, and in the justification of the enterprise whether intellectual or practical or moral, the history of science has been the history of argument. Scientific argument forms the substance of the scientific movement, a discourse using experiment and observation, instruments and apparatus, mathematical reasoning and calculation, but with significance always in relation to the argument. The scientific movement brought together in its common restriction to answerable questions a variety of scientific methods, or styles of scientific inquiry and demonstration, diversified by their subject-matters, by general conceptions of nature, by presuppositions about scientific validity, and by scientific experience of the interaction of programmes with realizations. Throughout, methods of yielding accurately reproducible results were required equally by the practical commitment of technology and the arts to the control of materials, and by the theoretical commitment of science to establishing regularities or causal connections within a common form of demonstration. An historian needs to ask both what theories of scientific method contributed to science, and what methods were used by scientists. We may distinguish in the classical scientific movement six styles of scientific thinking, or methods of scientific inquiry and demonstration. Three styles or methods were developed in the investigation of individual regularities, and three in the investigation of the regularities of populations ordered in space and in time. Each arose in a context in which an assembly of cognate subject-matters was united under a common form of argument. Thus (i) the simple method of postulation exemplified by the Greek mathematical sciences originated within the common Greek search for the rational principles alike of the perceptible world and of human reasoning. This was the primary ancient model, uniting all the mathematical sciences and dependent arts, from optics and music to mechanics, astronomy and cartography, (ii) The deployment of experiment, both to control postulation and to explore by observation and measurement, was required by the scientific search for principles in the observable relations of more complex subject-matters. Starting with the Greeks, the strategy of experimental argument was elaborated in medieval and early modern Europe as a form of reasoning by analysis


11

and synthesis in which the point at which experiment was brought into the argument, either for control or for exploration, was precisely defined. Moves towards quantification in all sciences may be traced to the general European growth both of mathematics and of the habits of measurement and recording and calculation arising from need in some special sciences, as in astronomy, and in the practical and commercial arts, where new systems of weights and measures and of arithmetical calculation were first developed. The scientific experimental method derived from the union of these practical habits with the logic of controls, with further quantification through new techniques of instrumentation and mathematical calculation. The rational experimenter was the rational artist of scientific) inquiry, (iii) Hypothetical modelling was developed in a sophisticated form first in application to early modern perspective painting and to engineering, and was then transposed from art into science as likewise a method of analysis and synthesis by the construction of analogies. The recognition that/in the constructive arts theoretical design must precede material realization anticipated the scientific hypothetical model. Each proceeding to a different end, artist and scientist shared a common style. The imitation of nature by art then became an art of inquisition; rational design for construction became rational modelling for inquisitorial trial, (iv) Taxonomy emerged first in Greek thought as a logical method of ordering variety in any subject-matter by comparison and difference. The elaboration of taxonomic methods and of their theoretical foundations may be attributed to the need to accommodate the vast expansion of known varieties of plants and animals and diseases following European exploration overseas, with attempts to relate diagnostic signs and symptoms to their causes and to discover the natural system that would express real affinities, (v) The statistical and probabilistic analysis of expectation and choice developed in early modern Europe again took the same forms whether in estimating the outcome of a disease, of a legal process, of a commercial enterprise, or natural selection, or the reasonableness of assent to a scientific theory. The subject-matter of probability and statistics came to be recognized through attempts to accommodate within the context of ancient and medieval logic situations of contingent expectation and uncertain choice, followed by the early modern discovery of the phenomenon of statistical regularities in adequately numerous populations of economic and medical and other events. Thus uncertainty was mastered by reason and stabilized in a calculus of probability, (vi) The method of historical derivation, or the analysis and synthesis of genetic development, was developed originally by the Greeks and then in early modern Europe first in application to languages and more generally to human cultures, and afterwards to geological history and to the evolution of living organisms. The subject-matter of historical derivation was defined by the diagnosis, from the

12

Science, Art and Nature in Medieval and Modem Thought

common characteristics of diverse existing things, of a common source earlier in time, followed by the postulation of causes to account for the diversification from that source. Clearly all this scientific diversity can be understood only within the diversity and the changes of thought in the whole historical context. The history of science is the history of argument: an argument initiated in the West by ancient Greek philosophers, mathematicians and physicians in their search for principles at once of nature and of argument itself. Of its essence have been its genuine continuity, even after long breaks, based on the study by any generation of texts written by its predecessors, its progress equally in scientific knowledge and in the analysis of scientific argument, and its recurrent critique of its moral justification. A subtle question is what continued and what changed through different historical contexts, in the scientific argument and in the cultural vision through which experience is mediated, when education and experience itself could furnish options for a different future. Styles of thinking and making decisions, established with the commitments with which they began, habitually endure as long as these remain. Hence the structural differences between different civilizations and societies and the persistence in each despite change of a specific identity. Hence the need for historical analysis in the scientific movement of both continuity and change. These like most human behaviour begin in the mind, and we its historians who belong at the same time to its history must look in a true intellectual anthropology at once with and into the eye of its beholder.

REFERENCES 1. This paper is based on the historiographical introduction to my book, Styles of scientific thinking in the European tradition (Gerald Duckworth, London, 1994), which contains full documentation and bibliography; cf. also A. C. Crombie, "Science and the arts in the Renaissance: The search for truth and certainty, old and new", History of science, xviii (1980), 233-46; idem, "Historical commitments of European science", Annali del' Istituto e Museo di Storia della Scienza di Firenze, vii, part 2 (1982), 29-51; idem, "What is the history of science?", History of European ideas, vii (1986), 21-31; idem, "Experimental science and the rational artist in early modern Europe", Daedalus, cxv (1986), 49-74; idem, "Contingent expectation and uncertain choice: Historical contexts of arguments from probabilities" in The rational arts of living, ed. by A. C. Crombie and N. G. Siraisi (Northampton, Mass.: Smith College studies in history, 1987): the first three of these papers are included in A. C. Crombie, Science, optics and music in medieval and early modern thought (Hambledon Press, London, 1990). 2. Michael Faraday, Experimental researches in electricity, i (London, 1839), 515; cf. pp. 195 ff. 3. John Tyndall, Faraday as a discoverer (London, 1868), 53-55.

2

The Western Experience of Scientific Objectivity * At a depressing period of the Pelopennesian War, Thucydides included in his famous account of the moral disintegration of society in revolution two points of immediate relevance to a discussion of the European experience of scientific objectivity. Revolution had brought many and terrible sufferings upon the Greek cities. Unscrupulous mendacity and opportunist treachery masqueraded as superior cleverness, the sweeter if a rival trusting a pledge of reconciliation were taken off his guard. Anyone who excelled in evil and anyone who «prompted to evil someone who had never thought of it were alike commended*. Conspirators used fair words for guilty ends with cynical confidence that others would hypocritically welcome them as cover for their own moral cowardice or indifference. United only through complicity in crime, greed and envy against the moderate and the honest, «neither had any regard for true piety, yet those who could carry through an odious deed under the cloak of a specious phrase received the higher praise». 1 Among all this violence against both truth and person he noted interestingly : «Words had to change their ordinary meaning in relation to things and to take that which men thought fit*. And, he argued, these calamities of behaviour «have occurred and always will occur as long as the nature of mankind remains the same». For «human nature, always rebelling against the law and now its master, gladly showed itself ungoverned in passion», setting gain above justice and revenge above religion : «For surely no man would put revenge above religion, and gain before innocence of wrong, had not envy swayed him with her blighting power» 2 . It was the same in the plague of Athens. Strong and weak were swept indifferently away, victims with unquench* 'H (ivaxotvoxjis aveYV<J>a6y) UTT& TOU xaOvj^ToO ERWIN SCUEUCU, 8i6n 6 et 310


selectively in the direction of the perpendicular, from which they were also stronger (i.5.14, pp. 7-8; i.5.18, pp. 9-10; i.5.25, p. 15; ii.1.4, p. 26; ii.2.42^4, pp. 57-58). Of the forms emitted by each point of the visible object, those which stimulated corresponding points of the anterior glacialis reproduced there the form of the whole object, made up of the forms of these separate points which maintained the order they had in the object. This form was a pattern of stimulations perceptible only from within by the sensitive power itself; it was not an optical image visible to an external observer such as was produced in a camera obscura.6 Each of the eyes corresponded exactly to the other in structure and in position relative to the common nerve, so that in normal binocular vision, when both their axes were directed towards an object, the form of the object would be reproduced at corresponding points in each eye. Thus the object was seen as one 'because the two forms coming from a single thing to the two eyes run together on reaching the common nerve and are superimposed one on the other and made into one form: and by means of that form made up of two forms the ultimate sentient apprehends the form of that thing'. If the spectator pushed one eye out of place he would see two things instead of one, so that the thing must be apprehended, sometimes as one and sometimes as two, not in the eyes but beyond them in 'another sentient' to which the two forms came either united or separately. The evidence that the forms of things seen are extended through the concavity of the nerve and come to the ultimate sentient, and after that vision is completed, is that an obstruction in that nerve destroys vision and when the obstruction is destroyed vision is restored. The art of medicine attests this'. But what it was that passed beyond the eyes was a problem. 'It could be said that the forms coming to the eye do not come through to the common nerve, but a sensation (sensus) is extended from the eye to the common nerve, just as the sensations of pain and touch are extended, and the ultimate sentient then apprehends that sensible thing'. Certainly 'the sensation reaching the common nerve is a sensation of light and colour and ordering, and that by means of which the ultimate sentient apprehends light and colour in some kind of form' (i.5.27, pp. 16-17). The problem was: what kind? The relation of the forms of light and colour to the optical physiological requirements of his theory of visual perception remained a problem to the end. Alhazen argued that 'transparent bodies are not changed by colours, nor are they altered (alterantur) by them with a fixed alteration, but the property of colour and light is that their forms are extended along straight lines' (i.5.28, p. 17). Nor were the lights and colours passing through a transparent medium affected by each other, as he showed by an experiment with a camera obscura. For 6

Cf. Sabra (1972: above n. 4).

The History of Optics: Alha&n and the Medieval Tradition

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when in one place several candles are put at various different points, all opposite an opening leading into a dark place (locus obscurus), with a wall or an opaque body opposite the opening, the lights of those candles appear on the body or that wall distinctly according to the number of the candles. Each one of them appears opposite one candle on a line passing through the opening. If one of the candles is screened off, only the light opposite that one candle disappears, and if the screen is removed the light reappears. This can be tried at any time: for if the lights intermixed in the air they would become intermixed in the air in the opening and would have to pass through intermixed, and they would not become separate later. But we do not find this so. Hence the lights are not intermixed in the air, but each one of them extends on straight lines. Thus the 'form of each and every light' was extended through the transparency of the air 'which does not lose its own form. And what we say about light and colour and air is to be understood of all transparent bodies, and the transparent coats of the eye' (i.5.29, p. 17). But the camera obscura was not a model for the eye, for in it all the forms of light and colour passing rectilinearly through the aperture to the screen would contribute to the image there, whereas in the eye only those falling on the anterior glacialis perpendicularly would contribute to the form of the object seen. 'Indeed the sentient member (membrum sentiens), namely the glacialis, does not receive the form of light and colour as the air and other nonsentient transparent bodies receive it, but in a way different from that way. Since that member is disposed (praeparatum) to receive that form, so it receives it in so far as it is sentient and in so far as it is transparent'. As he had already explained (i.5.26), 'its affection (passio) by that form is of the same kind as pain. Hence the quality of its reception from that form is different from the quality of reception by nonsentient transparent bodies'. Thus 'the glacialis is altered (alteratur) by light and colour to the extent that it senses (sentiat)\ by an 'alteration (alteratioy that 'is necessary but with a nature not fixed', for it disappeared when the light did. The glacialis was so 'disposed to be affected by colours and lights and to sense them' in a way that air and other transparent bodies and the transparent coats of the eye anterior to it were not. As again he had already explained (i.5.19), of the many forms of light and colour emitted into the air and transparent bodies, 'the eye... apprehends those according to the pyramid which is distinguished between them and the centre of the eye' (i.5.30, pp. 17-18). In the whole process the eye and all its parts 'are instruments by which vision is completed'. The cornea covering the pupil (foramen uveae) retained the fluid albugineous humour, which like the cornea was transparent 'so that the forms would pass through it and reach the glacial humour'. The black, strong, spherical uvea which contained the albugineous humour 'is black so that the albugineous humour and glacialis would be obscured in such a way that the forms of light would make their appearance in them weak: because weak light is more visible in a dark place and escapes notice in a place full of light'. This seems to suggest

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Fig. 5. From Roger Bacon, Opus maius, v. i. viii. /: Oxford MS Bodleian Library, Digby 234 (15 cent.) f. 247.The rays from the right (dextrum m) and left (sinistrum p) ends (labelled in reverse in MS) of the visible object pass perpendicularly through the anterior surface of the flattened glacialis (g, f) and are refracted at its posterior surface (q, u) so that instead of intersecting (below a) they reach the optic nerve (c) with the image correctly orientated. The rays passing into the vitreous humour (held to be optically denser than the glacialis) are refracted according to Ptolemy's rules towards the perpendiculars (bl, bs) meeting at its centre of curvature (b).

that the eye was like a camera obscura with the glacialis as its screen. The glacialis had 'many properties by which sensation is completed', but it was still an instrument to that end. 'But the optic nerve, on which the whole eye is constructed, is hollow so that the visual spirit may run through it from the brain and may reach the glacialis and may in turn give to it sensitive power (virtus sensibilis), and so that the forms may pass through in the subtle body running in its concavity until they reach the ultimate sentient which is the anterior part of the brain' (i.6.33, pp. 20-21). Alhazen's treatment of the fundamental problem that followed from this analysis exemplifies the decisive dominance of his optical theory by his commitment to finding an immediate explanation of visual perception. For

The History of Optics: Alhazen and the Medieval Tradition

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how did the 'sensible image' of the object made on the anterior glacialis maintain its necessary order in its passage through the posterior transparent media of the eye to the common nerve where it was finally perceived by the ultimate sentient? The first stage of the problem was geometrical, for if the forms coming on the visual pyramid reached its vertex at the centre of the eye they would be reduced to a point, which being dimensionless had no order; and if they passed beyond the vertex their order would be inverted and reversed. His solution again was to contrive further optical and anatomical postulates to prevent these happenings. He supposed that the centre of curvature of the posterior surface of the anterior glacialis — forming its interface with the posterior glacialis or vitreous humour — and that interface itself were in front of the centre of the eye, and that the anterior and posterior glacialis had different transparencies, that is optical densities. Then, applying Ptolemy's rules and constructions for refraction at plane surfaces to sections of spheres, he argued that the forms would be refracted at the posterior surface of the anterior glacialis in the directions preventing their meeting at the vertex of the pyramid (Figs 4 and 5). This would require that the vitreous humour was the denser. He structured his argument formally in hypothetical syllogisms leading by elimination to the one true conclusion: If therefore the form does not reach the concavity of this nerve arranged as it is on the glacialis, neither will it reach the common nerve with its proper arrangements. But the form cannot extend from the surface of the glacialis to the concavity of the nerve in straight lines and still preserve the proper positions of its parts: for all those lines meet at the centre of the eye, and when they continued straight on past the centre their positions would be reversed: what is right would become left and vice versa, and what is above would become below and below above. Thus, if the form was extended on straight radial lines it would be congregated at the centre of the eye and become as it were a single point. And . . . if it was extended on straight radial lines and passed through the centre, it would become reversed in accordance with the reversal of the intersecting lines along which it was extended. Therefore the form can come from the surface of the glacialis to the concavity of the nerve with its parts in their proper positions only on refracted lines, cutting across radial lines.... This refraction must occur before it reaches the centre, because if the lines were refracted after passing through the centre they would be reversed. It has been shown [i.5.18] that this form passes through the body of the glacialis on straight radial lines:... therefore the form is refracted only by its passage through the body of the glacialis. It has been said [i.4.4]... that the body of the glacialis is o unequal transparency and that its posterior part, called the vitreous humour, has a different transparency from the anterior part. There is no body in the glacialis different in constitution (forma) from the anterior body except the body of the vitreous. It is a property of the forms of light and colour that they are refracted when they meet another body of different transparency from the first. Therefore the forms are refracted only at their entry into the vitreous humour. This body has a transparency different from that of the body of the anterior glacialis only in order

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that the forms can be refracted in it. Its surface must be in front of the centre of the eye so that the forms are refracted at this surface before they pass through the centre; and this surface must be correspondingly ordered, because if it were not the form would appear monstrous after refraction (ii.1.2, p. 25).

The second stage of the problem concerned what happened after the forms had passed into the vitreous humour. For the radial lines play no part in the ordering of the thing seen except only at the glacialis, because at this member is the origin of sensation. It has also been shown [i.5.15, 16, 18] that it is impossible for the form of the thing seen to be ordered on the surface of the eye with the likeness (imago) of the thing seen and the smallness of the sentient thing except through these lines. These lines are then nothing but the instrument of the eye through which the apprehension of things seen is completed with their proper arrangement. But the arrival of the forms at the ultimate sentient does not require the extension of these lines rectitudinally (ii.1.3, pp. 25-26; cf. ii.1.8, p. 29).

Moreover, as he had asserted (i.5.30), the glacialis did not receive the forms like other transparent bodies 'because the sentient member receives these forms and senses them and they pass through it because of its transparency and the sensitive power that is in it. Thus it receives these forms according to the reception of sensation (sensus). But transparent bodies receive them only with the reception by which they receive for reflection (ad reddendwri), and they do not sense them'. Because of this difference 'the extension of the forms into the sentient body does not have to be in straight lines, as transparent bodies demand'. Hence 'only the anterior part of the glacialis is made appropriate for the reception of the forms on straight radial lines; but the posterior part, which is the vitreous humour, and the receptive power which is in that body, is not made appropriate to the sensation of those forms but only to the preservation of their ordering' (ii.1.4, p. 26). Therefore forms are refracted at the vitreous humour by two causes, of which one is the difference of transparency of the two bodies, and the other the difference of the quality of reception of sensation between these two bodies'. If their transparencies were the same, the form would be extended into the vitreous humour along the straight radial lines without refraction; 'but it would be refracted because of the difference of the quality of sensitivity (sensus); and thus because of refraction the form would be monstrous, or because of its arrangement there would be two forms'. In fact both causes acted corroboratively so that after refraction a single form passed from the glacialis through to the optic nerve. Therefore the forms reach the vitreous humour ordered according to their order on the surface of the eye, and this body receives them and senses them'. They were refracted by the two causes on entering the vitreous humour, and 'then this sensation and these


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forms are extended through this body until they reach the ultimate sentient', by way of the hollow optic nerve, 'like the extension of the sensations of touch and of pain to the ultimate sentient' (ii.1.5, p. 26; cf. i.5.25, p. 15; i.5.27, p. 16). The forms were not refracted on passing through the posterior surface of the vitreous humour into the visual spirit or 'sentient body, which is in the concavity of the nerve', because their transparency or density was the same (ii. 1.6, p. 27). Despite his geometrical model, Alhazen confined his whole analysis of the properties of the eye within the inherited Greek conception of it as a living sentient organ. He did not distinguish exclusively and consistently the different kinds of question involved in vision, which were to become clear only in the different conceptual context of the 17th century: fundamentally those of the physical properties of light and the operation of the eye as an optical instrument independently of its function in perception. It operated like a dead optical instrument only in so far as it shared the optical properties of insentient transparent bodies, but it was unlike them in being itself an active agent of perception. Alhazen's forms of light and colour were emitted in straight lines by all luminous or illuminated bodies whether or not there was an eye present to see them, and they entered the pupil just as they might enter any optical instrument. But once they had struck the anterior glacialis they were sorted, not by a purely geometrical optical process but by its selective directional sensitivity, into a sensible and not a geometrical optical image of the object seen. He tailored ocular anatomy to the requirements of this theory of sensation. These included the symmetry of the two eyes and optic nerves so that each of their images would be formed at corresponding points and could unite as a single image at the common nerve filled with the visual spirit, so to reach the ultimate sentient (i.5.27, pp. 16-17; cf. ii.1.6, pp. 26-27; ii.2.16, pp. 34-35; Hi.2.2-17, pp. 76-87; vii.6-36, pp. 267-268). He described how the eye, by its selective directional sensitivity operating through the central axis of the visual pyramid on which the forms struck the surface of the anterior glacialis perpendicularly, certified its perception of the whole visible object by means of rapid movements taking the axis over the separate points from which the forms were emitted (ii. 1.7-9, pp. 27-30; ii.2.42-44, pp. 57-58; ii.3.64-69, 75, pp. 67-71, 73-74; vii.6.37, pp. 268-270). But he never made clear whether it was the form of light and colour coming from the object seen, or its action in producing a sensible image in the anterior glacialis, or both together, that passed inwards from the posterior surface of that body to the ultimate sentient located in the region extending from the common nerve to the anterior part of the brain. Exactly how far its propagation continued to be optical and rectilinear, and where it became something different, remained ambiguous. Following Galen he distinguished between the sensation occurring in the anterior glacialis and the discriminative perception made by the ultimate

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sentient. Essential to this was that the sensation should retain its order as it passed through the visual spirit connecting them. Again the ambiguity over what passed produced a matching ambiguity as in Galen over the relative functions of those sentient bodies, but Alhazen explained the process of perception very clearly. The particular qualities (intentiones) that are distinguished by the sense of vision' he wrote 'are many, but generally divided into 22'. These included light, colour, distance, location, shape, size, number, motion, transparency, shadow. Others were perceived by combinations of these, as straightness or curvature, increase or decrease, dryness or wetness by the relative stability or movement of the parts, and emotions by the expressions produced by the movements of the face (ii.2.15, p. 34; cf. ii.2.12, p. 31). The qualities of light and colour going from the object seen into the eye thus differed in different ways which had to be distinguished and interpreted: And since it is so, distinction and inference (argumentatio) by the distinctive power (virtus distinctivd), and recognition of the forms and their signs, will occur only by the recognition or distinction of the distinctive power of the forms coming into the concavity of the common nerve to the apprehension of the ultimate sentient, and by the recognition of the signs of these forms. And so the sentient body extended from the surface of the sentient member all the way to the concavity of the common nerve, namely the visual spirit, is sentient throughout, because the sensitive power is in the whole of this body. Since therefore the form is extended from the surface of the sentient member all the way to the concavity of the common nerve, any part of the sentient body will sense the form; and when the form reaches the concavity of the common nerve, it is apprehended by the ultimate sentient, and then distinction and inference will occur.... In this way apprehension of the forms of visible things will occur in the sensitive power, the ultimate sentient, and the distinctive power..... But distinction occurs only by the distinctive, not the sensitive, power (ii.2.16, pp. 34-35).

Alhazen's Optica provided on its arrival in the Latin West in the 13th century a model of scientific argument, a guide to the relation of perceiver to perceived not simply in vision but in general, and the definitive treatment of optics in all its aspects for nearly four hundred years. The Latin Optica established the subject as a major experimental and mathematical physical science in the scheme of medieval theoretical and practical knowledge. Historically most important of all was the adoption by Roger Bacon, especially in the Opus maius (completed by 1267), followed by John Pecham and Witelo, of Alhazen's geometrical model of the eye as an image-forming device. Witelo wrote his Perspectiva or Opticae libri decem (in 1270 or soon afterwards) as a compendium of Alhazen's Optica and provided jointly with the latter the essential account of the subject (eventually to be published by Risner in 1572 in one integrated volume) until the 17th century. Bacon (in Opus maius v. 3.2.2-4) also developed Robert Grosseteste's conception of a magnifying glass by


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means of constructions based on those of Ptolemy for plane and of Alhazen for curved refracting surfaces. Spectacles were invented in northern Italy at the end of the 13th century.7 Some particular questions arose in two different contexts, that of the camera obscura and that of the eye, over Alhazen's assertion that rectilinear propagation was a fundamental property of light. The camera obscura became a familiar instrument in the second half of the 13thcentury, used for example in observing solar eclipses.8 The question here was how to account by means of rectilinear propagation for the circular shape of the image cast through an angled aperture with straight sides of a certain size at a certain distance from the screen. Why was it that when the aperture was relatively small or its distance from the screen relatively large the image assumed the shape of its luminous source independently of the shape of the aperture? Lacking the analysis into superimposed images made by Alhazen in an Arabic work not translated into Latin, different kinds of answer were proposed. Their essential features for present purposes, without going into details, was that they preserved the principle of rectilinear propagation within the wider principle that nature always acts for the best, and they made the operation of the camera obscura a familiar problem. The question for the eye was that faced by Alhazen concerning the propagation of the sensible image from the crystallinus or anterior glacialis through the vitreous humour and then through the winding optic nerves to the ultimate sentient in the brain. Bacon expounded Alhazen with an interesting new terminology. Since the rays of the visual pyramid or cone carrying the image must travel rectilinearly through the vitreous humour in accordance with the principles of geometrical optics, if they continued all the way in the same straight line they would intersect and then 'what was right would become left and vice versa, and what was above would be below, and so the whole order of the thing seen will be changed'. To prevent this 'nature has contrived' the position and the transparency of the vitreous humour so that the rays would be refracted at its interface with the anterior glacialis, and that there would be no further refraction of the images (species) on their passage from the vitrous humour into the nerve which 'is filled with a similar vitreous humour as far as the common nerve' (Opus maius v. 1.7.1). These optical principles belonged to what he called the common laws of nature and they operated necessarily in all inanimate media. But propagation in an animate medium 7

See E. Rosen, The invention of eyeglasses', Journal of the History of Medicine and Allied Sciences 11 (1956), 183-218; Crombie (1967: above n. 1); V. Illardi, Occhiali alia corte di Francesco e Galeazzo Maria Sforza (Milan, 1976a), and 'Eyeglasses and concave lenses in fifteenth-century Florence and Milan', Renaissance Quarterly 29 (1976b), 341-360. "See D. C. Lindberg, The theory of pinhole images from antiquity to the thirteenth century', Archive for History of Exact Sciences 5 (1968), 154-176; 'A reconsideration of Roger Bacon's theory of pinhole images', ibid. 6 (1970a), 214-223; The theory of pinhole images in the fourteenth century', ibid. 6 (1970b), 299-325. See also Straker (1971: above n. 4), and his 'Kepler, Tycho, and the 'Optical part of astronomy': the genesis of Kepler's theory of pinhole images', Archive for History of Exact Sciences 24 (1981), 267-293.

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Fig. 6. Alberti's grid (1435): from Diirer, Underweysung der Messung (1538).

Ciuitaiij I poM

Fig. 7. A painting as a cross-section of the visual pyramid: from Fludd (1618).

does not hold to the common laws of nature (leges communes nature), but claims for itself a special privilege. This propagation does not take place except in an animate medium, as in the nerves of the senses; for the image follows the tortuosity of the nerve and pays no attention to the straight path. This happens through the power of


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the soul in regulating the path of the image, according to what the operations of an animate thing require (iv.2.2).

Thus for the benefit of natural order 'the capability of the power of the soul' could dispense the image from the 'common laws of natural propagations (leges communes multiplicationum naturalium)' (v. 1.7.1) shared by light and other forms of energy.9 Pecham a little later used similar terminology and noted in discussing the possibility of deviation from rectilinear propagation in the camera obscura that this must happen in the visual spirits in the optic nerve in order to preserve the image. Here 'the mode (via) of the spirits brings about that advance of the image partly outside the rectitudinal', but in the camera obscura this would be done by a 'natural fittingness (convenientta)'. But, he added, 'these things are asserted without prejudice to a better opinion'.10 The Latin perspectivists established Alhazen's geometrical model of vision and made these related optical problems familiar in the West equally for mathematical natural philosophers and for visual artists. Thus Lorenzo Ghiberti, belonging to the first generation of artists to exploit the new technique of linear perspective invented early in the 15th century by Filippo Brunelleschi, used in his discussion of the theory and practice of the method in sculpture all the main optical writers from Aristotle and Euclid to Bacon, Witelo and Pecham and an Italian version of Alhazen's Optica made in the century before.11 The theory of perspective, described for the first time by his younger contemporary Leon Battista Alberti, was based on the visual pyramid or cone extending from the eye as its apex to the object seen as its base. A drawing in true perspective was then a plane cross-section of this pyramid: he described how to make it correctly by viewing the object through a chequered screen or grid (Figs 6 and 7).12 The technique of perspective, showing by means of calculated visual clues how to represent a three-dimensional object on a plane surface, produced in effect a perceptual model of the scene before the eyes. Its exact measurement and true scaling introduced into science and technology a completely fresh means of communicating information through pictorial illustrations, and at the same time a new conception of modelling. Especially dramatic were the effects on the depiction of the external and 9 Cf. Roger Bacon, De multiplicatione specierum, ii.2, ed. and transl. by D. C. Lindberg in Roger Bacon's Philosophy of Nature (Oxford, 1983), pp. 102-103; Lindberg (1970a: above n. 8). '"John Pecham, Perspectiva communis, ed. and transl. by D. C. Lindberg in John Pecham and the Science of Optics (Madison, Wisconsin, 1970), i. 7 revised, pp. 78-81. "Lorenzo Ghiberti, 7 Commentarii, i. 1, ii. 12, 22, iii. 2, J. von Schlosser (ed.) (Berlin, 1912); cf. G. F. Vescovini, 'Contribute per la storia della fortuna di Alhazen in Italia', Rinasdmento 2nd Series, 5 (1965b), 17-49. 12 Leon Battista Alberti, De pictura (1435) in On Painting and On Sculpture, C. Grayson (ed.) (London, 1972); cf. Albrecht Diirer, Underweysung der Messung (Nuremberg, 1525, revised 1538); E. Panofsky, The Life and Art of Albrecht Diirer (Princeton, N.J., 1943, revised 1955); S.Y. Edgerton Jr., The Renaissance Rediscovery of Linear Perspective (New York, 1975); F. Borsi, Leon Battista Alberti (Oxford, 1977; M. Kemp, The Science of Art (New Haven, Conn., 1990).

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internal structures of animals, plants and minerals and their arrangements and of those of machines. Depiction became an instrument of research. Most compelling in the exact information they could provide were the views showing sections cut through an anatomized corpse or a machine at different angles and through different parts, the views with the outside cut away to reveal the internal parts in position, the rotated view as developed by Albrecht Diirer, and above all the transparent view of the internal arrangements and the exploded view depicting both the whole and the parts taken out and shown separately in accurately scaled diagrams. Through the 15th century the new techniques of perspective and chiaroscuro rapidly transformed the working drawings of architecture and engineering as they had the design of paintings. The Sienese engineer Mariano di Jacopo called Taccola, who knew Brunelleschi, and a generation later Francesco di Giorgio Martini, both seem to have designed their machinery by means of inventive drawing on paper before building it. The new pictorial language was used with even greater sophistication by Leonardo da Vinci, and with the printed book it became in the 16th and 17th centuries as normal a means of finding out and conveying information as the written word. Thus appeared the presentation of the mechanisms of pumps, water-driven mills and other devices by Agricola in his treatise on mining and metallurgy, and by Jacques Besson, Agostino Ramelli and Vittorio Zonca in their richly illustrated volumes on machines. There was likewise the increasingly sophisticated presentation of their anatomical researches by Leonardo da Vinci with his drawing of the skull and its contents; by Andreas Vesalius with his illustrations also of the skull, of the opened heart and its valves, and of the eye as a whole and in transverse vertical section accompanied by the dissected parts taken out and shown separately; by Felix Plater with his exploded views of the parts of the eye; by Girolamo Fabrici da Aquapendente and later by Giulio Casserio depicting the organs of the five senses with attention to comparative anatomy.13 Comparisons of living organs with inanimate artifacts were not at this time new, but the familiarity of two such artifacts provided especially efficacious conditions for modelling the eye. The glass or crystal lens became well known during the 16th century as a focusing device in spectacles. The camera obscura was likewise widely used both in astronomy for observing solar eclipses and in art for demonstrating the projection of a scene in perspective upon its translucent screen. Artists as well as mathematicians and natural philosophers began to turn their attention to how the eye itself, receiving the visual clues from the scene or painting in front of it, operated as an instrument of vision. It seems to have been Leonardo who first proposed a camera obscura "Cf. S. Y. Edgerton Jr., The Renaissance development of scientific illustration', in Science and the Arts in the Renaissance, J. W. Shirley and F. D. Hoeniger (eds) (Washington, D.C., 1985), pp. 168-197; Crombie, Styles chs. 8,13 (above n. 1).


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Fig. 8(a). From Leonardo da Vinci, Codex Atlanticus, f. 337 illustrating his comparison of the eye with a camera obscura. In this construction the rays intersect for a second time in the centre of the lens in order to preserve the correct orientation of the image at the optic nerve. The ocular anatomy is peculiar, showing the aqueous humour extending all round inside the dark choroid (uvea), and the vitreous humour in front of the spherical crystallinus.

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Fig. 8(b). From Codex D,f.3v: model of the eye (top right). A hollow glass sphere cut away at the top (— right) is fitted in a box with a small hole in the bottom as the pupil, and filled with water: inside is a smaller glass sphere as the crystallinus. With his face in the water the observer's eye would receive the image of the object seen on the visual pyramid entering the pupil hole on the rays coming from s t. At the left is a matching diagram of the eye itself with the optic nerve emerging on the right at a place corresponding to the observers eye in the model.


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Fig. 9. From Gemma Frisius, De radio astronomico et geometrico (Antwerp, 1545) f.31rv: observing a solar eclipse in a camera obscura.

incorporating a glass lens as a model of the eye, and thus he introduced the conception of the image formed in the eye as a picture on a screen (Fig. 8).14 He introduced at the same time into the analysis of vision the idea of exploiting the conformity of nature with art and of living with dead. But he still looked with Alhazen his analysis for an immediate explanation of visual perception. He recognized the need to explain optically the path through the eye of the rays forming the image. He assumed that the visual power lay not in the crystallinus but in the widened extremity of the optic nerve, which received the images and transmitted them to the common sense in the seat of judgement. The crystallinus was simply a refracting device whose essential function was to prevent the image from reaching the visual power inverted, as in a camera obscura. The eye was not simply a passive instrument like a camera obscura, but a living organ with active vital powers of selection, but for it to see correctly the image must be orientated as well as ordered in the same way as its object. This brilliant model was not known in print in time to have any influence, but the camera obscura itself was widely publicized by writers both on astronomy and on art. Gemma Frisius described and illustrated how to observe solar eclipses in a darkened room in which sunlight admitted through a small hole would produce an inverted image of the Sun on a suitably placed 14 Leonardo da Vinci, Codex D in Les manuscrits, M. C. Ravaisson-Mollien (ed.), 6 vols. (Paris, 1881-1891); // Codico Atlantico nella Biblioteca Ambrosiana di Milano, transcribed by G. Piumati, 8 vols. (Milan, 1894-1904); cf. The Notebooks, arranged etc. by E. MacCurdy, 2 vols. (London, 1938); M. Kemp, Leonardo da Vinci: The marvellous works of nature and art (London, 1981).

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screen (Fig. 9).I5Daniele Barbaro in his standard textbook on perspective gave an account of a similar darkened room with an eyeglass set in the small hole, through which the external scene would be projected onto a sheet of paper placed at the correct distance. There it could be traced with a paint-brush.16 The attention given meanwhile to the eye itself indicates the problems perceived and the characterization of its essential visual parts. Vesalius in his classical dissection published in De humanis carports fabrica libri septem (1543), with woodcuts of the whole eye in transverse vertical section and of the parts taken out and drawn separately, established the standard ocular anatomy to be copied or imitated even when corrected for nearly a century (vii. 14, pp. 643-646). He described the crystallinus as magnifying like eyeglasses (specilla) and its shape, flattened front and back, as 'like a lentil' (ad lentis similitudinem): hence what was to become the standard term 'lens' (p. 646).17 He doubted whether this was the principal organ of the eye, but on how the eye functioned and the controversies of philosophers and medical men he could say nothing (pp. 649-650). Of the retina he wrote enigmatically that 'this c o a t . . . is considered by many the principal organ of sight' (iv. 4, p. 424) but nothing further. Vesalius was corrected later on some important details by Realdo Colombo who pointed out that the lens was located forward of the centre of the eyeball and was flatter in front than behind; and by Giulio Cesare Aranzi who noted that in horses and cattle the optic nerve entered the eyeball to one side, although he still supposed that it entered centrally in man. Aranzi tried to demonstrate vision by means of an experiment on the eye of an ox. After dissecting it out of its socket, he cut an opening in the back as far as the vitreous humour, set it 'in a dark place' illuminated in front of it, then closed one eye and applied the other to the opening in the position of the optic nerve: 'the visual power (vis visiva) of the observer comes through the vitreous to the crystallinus and thence to the cornea through the opening of the uvea to the objects' illuminated.18 Later Felix Plater, professor of medicine at Basel, asserted for the first time explicitly that the retina was the sensitive visual receptor. In his De corporis humani structura et usu (1583) he wrote that through the pupil: 'The illumination of external things irradiating the cornea is sent into the dark chamber (camera obscura) of the eye'. This led him to: l5

Cf. Straker (1981: above n. 8). Daniele Barbaro, La prattica della perspettiva (Venice, 1568). The term specilla, short for ocularia specilla as used by Girolamo Fabrici, meant eyeglasses, as perspicillum used by Felix Plater meant eyeglass (see below), not mirror as supposed by Lindberg (1976: above n. 4) 173 n. 137, 275 n. 151; similarly Francesco Maurolico used conspicilia (below), and later Galileo in the Sidereus nuncius (1610) introduced his telescope under the name perspicillum, in which he was followed by Francis Bacon, Novum organum, ii.39 (1620) in Works, J. Spedding, R. L. Ellis and D. D. Heath (eds), i (London, 1857), pp. 307-308. 18 Iulius Caesaris Arantius, Anatomicarum observationum liber, cc. 18, 21 (Venice, 1587), pp. 71. l6

17


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The primary organ (pars) of vision, namely the optic nerve dilated into the grey hemispherical retina (retiformis) after it enters the eye: which receives and discriminates the forms (species) and colours of external things that fall with the illumination into the eye through the aperture of the pupil and are presented to it by its eyeglass (perspicillwri) It has affinity with the substance of the brain, with which through the nerve it is continuous. Later he came to: Three very clear humours, which in distinct situations fill the cavity of the eye and assist the act of vision.... First, the crystalline humour, which is the eyeglass of the visual nerve: placed facing this nerve and the aperture of the pupil, it collects the images (species) or rays falling into the eye and, spreading them over the area of the whole retiform nerve, it presents these magnified, in the manner of an internal eyeglass (perspicilli penitus modo), so that the nerve can take possession of them more easily (pp. 186-187)." Plater like Vesalius did not consider how the eye operated as the instrument of vision. Hence the question of the inverted image did not arise. They illustrate the insulation of the anatomists of the medical faculties from the mathematical sciences and arts and the fundamental illumination they had brought to the physiology of vision, as likewise of hearing. But clearly, besides Plater's radical identification of the retina as the sensitive visual receptor, reducing the crystallinus simply to a lens, an accurate general ocular anatomy was essential for a true optical analysis of its physiology. The culmination of these anatomical investigations was the superbly illustrated triple treatise by Girolamo Fabrici, De visione, voce, auditu (1600), with 'De oculo visus organo liber' as its first book. Fabrici incorporated in 'De oculo' the corrections to Vesalius made by Colombo and others, with an accurate woodcut of the crystallinus (p. 35), but he still showed the optic nerve entering the eyeball centrally (iii.8, p. 105). His visual theory was essentially a combination of the formulations of the problem by Aristotle and Galen with a version of the optical scheme with which Alhazen had prevented the reversal of the image as the visual cone passed through the transparent media. He likened the crystallinus to eyeglasses (ocularia specilla), 'in which art excells nature' in restoring youth to old eyes by means of refraction (iii.5, pp. 82-83; cf. iii.l, 2, pp. 61, 73-78, iii.7, pp. 102-103). But the crystallinus was also 'the special organ of vision' (iii.7, p. 96) entirely responsible for visual perception within the eye (ii.7, pp. 51-54; iii.7, pp. 96-104). He specifically denied visual sensitivity to the retina and the arenea (iii.8-9, pp. 104-106), and insisted that any transmission of images beyond the crystallinus was both anatomically and optically impossible (iii.10-11, pp. 106-114). With some concessions to optical science, he remained firmly within the medical tradition. "Cf. Crombie (1967: above n. 1); H.M. Koelbing, Renaissance der Augenheilkunde 1540-1630 (Bern. 1967).

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It was the mathematicians who came to reform visual theory by proceeding through an optical analysis of ocular physiology, exploiting the models of eyeglasses and the camera obscura, and thus reformulating the problem itself. The Sicilian mathematician Francesco Maurolico completed in 1554 an optical analysis of both the camera obscura and the eye without connecting the two. His Photismi de lumine et umbra with Diaphanorum panes containing these original results were published only in 1611, and although his manuscripts may have been known, through Christopher Clavius or otherwise, they had no known influence. He based his optics on Alhazen, Roger Bacon, Pecham and Witelo and departed from them only in specific innovations. In Photismi he solved for the first time the fundamental optical problem of how the camera obscura focused the image on its screen. The essential variables were the size of the aperture and its distance from the screen. Maurolico demonstrated geometrically that the inverted image, formed by the superimposed images of the separate points of a luminous source, must come to conform to the shape of the source, regardless of that of the aperture, as these variables came to a certain ratio. He gave the solar and lunar images, in eclipse or not, as particular examples of this general theorem (Theorem 22, corol. 1 and 2, 1611, pp. 17-22).20 He defined the problem of vision in Diaphanorum panes iii: 'On the structure of the visual organ and the forms of spectacles (conspicilid)\ writing that 'since the organ is transparent, the matter is entirely one of transparent bodies'. Sharing the accepted commitment to the orientation of the image in the eye, he attempted to trace the paths of the rays through it, by the conformity of its refractions to those of eyeglasses, in such a way that this orientation would be preserved. 'Among those parts that pertain to vision' he wrote, 'the summit of rank is held by the glacialis or crystalline humour, which in my opinion we can call also the pupilla, in which the visual power takes its position as on a throne. This is convex on both sides, but not spherical but compressed, and more so in front'. Under the heading 'On spectacles' he made apparently for the first time an analysis of nonspherical lenses as exemplified by spectacles and applied the properties of this model to the eye. The crystallinus or pupilla was in effect a biconvex lens, placed in front of the middle of the eyeball but not spherical lest the perpendicular visual rays should pass through the centre of the sphere, intersect there, and carry to the optic nerve an altered, that is inverted orientation (situs) of the thing seen, so that things appear inverted to the spectator . . . . So it happens that the visual rays falling on the anterior surface of the 20 Cf. Crombie (1967: above n. 1), Straker (1971: above n. 4), Lindberg (1976: above n. 4): the last by a double misreading (pp. 180, 276 n. 7) applied to Maurolico what I wrote of Leonardo da Vinci in my Robert Grosseteste (Oxford, 1953, 1971), p. 281, and my 'Kepler: de modo visionis', in Melanges Alexandre Koyre, i (Paris, 1964) p. 141; cf. Crombie (1967), 45-46 n. 72 for my correction of a mistake I did make in supposing that Maurolico had shown the focusing of the image on the retina.


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pupilla and carried through its depth without meeting, that is before coinciding, are carried in their own proper orientation (in suomet situ) to the optic nerve and present the image (species) in its proper position (in sua positione).

The pupilla (crystallinus) was not simply a lens but also the sensitive visual receptor, constituted 'for suffering affection' (adpatiendwri) and 'for sensation' (ad sentiendwri): it received the images of things at its anterior surface and transmitted them from its posterior surface through the optic nerve to the common sense. 'But how vision is effected, whether under some law of refraction (lex fractionis) or of spirits, was by no means easy to decide'. He wished that he could take his account either 'from natural philosophy (physica) or from mathematics alone: because we would reach the goal of truth by following either the one or the other, whether by borrowing the sensitive power from natural philosophy or the law of the refraction of rays from mathematics' (pp. 72-74). He went on to adapt Alhazen's construction for bringing about a point-point correspondence between object and image to show how the crystallinus, with its 'lenticular shape' (figura lenticularis) (p. 75, cf. 76), must refract and transmit the rays according to the law of refraction in such a way that there was no inversion. If he remained bound by the spell of the erect and correctly orientated image, his technical analysis of lenses marked a considerable advance in scientific knowledge of the natural organ and the artificial model alike. He related defective types of vision to the shape of the lens, and prescribed different kinds of spectacles to 'correct the failure of nature' in short and long sight (pp. 76-78). Thus, again using pupilla for crystallinus, 'because the transmission of the visual rays through the pupillae happens no differently from that through spectacles convex on both sides, we may not at all unjustly define the pupillae as the spectacles of nature' (p. 80). Maurolico's optical writings, like Leonardo's, did not become publicly known until after the crucial period of these investigations. It was Giovanni Battista Benedetti who, two years after Plater, published a geometrical comparison of the eye with a camera obscura in which the images of external things were projected through the pupil onto the retina. Benedetti was familiar with Daniele Barbaro's account of a camera obscura with a lens, which he paraphrased in one of the letters included in his Diversarum speculationum mathematicarum et physicarum liber (1585; p. 270). He published his geometrical comparison of the optics of the eye with that of a camera obscura in another brief letter 'De visu'.21 In the eye the rays that would form the optical image of an object were projected through the small pupil and the refracting humours onto the branching nerve (i.e. retina) at the back of the eye as onto the screen of a camera obscura, and the same would happen if they were to proceed directly without refraction 'yet not in its place (in suis locis)\ By this laconic 2l Cf. T. Frangenberg, 'II "De visu" de G. B. Benedetti', in Giovan Battista Benedetti e il suo tempo, presented by A. Ghetti (Venice, 1985), pp. 271-282.

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comment he seems to have meant that without refraction the image would be inverted, as it was in his geometrical account of the camera obscura which had no lens or other refracting medium. These puzzles indicate how difficult these optical problems were both technically and conceptually even for a mathematical scientist as sophisticated as Benedetti. Benedetti's analysis of vision like that of music published in the same volume was apparently not read by contemporaries, but a comparison of the eye with a camera obscura first mentioned briefly by Giambattista della Porta in the first edition of his Magia naturalis (1558) became widely known in the much enlarged edition of 1589. He presented it in the context not of science but of entertainment and optical conjuring. After describing the inverted and reversed scenes that could be projected onto the screen of a camera obscura, he wrote: 'If you put a small lenticular crystal glass (crystallina lens) to the hole', these could be made clearer and restored 'upright, as they are'. The instrument could be used to copy a sunlit picture by placing a white sheet of paper inside the hole, and moving it forwards or backwards until a 'perfect representation' of the picture was cast upon this table (tabula) or screen: then one 'must lay on colours where they are in the table', so that when all is done and the original picture removed, the picture (impressio) will remain on the table.... From this it may be clear to philosophers and opticians where vision is effected; and an end is put to the question of intromission agitated for so long, nor can both be demonstrated by any other artifice (artificium). The image (idolum) is sent in through the pupil, as by the opening of a window, and the part of the crystalline sphere located in the middle of the eye takes the place of the screen (tabula).... It is described more fully in our optics (xvii. 6, pp. 266-26V).22

In his optical work De refractione (1593) Porta firmly located the full power of vision in the crystallinus, where the image was received correctly orientated to correspond to the object seen. To prevent inversion he argued contrary to Vesalius that the crystallinus must be found in front of the centre of the eyeball where the intersection of the rays would occur (iii.l, 13-15, pp. 65-68, 83-86). It was then the anterior surface of the crystallinus that corresponded to the screen of the camera obscura: 'I say that just as light passing through the confined opening of a window represents bodies illuminated by the Sun on a paper underneath, so likewise it depicts on the crystallinus the images (spectra) of seen things entering through the opening of the pupil' (iv.l, p. 91; cf. iv. 1-2, pp. 87-95). He rejected as anatomically impossible Alhazen's theory that vision was completed by the transmission of images beyond the crystallinus through the optic nerves (vi. 1, pp. 139-146).

"Porta, Magiae naturalis libri xx (Naples, 1589), transl. as Natural Magick (London, 1658) with corrections; De refractione optices parte libri novem (Naples, 1593).

Part II: Kepler and Descartes WHEN KEPLER took up the problem of vision no one had questioned the essential assumption that ocular physiology must yield an immediate explanation of visual perception, so that what was seen in the object was only and exactly what was present in the image formed in the eye. The essential geometry remained that of the Euclidean perspective cone, with its base on the visible object and its apex in the eye, as developed by Alhazen into a pointpoint correspondence between the image and the object. Alhazen's account of the ocular image as an internal pattern of stimulated points formed by a combination of optical refraction and selective sensitivity left the relation of the physical to the animate aspects of the process ambiguous, and his theory that visual perception was completed in the common sense located in the brain left the persistent enigma of the nature of the image or information transmitted from the sensitive ocular receptor inwards through the non-optical medium of the optic nerves. The separation of the physical from the animate began with the identification of the crystallinus with a glass lens and the analogy of the whole eye with a camera obscura which formed a wholly different kind of image, an optical image focused on its screen. But the essential commitment to finding an exact correspondence in orientation and order between the image and the visible object remained as an obstruction to a purely optical analysis. Porta made the front of the crystallinus analogous to the screen in his eye. When Plater identified the retina and not the crystallinus as the sensitive ocular receptor he did not consider the optical geometrical consequences. If Benedetti's optical analysis located an inverted image on the retina as on the screen of a camera obscura he did not consider the consequences for the whole science of vision. It remained for Kepler to begin the explicit separation of the distinct questions involved. Kepler was led to his reluctant philosophical innovation, breal^ng with fundamental commitments of the Greek conception of optics, by the inescapable precision of his scientific argument. To the form and expectations of that argument we must pay close attention. Kepler had been introduced to the problem of image formation in a camera obscura by the anomalous results obtained by Tycho Brahe in using this

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instrument to measure the apparent sizes of the sun and moon in solar eclipses. Having adapted a form of dioptral camera for the purpose, Tycho came to realize that systematic allowance had to be made in his observations for the size of the aperture. He measured this and subtracted it from that of the image from which he computed the apparent solar diameter. Then he found to his surprise that the apparent diameter of the moon calculated from observations of the solar eclipse of 1598 was about one fifth smaller during the eclipse than it was at other times when astronomical theory showed the moon to be equally distant. Since he found the same anomaly on all occasions he revised his lunar tables accordingly, and looked for an optical cause in the moon itself. When Kepler, already familiar with the camera obscura for observing solar eclipses, heard of this 'optical paradox' he looked first in the same direction, but he refused to accept Michael Mastlin's anodyne comment that 'observation cannot be perfectly exact', and hoped that 'I could elicit a sure response by means of skilful methods'. After visiting Tycho near Prague in 1600, he returned in June to Graz ready for the solar eclipse expected in July 'with a skilful observation which I am considering' and 'especially to explore by observation ... the striking affirmation' made by Tycho.1 This he did with a dioptral camera with a movable screen. Having learnt from Tycho to measure not only the object being observed but also the essential variables of the size of the aperture and its distance from the screen in the instrument, what he came to explore was the optics of the camera obscura and the experimental error to which the method of observation itself gave rise. He recorded his results in his 'Eclipse Notebook' written during July 1600 and concluded with a set of numbered propositions.2 Early on he asserted the principle that light was propagated rectilinearly in all directions from all points of a luminous source (proposition 6), and then developed his analysis by treating a finite aperture as an assembly of points through each of which an inverted image of the source was cast on the screen (proposition 13). Like Maurolico he demonstrated that at a given ratio between the size of the aperture and its distance from the screen the composite image must conform to the shape of the source; if the aperture were enlarged or its distance decreased the image would assume the shape of the aperture (proposition 14). During July, he reported later in the year to Mastlin, 'I have written a Paralipomena to the Second Book of the 'Kepler to Herwart von Hohenburg 30.v. 1599, in Kepler's Gesammelte Werke, edited by W. von Dyck, M. Caspar and F. Hammer. 18 vols (Munich, 1937-1959), xiii, 339; Mastlin to Kepler 2.V.1598 and Kepler to Mastlin 8.xii.l598, ibid., 213, 253; cf. S.M. Straker, Kepler's Optics (Indiana University Ph.D. thesis, 1971; Ann Arbor, Mich., 1980), and 'Kepler, Tycho, and the "Optical part of astronomy": the genesis of Kepler's theory of pinhole images', Archive for History of Exact Sciences 24 (1981), 267-293. On Kepler's optics see also F. Hammer, 'Nachbericht', in Gesammelte Werke, ii (1939), 393-436; A.C. Crombie, 'The mechanistic hypothesis and the scientific study of vision', Proceedings of the Royal Microscopical Society 2 (1967), 3-112, reprinted in Science, Optics and Music in Medieval and Early Modern Thought (London, 1990); and D.C. Lindberg, Theories of Vision from al-Kindi to Kepler (Chicago, 1976). 2 So named with essential references and analysis by Straker (1981: above note 1).

The History of Optics: Kepler and Descartes

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Optics of Witelo'. As for Tycho's anomaly, this was an artifact arising from the instrument: 'Therefore any eclipses that have been observed in this manner stand in need of correction'.3 He wrote again about the camera obscura in December 1601: 'Why should it not happen in the eye what I demonstrated in the aperture, that lights are amplified and shadows are constructed? For there is an aperture in the eye'.4 Kepler's Eclipse Notebook was in effect a draft for Ad Vitellionem paralipomena, quibus astronomiae pars optica traditur (1604): Things appended to Witelo, in which the optical part of astronomy is treated, a critique using Risner's standard Latin edition of 1572 of the texts of both Witelo and Alhazen. This he set out over the following three years in the same order of topics, linked by his analysis of image formation in the camera obscura. In the first five chapters he covered critically the optical questions of the nature of light and colour, the camera obscura, the location of the image reflected by plane and curved surfaces, the measurement of refraction in different media, and the operation of vision. In the last six chapters he dealt with the application of optics to astronomy. He explained this programme in his dedicatory letter to the Emperor Rudolph II, concluding: '... nor have I satisfied the mind with the speculations of abstract geometry, to wit with pictures . . . but I have tracked down geometry through the manifest bodies of the world, having followed the footsteps of the Creator with sweat and panting'.5 Since light was the vehicle of observation and also of its deceptions, knowledge of its properties was necessary for scientific practice. Because, he wrote in chapter I 'De natura lucis', 'nature must exhibit God the primary founder of all things in so far as it could', and the spherical form assumed by light was 'the image of the Trinity', and light was likewise 'the natural and fittest image of the corporeal world', introduced by Moses as 'a sort of instrument of the Creator' and 'the link between the corporeal and the spiritual world', knowledge of it was essential for fundamental physical and metaphysical theory. Kepler started from 'Euclid, Witelo and others'. Light he continued 'illuminates everything all around' (chapter I, proposition ii); 'the lines of these emissions are straight, called rays' and 'the shape of a sphere is assumed by light' (proposition iv); its 'motion is not in time, but in a moment' therefore 'the speed of light is infinite' (proposition v). But the 'ray of light is not the light itself going out' for 'the ray is nothing but the motion of light. Just as in physical motion the motion is a straight line, but the physical thing that moves is a body, so in the same way in light the motion itself is a straight line but what moves is a certain surface' (proposition viii). This led to the photometric law: 'As with spherical surfaces having a source of light for centre 'Kepler to Mastlin 9.ix.l600, Ges. Werke, xiv, 150-151. Kepler 10/20.xii.l601, ibid. 207. s Ges. Werke, ii, 8-10. References in the text are to this edition, where they are indicated by GW.

4

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the wider is to the narrower, so is the strength or density of the rays of light in the narrower to that in the wider spherical surface, that is conversely' (proposition ix; GW\\, 18-22). He devoted the whole of chapter II 'De figuratione lucis' (GW ii, 46-61) to the camera obscura, starting with the history, from Aristotle through Witelo and Pecham to Gemma and Tycho, of unsuccessful attempts to solve the problem of the shape of images projected through small openings, and concluding with a long presentation of his true solution in its most general form. He described how he came to see the truth by an experiment in which the geometry was displayed by threads replacing rays so that he eliminated 'the cover of the arcane nature of light' into which both Pecham (called here Pisanus) and Witelo had retreated. Diirer had explained perspective in 1525 by means of a similar physical model, but Kepler did not mention that.6 Kepler showed how the threads, and likewise the rectilinear rays, would produce an image either of the aperture or of the luminous or illuminated source entirely according to their geometrical disposition. Later in the astronomical part of his book he showed how he made the camera obscura an essential instrument for his solar observations, corrected Gemma's and Tycho's understanding of it, published his own computations, and so on (chapters VIII, XI; GW ii, 256257, 288-301). Essential for the accuracy of astronomy was the measurement of refraction to which he devoted his long chapter IV (GW ii, 78-143). He developed a theory of the causes of refraction explicitly by the use of varieties of analogy. This involved a study of conic sections, presented as a system, for which he introduced the term focus (literally, hearth). 'We must use the geometrical languages (voces) of analogy' he wrote; 'for indeed I greatly love analogies, the most trustworthy of my instructors, the confidants of all the secrets of nature: especially to be esteemed in geometry', where 'they brilliantly put in front of the eyes the whole essence of any thing' (chapter IV, pp. 91-92). He proposed an approximation to the still undefined ratio between the angles of refraction and incidence, and improved on Ptolemy's tables as published by Witelo.7 He came to the central subject in chapter V: 'De modo visionis' (GW\\, 143197).8 The 'deception of vision' in the recorded measurements of planetary diameters and of solar eclipses, he began, 'arises partly from the instruments of observation, as we discussed above in chapter two, and partly just from vision itself; and this, as long as it is not counteracted, makes considerable trouble for 'Straker (1971: above, note 1) 390 sqq. (1981, above note 1), and The eye made "other": Diirer, Kepler, and the mechanization of light and vision', in L. A. Knafla, M. S. Staum and T. H. E. Travers (eds), Science, Technology, and Culture in Historical Perspective (Calgary, Canada, 1976), pp. 7-24. 7 Cf. G. Buchdahl, 'Methodological aspects of Kepler's theory of refraction1, Studies in History and Philosophy of Science 3 (1972), 265-268. "Translated by Crombie, 'Kepler: de modo visionis', in Melanges Alexandre Koyre, i (Paris, 1964), p. 141, with slight changes; see also»Crombie (1967: above note 1).


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Fig. 1. From Kepler, Ad Vitellionem paralipomena, v. 2 (Frankfurt, 1604), after Plater, De corporis humani structura et usu, tabula xlix (Basel, 1583). The two unshaded diagrams at the bottom right are of the middle ear.

investigators and detracts from scientific judgement. The source of the errors in vision is to be sought in the structure and functioning of the eye itself. Had Alhazen and Witelo and then the anatomists dealt with the matter properly he would not have had to add this chapter to his Paralipomena ad Vitellionem. As

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it was he would 'put together, as it were as principles, an account of the relevant parts of the eye based on the most approved anatomists'; secondly 'sketch in summary the way vision takes place'; thirdly 'demonstrate each particular point'; fourthly 'lay bare what escaped the reasonings of the opticians and medical men concerning the functioning of the eye'; and lastly 'explain deceptions of vision arising from instruments, and apply this to astronomical practice' (pp. 143-144). His authorities for ocular anatomy, for which he had 'never seen or taken part in' a dissection, were 'the illustrations in Felix Plater's De corporis humani structura et usu, which were published in 1583 and reprinted this year, 1603' (Fig. 1); and the Anatomia Pragensis (1601) of his friend Johannes lessen. In 1600 lessen had been professor of medicine at Prague where he had assisted in the negotiations for Kepler to work there with Tycho Brahe, leading on Tycho's death in 1601 to his own appointment as Imperial Mathematician.9 lessen, according to Kepler, had profited 'by following Aquapendentius' (Girolamo Fabrici) as well as from his own 'anatomical experience'. He himself was a 'mathematician' (v.l, p. 144), but he did not hesitate to choose what he thought correct and relevant to his problem. Contrary to lessen, 'I agree more with Platter' he wrote on the important question whether the crystallinus was anatomically joined to the retina. lessen needed this because he followed Witelo in supposing that 'the power of recognizing visible things' lay in the crystallinus to which it was transferred through this connection from the optic nerve. Platter did not need the connection because he 'left the power of recognizing in the retina, which is nearer the truth' (v.l, p. 150, cf. v.2, pp. 156-157, v.4, p. 183). Kepler disagreed with lessen also on the shape of the crystallinus (p. 151), and noted the control of the light entering the eye by the dilation and contraction of the circular pupil (v. 2, p. 158). He reproduced Plater's plate with its explanatory notes showing the whole eye in vertical section and the parts dissected out and drawn separately, with the slightly bulging cornea (as observed by Leonardo de Vinci) indicated by a dotted line (Fig. 1; v.2, pp. 159-161). In his account in Ad Vitellionem paralipomena (v.4; GW \\, 183-189) of the failings of his predecessors, Kepler identified two sources of ideas for his new theory of vision and stated how he differed from them. 'Plater' he wrote after discussing lessen 'grasped the office of the crystallinus much better, although again not clearly its function. Vision he said happens by the ministry of the retiform coat'. But Kepler corrected Plater's conception of the crystallinus as an internal eyeglass, and showed exactly how changes and defects of vision corresponded precisely to what was painted on the retina: 'For as is the picture, so is vision'. Plater had not understood the difference between the image seen when we looked through a lens at something and the real picture 9 Cf. M. Caspar, Kepler, translated and edited by D. Hellman (New York, 1959), pp. 105-107, 121-123, 166.


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painted on our retina, which Kepler had pointed out in his proposition xxiii (below). 'It seems that Plater was led to this opinion by that anatomical experiment, of which I have heard from other medical men, namely that if the crystalline humour, having been taken out from the other humours, is placed on top of tiny letters it shows those larger. But this is something different from this matter. For vision occurs by means of the picture on the retina. But this deception happens not through a picture, but because of the image. Hence this magnification of letters by the crystallinus (or something analogous to it in the eye) does not fashion vision'. Thus he concluded: 'Compare the true mode of operation (modus) of vision proposed by me with that given by Plater, and you will see that this famous man is no farther from the truth than is compatible with being a medical man who deliberately does not treat mathematics' (pp. 185-187). Of Porta he wrote that it was he who 'in Magia naturalis xvii.6 first proposed the artifice (artificiwri) of that matter of which in the second chapter above I have set out a formal demonstration: namely by what cause all the things outside illuminated by the Sun are seen with their colours in the darkness' of the camera obscura. Next, Kepler continued, Porta 'added a few words de modo visionis1, and he quoted Porta's passage on making it 'clear to philosophers and opticians where vision is effected' and how 'the crystalline sphere located in the middle of the eye takes the place of the screen'. But, he addressed Porta, 'if I understand you well, when you ask where vision is effected, you reply on the surface of the crystallinus or screen'. For Porta had said that 'vision comes from that kind of picture (picturd)' which Kepler had demonstrated in his second chapter (prop, vii): 'and so to conclude, most skilful Porta, if you had added to your opinion only this': that the picture on the crystallinus is still confused by the wide opening of the uvea, and vision does not come about by the conjunction of light with the crystallinus, but the light descends onto the retina, with the separation and then reunion of the radiation to a point, 'and the place of gathering together to a point is on the retina itself, which exhibits the clearness of the picture, and it comes about that through that intersection the image (imago) is inverted and through this gathering together that it is most distinct and clear: if you had added this I say to your opinion, clearly you would have unravelled the mode of operation (modus) of vision' (pp. 187-189; cf. v.2, pp. 151-158; below). Kepler here made explicit his debt to Porta's artifice or model. He followed Porta in his comparison between a camera obscura and the eye as far as the anterior surface of the crystallinus onto which an optical image was cast as onto a screen (cf. v.2, p. 155; v.3, pp. 162, 177-178; below); then going beyond Porta he identified the function of the crystallinus as a lens which focused the image onto the retina, and he dealt with the geometry of how this happened. The image, as Porta had failed to understand, was inverted and reversed on the crystallinus and remained so on the retina. In an autographical passage Kepler

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described how he himself like all his predecessors was at first embarrassed by the inverted and reversed image and looked hard for means to show that it was rectified (p. 185; see below). But he was forced to accept the conclusions of his geometrical optical analysis which he set out in chapter V 2-4. In a new intellectual context Kepler's treatment of the operation of the eye as an optical instrument marked a radical change in the conception of vision accepted by his ancient and medieval predecessors, which enabled him to open a new approach to the relation of physiology to perception, even while he used many of the same analytical techniques. The analogy of the camera obscura, a formal analogy without identity of material parts, enabled him to isolate the geometrical optics of the eye as an immediately soluble physical problem to be treated first and apart from all questions of sensation and perception. With this new conception of the subject-matter he could reduce physiological optics to inanimate physics and banish from this passive physical mechanism any active sensitive power to look at an object or to receive stimuli selectively. He could formulate the fundamental problem of the image not as Alhazen had done, as that of how the eye produced an internal pattern of stimulated points, but as the wholly different problem of how the eye focused a completely different kind of image, an optical image itself visible from without like the inverted image focused on the screen of a camera obscura. Alhazen's eye did not focus but selected the image; he attributed to it explicitly vital sensitive properties which enabled it to deliver to the back of the eye an erect image both ordered and orientated as its object appeared to the viewer. Kepler's image made the need to avoid confusion by the selective perception only of the perpendicular rays irrelevant. The camera obscura became the true model of the eye. Kepler's restructuring of optical geometry to make it not a vital perceiver of a correctly ordered and orientated image conducted on the Euclidean persective cone, but like any inanimate focusing device, immediately raised in a precisely geometrical form the question of the identity and location of the sensitive receptor on which the image was cast. He could undertake a purely geometrical analysis of the paths of the rays of physical light through the crystalline lens and other physical refracting media until they were focused as an optical image on the retina as a screen. Of the innumerable physical rays, going in all directions from every point of a luminous or illuminated source, some fell on the pupil. He demonstrated how an inverted and reversed image must be focused in the eye by means of a construction which at the same time showed that the image must fall on the retina, and hence that this (as Plater had suggested) must be the sensitive receptor. He demonstrated how from an apex at each point on the visible object a multitude of radiant cones passed through the pupil, intersected, and went to a common base on the anterior surface of the crystalline lens, where their positions were reversed and inverted. This surface corres-


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Fig. 2. From Descartes, La dioptrique, v (Leiden 1637): illustrating Kepler's ocular dioptrics. Rays from each point on the object (VXY) are refracted through the cornea (BCD) and lens (L) to foci (RST) on the retina where they form an inverted image of the object. The man looking at the eye, with its back removed, set in a camera obscura would see the inverted image on the translucent retinal SCREEN.

ponded in this way to the screen of a camera obscura, which became as Porta had recognized the true model of the eye up to this location. But Kepler for the first time and for good anatomical reasons carried his optical analysis beyond this. He showed how the lens then focused each radiant cone from the common base in a matching cone to a point on the retina corresponding to that on the object from which it came. The multitude of such points recomposed the image SHIPS 22:1-G

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of the object (Fig. 2), just as did analogously the multitude of double pyramids in the camera obscura without a lens.10 He related this inverted and reversed image to the scene perceived by a simple geometrical rule making the points of this composite picture correspond to their sources on the object but not in orientation. But at the retina optics ended and the rays of light were succeeded by a different kind of motion. This, and how the visual faculty of the soul effected perception by means of the retinal image, he put outside his optical analysis as a problem for natural philosophy. Thus: I have described how vision takes place in such a way that the functions of each separate part can be seen, these so far as I know, having been investigated and discovered by no one else. And so I ask mathematicians to study this carefully, so that something certain about this noblest of functions may at last take its place in philosophy. I say that vision occurs when the image (idolum) of the whole hemisphere of the world which is in front of the eye, and a little more, is formed on the reddish white concave surface of the retina (retina). I leave it to natural philosophers (physici) to discuss the way in which this image or picture (picturd) is put together by the spiritual principles of vision residing in the retina and in the nerves, and whether it is made to appear before the soul or tribunal of the faculty of vision by a spirit within the cerebral cavities, or the faculty of vision, like a magistrate sent by the soul, goes out from the council chamber of the brain to meet this image in the optic nerves and retina, as it were descending to a lower court. For the equipment of opticians does not take them beyond this opaque surface which first presents itself in the eye. I do not think that we should listen to Witelo (book iii, proposition xx), who thinks that these images of light (idola lucis) go out farther through the nerve, until they meet at the junction half way along each optic nerve, and then separate again, one going to each cerebral cavity. For, by the laws of optics (leges optices), what can be said about this hidden motion which, since it takes place through opaque and hence dark parts and is brought about by spirits which differ in every respect from the humours of the eye and other transparent things, immediately puts itself outside the field of optical laws? (And yet it is this motion that brings about vision, from which the name optics is derived; and so it is wrong to exclude it from the science of optics simply because, in the present limited state of our knowledge, it cannot be accommodated in optics)... This image (species) existing separately from the presentation of the thing seen is not present in the humours or coats of the eye, as shown above; hence vision takes place in the spirits and through the impression (impressio) of these images (species) on the spirit. But really this impression does not belong to optics but to natural philosophy (physicd) and the study of the wonderful. But this by the way. I will return to the explanation of how vision takes place. Thus vision is brought about by a picture of the thing seen being formed on the concave surface of the retina. That which is to the right outside is depicted on the left on the retina, that to the left on the right, that above below, and that below '"See Straker (1981: above note I) 291-292. Lindberg (1976: above note 1) 202-206 seems perverse in denying this debt and in continuing to maintain that 'Kepler himself remained firmly within the medieval framework' (p. 207), and similarly later, e.g. 'Continuity and discontinuity in the history of optics: Kepler and the medieval tradition', History and Technology 4 (1987), 431448; followed in this by J.V. Field, Two mathematical inventions in Kepler's Ad Vitellionem Paralipomena', Studies in History and Philosophy of Science 17 (1986), 449-468.


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above. Green is depicted green, and in general things are depicted by whatever colour they have. So, if it were possible for this picture on the retina to persist if taken out into the light by removing the anterior parts of the eye which form it, and if it were possible to find someone with sufficiently sharp sight, he would recognize the exact shape of the hemisphere compressed into the confined space of the retina. For a proportion is kept, so that if straight lines are drawn from separate points on the thing seen to some determined point within the eye, the separate parts are depicted in the eye at almost the same angle as that at which these lines meet. Thus, not neglecting the smallest points, the greater the acuity of vision of a given person, the finer will be the picture formed in his eye. So that I may go on to treat this process of painting (pingendi) and prepare myself gradually for a demonstration of it, I say that this picture (picturd) consists of as many pairs of cones as there are points on the thing seen, with both always having the same base, namely the width of the crystallinus or part of it. Thus while one of the cones has its vertex at the point seen and its base on the crystallinus (varied to some extent by refraction on entering the cornea), the other has the same base on the crystallinus as the first one and the vertex extends to some point of the picture on the surface of the retina; this cone undergoes refraction on passing out of the crystallinus (Figs 2 and 3). All the outer cones meet in the pupil, so that they intersect in that space, and right becomes left... In fact more or less the same thing happens as we showed in chapter ii in a closed chamber (camera clausd). The pupil (pupilld) corresponds to the window and the crystallinus to the screen (tabula) opposite it, provided that the pupil and crystallinus are not so near that intersection is incomplete and everything is confused.... And so if finally straight lines are drawn from points on the visible hemisphere through the centre of the eye" and the vitreous humour, these lines will imprint points forming a picture of the radiating points on the retina opposite. If this did not happen the size of things seen indistinctly to the side would keep changing when the eyes were turned, as happens when spectacles are worn. For these, although fixed immovably in relation to the eye, if they are moved round with it represent things at rest as having some motion, because of the varying amount of the hemisphere appearing at the sides Finally the sensory power (virtus sensorid) or spirit diffused through the nerve is more concentrated and stronger where the retina meets direct cones, because of its source and where it has to go: from that point it is diffused over the sphere of the retina, gets farther from the source, and hence becomes weaker Thus when we see a thing perfectly, w see it within the whole surrounding area of the visible hemisphere. For this reason oblique vision satisfies the soul least and only invites the turning of the eyes in that direction so that they may see directly . . .

The pupil did not affect the focusing of the light, but by dilating or contracting controlled the amount of light entering the eye. Thus the position of the aperture (foramen) is where the rays intersect, and it exists for the sake of the crystallinus...' (v. 2, pp. 151-158). Demonstration of the conclusions stated concerning how vision takes place through the crystallinus. Nearly everything said so far about the crystallinus can be observed in everyday experiments with crystal balls and glass urinary flasks filled with clear water. For if one stands at the glazed window of a room with a globe of this kind of "The sense requires oculi instead of retinae as in the printed texts.

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Fig. 3. From Kepler, Ad Vitellionem paralipomena, v. 3, prop xxiii (Frankfurt, 1604): illustrating his model for demonstrating ocular dioptrics using for simplicity a spherical lens made of a flask of water (a) placed inside the small window fe f) of a camera obscura. Kepler explained how rays from each point (i) of the object were brought together through n m to form in his model a somewhat indistinct image on the screen placed at k 1.

crystal or water, and arranges a sheet of white paper behind the globe at a distance equal to half the diameter of the globe, the glazed window with the fluted wooden or leaden divisions between the lights will be very clearly painted on the paper, but inverted. The same effect can be obtained with other things, if the place is darkened a little. Thus, using a globe of water set up in a chamber opposite a small window, as we described above in chapter ii, proposition vii, everything that can reach the globe through the width of the small window or opening will be depicted very clearly and


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delightfully on the paper opposite. Since the picture is clear at this one distance (namely with the paper a semi-diameter of the globe away from it), it will become indistinct at positions in front of or behind this one. But the direct opposite happens using the eyes...

If the eye were put in the place of the paper, things would be seen erect where they had been inverted on the paper. Since the crystallinus is convex and is denser than the surrounding humours, just as the water in the glass flask is denser than the air, therefore whatever we have demonstrated in this way with the globe of water, and using these media, will have been proved also for the crystallinus, except in so far as it has a different convexity from the globe. So let us proceed with the demonstration of matters belonging to the crystalline or glass globe... (v. 3, p. 162).

'Definition. Whereas up to now the image (imago) has been an entity of reason (ens rationalis), the shapes (figurae) of things really present on the paper, or on any other screen, will be called pictures (picturae)' (p. 174). To demonstrate the focusing of the picture in the eye he used in proposition xxiii the simplified model of a spherical globe of water (a) placed inside the aperture (ef) of a camera obscura (Fig. 3), but he argued that the radiation entering the eye was refracted by the crystallinus not alone but in combination with the cornea and the aqueous humour. His phrase 'within the limit of the intersections of the parallels' meant within the caustic of refraction formed by a spherical lens refracting parallel rays (cf. props, xv-xvi, xx). He explained how rays from each point (i) on the visible object (hi) were brought together through their intersections in the width mn to form in this model a somewhat indistinct reversed picture on the screen placed at kl. When a screen with a small window is placed in front of the globe within the limit of the intersections of the parallels, and the window is smaller than the globe, a picture of the visible hemisphere is projected onto the paper, formed by most of the rays brought together behind the globe at the limit of the last intersection of the rays from a luminous point. The picture is inverted, but purest and most distinct in the middle. So great is the uncertainty in this matter and indeed such its novelty that, unless we take the greatest care, it may easily become confused. Indeed I was held up myself for a long time, until I convinced myself that all the different effects had the same explanation.

'Thus' he added in a note, 'we may seek some light from method', for there was one 'form of refraction through a globe by which vision is deceived by imagining to itself simulacra which are not real (we called them imagines)' (cf. props, vii, xvii-xviii), and another 'by which real pictures of things are formed' (cf. props, xix-xxii and xxiii). He concluded with the corollary: 'Here is seen the function of the pupil (foramen uveae) in the eye; also why the sides of the retina are nearer the crystallinus than the bottom' (prop, xxiii, pp. 177-178). In the next proposition he used his knowledge of conic sections, citing Apollonius, to

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demonstrate the operation of his model lens, concluding with the corollary: Thus is seen the design of nature concerning the posterior surface of the crystalline humour in the eye. She wants all the rays entering the pupil from a visible object to come together at one point on the retina, both so that each point of the picture will be so much the clearer, and so that the other points of the picture will not be accidentally confused with other, unfocused or focused rays. It is also seen that the dilation of the pupil has no other purpose than that which I said above, nor does it confuse the picture but only makes it clearer' (prop, xxiv, pp. 178-179), He went on to face the question of visual perception: The sensation (passio) of vision follows the action of illumination, in measure (modus) and proportion. The retina is illuminated distinctly point by point from individual points of objects, and most strongly so at its individual points. Therefore in the retina, and nowhere else, can distinct and clear vision come about. This is so much the more evident because distortion of the proportions of the picture leads to faults of vision, as has been demonstrated. And I do not know whether Democritus was celebrating with his name idolum rather this picture, by which vision happens, than that mirroring ... But 'the inversion of my picture can be brought against me, which Witelo with great assiduity dodged — And I really tortured myself for a long time in order to show that the cones, having turned right into left in the entrance of the pupil, are made to intersect again behind the crystallinus in the middle of the vitreous humour, so that another inversion is brought about, and what were made left again become right, before they reach the retina'. But he gave up 'this useless trouble'. And so if you are bothered by the inversion of this picture and fear that this would lead to inverted vision, I ask you to consider the following. Just as vision is not an action (actio), simply because illumination is an action, but contrary to an action an affection (passio), so also, in order that the positions may correspond, the capacity for affection (patientia) must be in a direction opposite to the agents. Now the positions are perfectly opposite when all the lines connecting opposite points run through the same centre, which would not have been so if the picture had been erect. And so in the inverted picture, although right and left are interchanged everywhere and with respect to any common line, nonetheless with respect to themselves the right-hand parts of the object are perfectly opposed to the right-hand parts of the picture, and the upper parts of the object to the upper parts of the picture, as a hollow to a hollow . . . Therefore with the picture inverted none of that absurdity is committed from which Witelo so much ran away, and in which lessen followed . . . (v.4, pp. 184-186). In this somewhat contrived way Kepler was saying that so long as the parts of the image retained with respect to themselves the order found in the visible object, the reversal and inversion of their orientation did not matter. The question nevertheless still puzzled contemporaries like Johann Brengger.


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Kepler never found a satisfactory way of answering this question which he rightly placed outside optics in natural philosophy, or more specifically in what became sensory physiology and psychology, but without being able to conceive in any fresh way what happened to the image beyond the retina. He made his next and final contribution to optics in his Dioptrice (1611), written in response to Galileo's Sidereus nuncius as a theoretical, mathematical analysis of how images were formed by lenses singly and in combination. One result was his new astronomical telescope. At the same time he developed his theory of light and vision. Intromission and extromission were for certain purposes interchangeable he wrote, but 'if we are concerned with the nature of luminous things, it is an advantage to express ourselves clearly and to insist on having nothing but the emissions of rays from luminous points' (Praefatio; GW iv, 341). Again he preceded his discussion of vision with an account of the camera obscura: To paint visible things on a white screen with a convex lens (lens)' (problema xliii); The picture with the lens is inverted' through the pairs of cones sharing a common base on the lens (prop, xliv); Tor the sake of instruction we shall call each of such pairs a paint-brush (penicillum)''; these painted the picture on the retina when 'all the paint-brushes of all the points come together on the lens as on the common base of the cones' and pass through inverted to it (definitio xlv; GW\\, 367-368). Kepler seems to have left no doubt of the provenance of his ocular model in the visual arts.12 But when he came to what happened next in vision he could only remain puzzled: Vision is the sensation (sensio) of the affected (affectd) retina filled with visual spirit; or, to see is to sense the affected retina to the extent that it is affected. The retina is painted with the coloured rays of visible things. This picture or representation (pictura seu illustratio) is a kind of affection (passio), but not superficiary,13 as when chalk is rubbed on a wall or light shines on it, but a qualitative affection penetrating the spirits . . . But this picture does not complete the whole of vision unless the image (species) on the retina, capable in this way of affection (patiens), passes through the continuity of the spirits to the brain and is there delivered to the threshold of the faculty of the soul . . . But inside within the brain is something, whatever it may be, which is called the sensus communis, on which is impressed the image of the instrument of the affected vision, that is painted by the light of the visible thing ... But this impression is hidden from our understanding . . . (prop. Ixi, pp. 372-373).

Some years later in 1620 the English diplomat Henry Wotton described to Francis Bacon a moving visit he had made to Kepler at Linz. This 'famous man in the sciences', to whom Wotton proposed to bring one of Bacon's books, was using a camera obscura as an aid to painting a scene just as Daniele Barbaro had advised. Kepler had in his study a landscape which he said that l2 Cf. dedicatory letter, Ges. Werke, iv, 331, and Dissertatio cum Nuncio Sidereo (1610), ibid. 293 on Porta's 'perspicilla'; Straker (1971: above note 1), 467-479, with M. Caspar und F. Hammer, 'Nachbericht' in Kepler, ibid, iv (1941) 415^21. "The term superficiaria in Roman law meant situated on another man's land

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he had done himself, 'non tanquam pictor, sed tanquam mathematicus'. He described how he set up a little black tent with a small hole in it 'to which he applies a long perspective-trunke... through which the visible radiations of all the objects without are intromitted, falling upon a paper, which is accommodated to receive them, and so he traceth them with his pen in their natural appearance, turning his little tent round by degrees till he hath designed the whole aspect of the field' (GW xviii, 42).u Just after this Jean Leurechon published in his popular Recreation mathematique (1624) an account of the camera obscura, for artists as an aid to painting, and 'for philosophers, it is a fine secret to explaine the organ of the sight, for the hollow of the eye is taken as the close chamber, the balle of the aple of the eye, for the hole of the chamber, the crystalline humour for the lens of glasse (respond ... a la lentille de verre), and the bottome of the eye, for the wall, or leafe of paper' (probleme ii).15 Kepler's intellectual behaviour when investigating the operation of the eye conforms exactly to the precept and practice of his investigation of the operation of the celestial system. He would not remain satisfied with anodyne indecision but drove his analysis of each problem to its end in either an acceptable solution or an acknowledged defeat. This he did by attending strictly to quantitative details. He insisted in the Mysterium cosmographicum (1596) that while the Ptolemaic and Copernican hypotheses were observationally equivalent, the reason for this must itself be investigated, and one could not remain undecided for there were important phenomena for which the former could provide no causes whereas in Copernicus their relations were 'so beautifully apparent, there must be some inherent cause of all these things' (c.l; GW i, 15-16). He made the discovery of that cause his research programme. Likewise he refused to retreat from the problem of the camera obscura either with Witelo and Pecham into ignorance of the obscure nature of light or with Mastlin into the unavoidable inaccuracy of all human observation. Again he insisted in his astronomy both that 'an hypothesis is built upon and confirmed by observations' and that he was looking for 'physical causes', so that he could show that 'the celestial machine' was like 'not a divine living thing' but 'a clockwork' in which 'manifold movements' came from a simple 'corporeal force', which could 'be determined by numbers and geometry'.16 This was his approach to the operation of vision. The key to his success in both of his principal inquiries was that in each he set out by heroic analytical labours to identify the essential scientific questions belonging to the subject-matter, to '"Wootton to Bacon 1620, in Kepler, Ges. Werke, xvii, 42; cf. Straker (1976: above note 6). ''French edition published under the pseudonym Henri Van Etten (Pont-a-Mousson, 1624), English transl. as Mathematical Researches (London, 1633) with the 'for the lens of glasse' substituted for a mistranslation of the bracketed French. l6 Kepler to David Fabricius 4.vii.l603, Ges. Werke, xiv, 412, and to Herwart von Hohenburg 10.ii.1605, ibid, xv, 146.


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distinguish these according to their categories, and to answer them in the appropriate order. This involved the extraction and separation of the quite different questions confused in the received presentation of the subject, and the recognition that despite the ancient tradition of both astronomy and optics within the mathematical sciences and natural philosophy, both contained essential questions that remained still open. Thus in astronomy the primary question was to establish the geometry of the planetary orbits, after which came the question of how these were caused. In the optics of the eye and the camera obscura the primary question was to establish the geometry of the rays that formed the image, after which came the question of how this enabled us to see with the eye as we do. In both subject-matters he broke with received commitments: in astronomy with the circularity imposed by ancient metaphysical beliefs; in ocular physiology with the ancient supposition that since the eye was a living sentient organ, any account of its operation must provide an immediate explanation of our visual perception. Kepler rethought the geometry and more fundamentally the essential commitments of both subjects from as near to the beginning as he could get. Kepler's new theory made possible a precise geometrical analysis, led by himself in his Dioptrice, of the functions of the different parts of the eye in focusing and controlling the picture on the retina. By his decision to solve first this geometrical problem of vision, isolating the operation of the eye as an optical device from whatever might follow from it, he opened the way to formulating purely physiologically or physically numerous further problems of accommodation, myopia and hypermetropia, astigmatism, cataract, binocular vision, the design of spectacles to correct visual defects, and the design of optical instruments. It was the mathematicians who pursued these lines of inquiry, and from them that the medical profession came eventually to grasp the new ocular physiology and its medical applications. Influential in this were Vopiscus Fortunatus Plempius with his Ophthalmographia (1632, 1648) who as professor of medicine at Louvain began to promote Descartes's physiological programme; Descartes himself; and later Isaac Newton's physician friend William Briggs with his Ophthalmographia (1676, 1686).17 Kepler's methods were notably exploited by Christopher Scheiner at the Collegio Romano. Scheiner in his Oculus (1619) published for the first time a vertical section of the eye showing the optic nerve entering the eyeball to one side (Fig. 6; i.1.9, p. 17). He made a study of refraction through the different parts of the eye and its fluids which he put into glass ampullae (ii.1.5-12, pp. 61-73; ii.2.1-16, pp. 77122) and described a model of the whole eye which consisted of a camera obscura with a cornea and lens, a spherical glass retina, and aqueous and "Cf. J. Hirschberg, Geschichte der Augenheilkunde, iii.l (Leipzig, 1908); G. Ovio, Storia deU'oculistica (Cuneo, 1950-1952); H. M. Koelbing, 'Ocular physiology in the seventeenth century and its acceptance by the medical profession', Analecta medico-historica 3 (1968), 219-224.

346 Ari

ct

Oculj,

in

ipecielui

ioUritj

patienUndis

con&nfuf'.

N.°

3.

Fig. 4. from Schemer, Rosa ursina, ii. 23 (Bracciani, 1630): illustrating his comparison between the eye and a camera obscura with a lens system, and the effects on each of using further lenses.

vitreous humours enclosed in two glass chambers (iii.1.1-11, pp. 123-161). Beginning with the heading 'Applicatio dictorum ad oculum' (iii.1.12, pp. 161163), he applied his model to show that in the eye a reversed and inverted image or picture of the visible object was thrown onto the retina (iii. 1.12-26, pp. 161-193), and that this and not the lens was the sensitive organ (iii.1.27-34, pp. 193-216). Later in his Rosa ursina (1626-1630) he described experiments carried out in Rome in 1625, in which the formation of the image on the retina was observed directly. This he wrote 'I saw most clearly in the human eye here in Rome in the Jubilee year, where, after the sclerotic had been scraped off the bottom of the eye, the light of a candle sent in through the pupil, the rays having intersected, fell upon the retina; something that has often been proved by experiment in the eyes of many animals' (ii.23, pp. 110-112). He went on to


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exemplify 'the admirable agreement of nature and art' (ii.23-33, pp. 106-136) in a detailed comparison between the eye and a camera obscura containing a system of lenses, studying the effects on each of adding further lenses as with spectacles and in the telescope, helioscope and microscope (cf. Fig. 4).18 Scheiner helped to establish the camera obscura as a model of the eye. Thus Johann Christoph Kohlhans in his Tractatus opticus (1663) cited Schemer's two books for his account: 'Of the application of the camera to the eye' (ii.2.3, p. 257); 'The agreement of art and nature is wonderful: thus as the eye is a natural camera obscura, so is the camera obscura an artificial eye' (p. 501). Likewise Johann Christoph Sturm in his Collegium Experimentale (1676) asserted 'the eye to be nothing other than a little camera obscura' (ii, p.7).19 More original was Christiaan Huygens's demonstration in his Dioptrica (prop, xxxi; 1703), written probably during 1667-1691, of the optical system of a simplified eye reduced to a single spherical refracting surface and of a model constructed as a camera obscura with a cornea, a lens and a diaphragm corresponding to the iris.20 But the new theory was by no means evidently true even to everybody competent to understand it. The Jesuit mathematician Francois Aguilon in his Opticorum libri (i.l, 27, 1613, pp. 2-6, 26-27), a work covering the whole range of optical science from ocular physiology and perception through physics to perspective and geometrical projection, argued that the sensitive organ was the lens capsule (aranea), which he believed to be an extension of the retina and the optic nerve.21 Edme Mariotte provoked a long controversy, centred in the Academic Royale des Sciences and involving especially Jean Pequet and Claude Perrault, with Jean Mery and Philippe de La Hire, by questioning whether his discovery of the blind spot at the entry of the optic nerve still allowed the retina to be regarded as the sensitive organ of vision.22 If Kepler himself provided an exemplary model for the analysis of the composite problem of vision into its parts, so that his solution of ocular optics allowed the further psychological and philosophical questions of vision to be reintroduced on that scientific foundation, he still left these questions largely "Cf. M. von Rohr, 'Ausgewahlte Stiicke aus Christoph Scheiners Augenbuch', Zeitschrift fur opthalmologische Optik 7 (1919), 35^4, 53-64, 76-91, 101-113, 121-133, 'Zur Wurdigung von Scheiners Augenstudien', Archiv fur Augenheilktinde 86 (1920), 247-263; Crombie (1967: above note 1). "Cf. also Johann Andrea Volland, Oculus (Altdorf, 1679) on the eye as a camera obscura; and Johann Gabriel Doppelmayr, Dissertatio visionis sensum (1699), published Gottingen (1748), 169, on Schemer's experiments removing the back of the eye. 20 Huygens, Dioptrica in Opera posthuma (Louvain, 1703), 112-116; cf. J. P. C. Southall, 'The beginnings of optical science1, and 'Early pioneers in physiological optics', Journal of the Optical Society of America 6 (1922), 292-311, 827-842. 21 Cf. M. von Rohr, 'Auswahl aus der Behandlung des Horopters bei Fr. Aguilonius um 1613', Zeitschrift fur opthalmologische Optik 11 (1923), 41-59. 22 Cf. M. D. Grmek, 'Un debat scientifique exemplaire: Mariotte, Pecquet et Perrault a la recherche du siege de la perception visuelle', History and Philosophy of the Life Sciences 7 (1985), 217-255.

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unformulated, let alone answered. There were such psychophysiological problems as the relations between direct and indirect vision and between the visual fields of the two eyes. There was the perennial philosophical problem of the relation between physical stimuli of any kind and unphysical sensations. It was Descartes who explicitly clarified the analysis of vision into its component problems, with full acknowledgement to Kepler.23 In doing so he showed how to use the modelling of nature by art as an instrument not simply of technical, but more generally of logical and conceptual analysis and exploration. Following Kepler's convincing lead, the mathematicians from Scheiner and Descartes down to Huygens and Newton who investigated the technical frontiers of visual physiology came to see in the precise relating of perceiver to perceived a central problem of the scientific movement. Descartes shared with all concerned the ancient ambition to improve nature by art, for he opened La dioptrique (i, 1637; Oeuvres, vi): 'The whole conduct of our life depends on our senses, among which vision being the noblest and most universal, there can be no doubt that inventions serving to increase its power are the most useful there can possibly be'. It would be difficult to find a better example than the telescope, but 'to the shame of our sciences this invention, so useful and so admirable, was found first only by experiment and chance' by someone without mathematical knowledge. He proposed to develop a true science of optics. His more general contribution to scientific thinking was to show that by liberating systematically from each other the different kinds of question and frontier involved in the traditional formulation of vision, each could then be explored without confusion from the others. Descartes, with Marin Mersenne, approached the question left by Kepler of how the retinal image could give us sensations and perceptions by distinguishing, on more "Descartes to Mersenne 31.iii.1638, Oeuvres, eds C. Adam and P. Tannery, 12 vols (Paris, 18971913), ii, 86; cf. for Descartes's optics J. Pucelle, 'La theorie de la perception exterieure chez Descartes', Revue d'histoire des sciences 12 (1935), 297-339, M. H. Pirenne, 'Descartes and the body-mind problem in physiology', The British Journal for the Philosophy of Science 1 (1950), 4359, Vision and the Eye, 2nd edn (London, 1967), G. Leisegang, Descartes Dioptrik (Meisenheim am Glan, 1954), R. L. Gregory, Eye and Brain (London, 1966), The Intelligent Eye (London, 1970), Crombie (1967: above note 1), N. Pastore, Selective History of Theories of Visual Perception: 16501950 (New York, 1971), W. Van Hoorn, As Images Unwind: Ancient and modern theories of visual perception (Amsterdam, 1972), G. Simon, 'On the theory of visual perception of Kepler and Descartes' in A. Beer and P. Beer (eds), Kepler: Four Hundred Years (Vistas in Astronomy 18; Oxford, 1975), G. C. Hatfield and W. Epstein, The sensory core and the medieval foundations of early modern perceptual theory', Isis 70 (1979), 363-383, A. M. Smith, Descartes' Theory of Light and Refraction. (Transactions of the American Philosophical Society, 77) 3; (Philadelphia, Pa., 1987); and for the discovery of the sine law of refraction J. W. Shirley, 'An early experimental demonstration of Snell's law', American Journal of Physics 19 (1951), 507-508, E. Rosen 'Harriot's science: the intellectual background', in J. W. Shirley (ed.), Thomas Harriot: Renaissance Scientist (Oxford, 1974), pp. 2-4, J. A. Lohne, 'Zur Geschichte der Brechungsgesetzes', Sudhoffs Archiv 47 (1963), 152-172, D. J. Struik, 'Snel, Willebrord (1580-1626)', in Dictionary of Scientific Biography 12 (1975), 499-502, P. Costabel, Demarches originates de Descartes savant (Paris, 1982), pp. 63-76. After the announcement of the sine law by Descartes to Marin Mersenne in June 1632, it was the latter who published it for the first time in his Harmonie universelle, Traitez de la nature des sons ...', i, prop, xxix (Paris, 1636), 65-66, cf. Correspondance, ed. C. De Waard, 2nd edn, iii (Paris, 1969), pp. 316, 318-319.


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general philosophical grounds, the case of men from that of animals acting simply as natural automata made by God, responding to physical stimuli from which God had given them no capacity to receive sensations. The image formed in the eyes of animals was purely physiological. In the animal machine he could push Kepler's optical analysis to the limit by asking what purely physiological motions followed from this physiological image and passed through the body. Thus he could complete the technical isolation of the formation of the image from the logical or ontological problem (recognized since Plato) of how any physical image or motion could cause sensation and perception, effects in a different category, in a sentient body. La dioptrique is an essay at once in mathematical and experimental science and in the use of hypothetical models, the most elegant and the most successful of his scientific writings. In it he disposed of certain technical advantages over his predecessors, in particular by his knowledge of the sine law of refraction, discovered independently long before by Thomas Harriot and Willebrord Snel and perhaps also independently by himself. He surpassed them all in presenting a new science of vision within the context of a new science of the senses in general. By this time he had developed several different and not wholly reconcilable hypothetical physical models for light and its effects in vision. He would begin his account of vision with 'the explanation of light and its rays' but, since he was concerned here only with how it entered and was refracted through the eye, 'there is no need for me to undertake to say what truly is its nature'. Our embodied soul could know external objects only through the motions which these produced in our nerves. We were in a position like that when we found our way about in the dark with a stick, or that of men born blind who had found their way about by touch all their lives so that 'one could almost say that they see with the hands'. Now we could suppose that light is nothing but 'a certain movement, or a very rapid and very lively action' that passed through transparent media into our eyes, just as the movement or resistance encountered by the stick passed into the hands of the blind man (i). The operation of the senses in animals was purely physical and physiological. But in man 'we know already well enough that it is the soul that senses, and not the body . . . And we know that it is not properly speaking because it is in the members that serve as organs of the external senses that it senses, but because it is in the brain, where it exercises that faculty called the common sense . . . Finally we know that it is through the nerves that the impressions that objects make on the external members reach the soul in the brain'. But we must take care not to suppose that, in order to sense, the soul needs to look at images which may be sent by the objects as far as the brain, as our philosophers commonly do; or, at least, we must conceive the nature of these images quite otherwise than they do. For . . . they do not consider in them anything else except that they must

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have a resemblance to the objects with they represent... instead of considering that there are several other things besides images that can stimulate our thought; as for example signs and words, which do not resemble in any way the things which they signify. And if, in order to separate ourselves as little as possible from the opinions already received, we prefer to acknowledge that the objects which we sense really send their images as far as the interior of our brain, we must at least note that there are no images which must resemble in everything the objects which they represent.

Just as Kepler had used the experience of painting to form his conception of the retinal picture, so Descartes did likewise to replace this simple conception by the sophisticated conception of symbolic representation of an object by sensory clues: Just as you see that engravings, made only of a bit of ink put here and there on a piece of paper, represent to us forests, towns, men and even battles and storms, even though, from the infinity of diverse qualities which they make us conceive in these objects, there may be none but the shape alone to which they have properly a resemblance; and even then it is a very imperfect resemblance, seeing that they represent on an entirely flat surface bodies elevated and sunk and that even, following the rules of perspective, they often represent circles better by ovals than by other circles, and squares by lozenges than by other squares, and likewise with all the other shapes: so that often, in order to be perfect as images, and to represent an object better, they must not resemble it. Now we must think in just the same way of the images that are formed in our brain, and we must note that it is only a question of knowing how they can furnish the soul with the means of sensing all the diverse qualities of objects to which they correspond, and not at all how in themselves they resemble them. Just as, when the blind man of whom we have spoken above touches some bodies with his stick, it is certain that those bodies do not send anything else to him except that, by making his stick move diversely according to the diverse qualities that are in them, they move by this means the nerves of his hand and then the places in his brain from which these nerves come; this is what gives occasion to his soul to sense as many of the diverse qualities in these bodies as there are varieties in the movements that are caused by them in his brain (La dioptrique iv).

'You see well enough then that, in order to sense, the soul does not need to look at any images similar to the things which it senses; but that does not stop it being true that the objects which we look at imprint quite perfect images in the bottom of our eyes'. This 'some people have already very ingeniously explained by comparison with what happens in a chamber', a camera obscura: 'For they say that this chamber represents the eye' with all its essential parts. One could demonstrate this by 'taking the eye of a man freshly dead, or failing that of an ox or some other large animal', cutting away the back and replacing it with a translucent white body such as a piece of paper or eggshell, and putting the eye into a hole in a dark room with its pupil facing a sunlit scene outside (Fig. 2). Then 'if you look at the white body RST you will see, not perhaps without admiration and pleasure, a painting which will represent very naturally in perspective all the objects that are outside towards VXY, proportioned to their distance, at least if you make sure that this eye keeps its natural


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Fig. 5. From Descartes, La dioptrique, v (Leiden, 1637): illustrating the transmission of light from the object (VXY) to form a visual image in each eye (RST, rst), and then of these images through the optic nerves to form corresponding patterns (789) in the cerebral cavities.

shape'. Now, 'having seen this painting in the eye of a dead animal, and having considered its causes, one cannot doubt that an entirely similar painting is formed in that of a living man, on the internal skin, in the place of which we have substituted the white body RST . . . Moreover, the images of objects are not only formed at the bottom of the eye, but they also pass beyond as far as the brain, as you can easily understand if you suppose that, for example, the rays that come into the eye from the object V (Fig. 5) touch at the point R the extremity of one of the little threads of the optic nerve which takes its origin at the place 7 on the interior surface of the brain 789'. Similarly for the other objects X and Y. 'From which it is clear that once more a painting 789 is formed, sufficiently similar to the objects V, X, Y, on the interior surface of the brain facing its cavities' (La dioptrique v). Thus 'although this painting, in passing thus as far as the inside of our head, always retains something of a resemblance to the objects from which it proceeds', vet it is not 'bv means of

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this resemblance that it makes us sense them . . . but rather . . . it is the movements by which it is composed that, acting immediately upon our soul in as much as it is united to our body, are instituted by nature to make it have such sensations'. And 'because it is the soul that sees, and not the eye, and because it sees immediately only by the intervention of the brain' (vi), any disturbance in the brain or the nerves must produce corresponding disturbances and illusions of vision. Descartes remained committed to his attempt to understand how the soul was related to the body, but by his line of analysis he, like the more sceptical Mersenne, turned the inquiry towards more immediately answerable questions. Stepping aside from the ontological question of how physical motions of any kind could cause sensations, events belonging to different categories, they directed attention to the physical and physiological clues that determined different sensations and perceptions. Together they pioneered, in the two major senses of vision and hearing, the empirical and experimental exploration of the correlation of sensations and perceptions with states both of the external world and of the nervous system, as these were observed and conceived in current physical and physiological theory. In this way they launched in the 17th century a new programme for the science of the special senses and more generally of the mediation of sensory information and its coordination in the behaviour of the animal body and in the perceptions of the human soul. It was in this context that consideration of other senses finally dissolved the visual model of the representative image, for if the pictorial resemblance of the retinal image to its object was merely accidental to the essential information received through the eye, an image of sound could more obviously mean likewise only an ordered correspondence of its motions with its source. Just as Mersenne did in his quantitative analyses of both musical and optical sensations, Descartes in L'Homme and in La dioptrique vi explored quantitatively how different visual clues and their relations gave us perceptions of the position, distance, size and shape of objects. He tried to show not only how our different sensations and perceptions were correlated with different physiological states of our nervous system, but also that if a particular physiological state were postulated, then particular sensations or perceptions must follow.24 The new empirical programme for the science of the senses was endorsed and developed by philosophers, physiologists and mathematicians alike, despite some considerable disagreements on both fundamental and more particular issues. Thomas Hobbes and Pierre Gassendi in somewhat different 24

Cf. Descartes, L'Homme (Oeuvres, xi), pp. 143-144, 174-177 and Meditationes de prima philosophiae, ii, vi (1641), Principia philosophiae, ii. 1-2, iv. 189 (1644), Les passions de I'dme, arts. 23, 36 (1649); A. C. Crombie (1967: above note 1), The study of the senses in Renaissance science', in Actes du X' Congres International d'Histoire des Sciences: 1962 (Paris, 1964), pp. 93-114, 'Mathematics, music and medical science', Actes du XIf Congres ... 1968 (Paris, 1971), pp. 295310, 'Marin Mersenne and the seventeenth-century problem of scientific acceptability', Physis 17 (1975), 186-204, Marin Mersenne (forthcoming).


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Xr

£ Fig. 6. From Schemer, Oculus, /. /. 9 (Oeniponti, 1619): showing the structure of the eye, with the refracting media of the cornea (E) and lens (MN), and the optic nerve (O) entering the eyeball to one side of the point of central vision on the retina (D).

ways met Descartes's stark division of the created world into extended unthinking body and unextended thinking mind by offering other accounts of the mediation and coordination of the information received through the senses. Hobbes elaborated especially in his optical writings a purely corporeal, mechanistic psychology.25 Gassendi set out from the Greek atomists to devise another conjectural model.26 Both agreed with Descartes that objects in the external world were represented symbolically in the motions they produced through the senses; both attempted to formulate clearly the problems of correlating sensory with physiological states; and both made valuable observations on this subject. A basic principle of the whole programme, however often it was breached, was that the speculative models designed to explore these problems should lead to solutions testable by observation. This opened two interesting questions. One concerned the differentation of the senses. Descartes had argued in La dioptrique and L'Homme that while the special sense organs were so designed that they were normally stimulated only by specific kinds of physical motion (as light, sound or pressure), the kinds of sensation that resulted were determined not by those kinds of external motion but by the part of the brain to which they were conducted. Against this Thomas Willis, influenced by Gassendi, maintained that it was the different kinds of external motion or particle that determined the specificity of the senses, and that those 'proportionate to one sensory are incommunicable to most others'.27 It was not technically possible to settle this dispute, but the second question proved easier. Descartes had assumed that the coordination of the information received through the different senses had been included in the inherited design of the animate body, so that a blind man groping about with two sticks would form a conception of the geometry of space exactly as did a sighted man. "Hobbes, 'Opticae', first published by Mersenne, Universae geometricae, mixtae mathematicae synopsis (Paris, 1644), pp. 567-589, and in Objectiones iii to Descartes, Meditationes ii. 26 Gassendi, Syntagma philosophicum, Physica, iii.2.2.1-4, vi.2, viii.2-4 in Opera, ii (Lyon, 1658), 237 sqq., 338 sqq., 402 sqq., and in Obj. v to Descartes, Meditationes ii, vi. "Willis, De anima brutorum, i.10 (Oxford, 1672), p. 159.

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Nicolas Malebranche on the contrary argued that coordination was a question for empirical research,28 and this was to be formulated precisely in the famous problem put by William Molyneux to John Locke: whether a man born blind and given sight would be able at once to recognize with his eyes differences in shape which he had already learned by touch with his hands.29 Molyneux and Locke thought not, and with this George Berkeley agreed for particular reasons. He argued that physiological theory could not determine what the man would see, and that in general we learnt by experience to judge shape, distance, size and so on for each sense separately and also by experience how the diffferent senses were coordinated. Results of operations for congenital cataract were to confirm this argument.30 Berkeley thus pointed to an explicitly autonomous empirical psychology of perception able to explore its subjectmatter independently of current physics and physiology. Alhazen, Kepler and Descartes were three supreme virtuosi who by creating expectations and commanding assent each dominated their subject for long periods. All were masters of the art of theoretical modelling. Kepler displaced the Greek commitment to an immediate explanation of visual appearances accepted by Alhazen, by accepting a different commitment making demonstrated physical principles apply as strictly to the animate organ modelled as to the inanimate model itself. Descartes succeeded in addressing afresh the problems of the cerebral physiology of perception left standing by Kepler, by pushing the mechanistic analysis still farther and asking what purely physical motions followed the focusing of the image on the retina, so reducing the whole physiological process involved in vision and sensation in general to one of purely physical coordination within an animal machine. Thus he could define physiology, and liberate the distinct physiological, psychological and ontological questions encountered in the animate and sentient body all from each other. 'The nature of things, hidden in darkness', Marcello Malpighi wrote a little before Leibniz's remarks on the subject, 'is revealed only by analogizing. This is achieved in such a way that by means of simpler machines, more easily accessible to the senses, we lay bare the more intricate'.31 It would be ill-advised to think that 'the human mind has uncovered all the secrets of nature', but it could 'uncover a good part of its artifices'. An inquirer examining the parts of the body "Malebranche, De la recherche de la verite, i (Paris, 1674), text established by G. Lewis (Paris, 1946). M Locke, Essay Concerning Humane Understanding, ii.9 (London, 1690). "Berkeley, Essay toward a New Theory of Vision (Dublin, 1709) and The Theory of Vision, or Visual Language ... Vindicated (London, 1733); cf. M. von Senden, Space and Sight: The Perception of Space and Shape in the Congenially Blind Before and After Operation (London; 1960). "Malpighi, Anatomes plantarum idea (1675), in Opera omnia (Louvain, 1687), p. 1 cf. Leibniz, Elementa Physica, ii. (c. 1682-4) in Philosophical Papers and Letters, translated and edited by L.E. Loemker, 2nd edn. (Dordrecht, 1969), p. 284.


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and so proceeding a priori has come to form models (moduli, modelli) and figures (typi) of them, with which he places before the eyes the causes of these effects and gives the reason for them a priori and, aided by their rational sequence, understanding the mode of operation of nature, he constructs physiology and pathology and then the art of medicine. A clear experimental proof of this is the optical camera, in which the mathematician produces all the effects that are observed in vision in the state of health and disease in animals, demonstrating a priori the necessity of those effects that follow from variation in the shape of the lens and from the too great distance or nearness of the parts; so that the mode of operation (ratio modo) and the defects of vision are demonstrated from knowledge of the mechanism made by man analogous to the eye.32

"Malpighi, Opera posthuma (Amsterdam, 1698), pp. 276, 289-290: completed 1687; in Latin and Italian.

And so, joining mathematical demonstrations with the uncertainty of chance, and reconciling what seemed contraries, taking its name from both, it justly arrogates to itself this stupendous title: the geometry of chance. (Pascal, Adresse a I'Academie Parisienne)

17 Contingent Expectation and Uncertain Choice: Historical Contexts of Arguments from Probabilities1 i

T

HE STORY of Aristomenes in the Roman novel Metamorphoses or The Golden Ass of Apuleius offers a peculiar view of chance and luck in the ancient world. Apuleius was writing in the second century A.D. His character Aristomenes finds on a journey a long lost friend miserably reduced to half-starvation in filthy rags. His friend responds to his greeting by urging him to keep away and let Fortune do what she would with him as long as she pleases. Instead Aristomenes takes him to the baths, scrubs him down, and gives him fresh clothes, a good meal, and a bed at the inn. But his friend's warning was just. Bad luck is catching, and soon Aristomenes becomes himself likewise afflicted, forced into exile, never again to return to home or happiness. We are here in a different moral cosmology from that of the Good Samaritan. We are in a different world also from that of Aristotle's ethics and of Greek medicine, let alone astronomy, for we are in an arbitrary world of chance whose consequences might be feared but were essentially unpredictable. We are in a region which Aristotle had placed for that reason essentially outside rational knowledge, yet it was part of the total world in which some people saw themselves living. That total world is something we should always i. This paper is based on corresponding chapters of my book Styles of Scientific Thinking in the European Tradition (London: Gerald Duckworth and Co., 1994), which contains full documentation both of original sources and of my considerable debt to other scholars. An earlier version was published as "Pari sur le hazard et choix dans 1'incertain", in Medicine et probabilities: Actes de la journ&e d'etudes du 15 decembie 1979, 6d. A. Fagot (Paris, 1982), pp. 1-42,. Basic information about most of the persons discussed will be found in the Dictionary of Scientific Biography, ed. C. C. Gillispie (New York, 1970-80; 16 vols.)

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keep in mind when we try to penetrate into the more scientific thinking of any period, meaning by that the thinking that solved problems and made discoveries which we can recognize as continuing features of nature and of human knowledge. The subject of contingent expectation and uncertain choice is the world of experience identified by Aristotle as being usually and for the most part consistent and regular, but not invariably or necessarily so. Hence arguments, demonstrations and conclusions about it could be only probable in varying degrees, never certain as in geometry. This was recognized by Plato and Aristotle and other Greek thinkers as the common experience of medical diagnosis and prognosis, of legal judgements, of weather prediction, of expectations from planting to harvest, of navigation, of outcomes of battles, and so on. To deal with this kind of experience a characteristic style of thinking came to be developed with a common form of argument for the variety of contingent situations and subject-matters in which it was met, a form distinct from that developed for such a subject as geometry and its applications for example in astronomy and optics. We can define what I call a scientific style by three characteristics: (i) its form of argument: its methods of discovery and demonstration,- (2) its conception of nature: beliefs about what there is in existence to be discovered; and (3) habits of mind: especially the expectations of and responses to innovation and change, the dispositions of a society and of individuals within it. The sources of an intellectual style of this kind must obviously be looked for not simply in natural science, but much more generally in the intellectual and moral commitments and history of a culture or society, commitments antecedent to any specific science. Commitments to a style may have a long gestation, and likewise a tenacious life. But a style may also be imposed by the subject-matter. The common problem in all contingent and uncertain subjects and situations was that those concerned, facing a succession of uncertain outcomes, might be obliged to make a decision, but on insufficient grounds: the march of events might force a decision, but the grounds available could make it only to some degree likely to be proved correct. The problem had a similar form equally for theoretical and for practical choice whenever the subject-matter

Contingent Expectation and Uncertain Choice

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could not be reduced to a simple logical or mathematical or dogmatic certainty. An experimenter exploring a complex subjectmatter could assent to a scientific hypothesis only contingently on the evidence obtained so far, just as a physician or judge or a navigator or a military commander or a merchant or a gamester must decide at the moment of action only on a contingent expectation from the choice which he judged the most likely to gain his ends. The history of Western thinking in probabilities on this kind of subject-matter has had then two main concerns, ( i ) It has been a search for dependable criteria of judgement that would reduce uncertain expectation to as exact a probability as the subject-matter would allow. We can ask historically then: On what grounds did people give, or not give, assent to evidence, explanations, theories, courses of action? (2) At the same time Western thinking has been an exploration of nature and its expectations, of the relation of expectations available to us to expectations embodied in nature, hence of possible conceptions of nature and its knowability. On what grounds then did people of a particular period expect that future events would happen, and that past events had happened, in any context? It is illuminating, indeed essential, to look at these issues comparatively in different historical contexts. Thereby we can see how some questions came to be asked (while others remained unasked) which came to establish the intellectual character of an age. I can best illustrate the comparative history of thinking in probabilities by pointing briefly to its central focus in examples from suitably different historical circumstances: ancient, medieval, and early modern, with a final glance at the theory of natural selection as a general theory of decision applied to human and natural choice alike. In each of these periods problems appeared under its own distinctive vision and in each the attempts to reduce uncertainty to probability were made within the limitations imposed both by that vision and by the subject-matter: persuasive when they could not be demonstrative, qualitative in antiquity, and quantified in early modern Europe by bringing the contingent and variable within the realm of mathematical order. Each through the survival of texts made its distinctive contribution to its successors.

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Science, Art and Nature in Medieval and Modern Thought II

The Greeks developed thinking in probability with great originality in medicine and law. Focusing on the different types of argument appropriate to different subject-matters, they provided a classification in which to place probable judgement of the uncertain situations both of nature and of practical human life. Let me illustrate this with a brief collage of quotations. First the Hippocratic Prognostic: "I hold that it is an excellent thing for a physician to practice forecasting. For if he discovers and declares unaided at the side of his patients the present, the past and the future, and fills in the gaps in the account given by the sick, he will be believed to understand the cases, so that men will confidently entrust themselves to him for treatment. Furthermore he will carry out the treatment best if he knows beforehand from the present symptoms what will take place later." But some diseases did kill: "it is necessary therefore to learn the nature of such diseases, how much they exceed the strength of men's bodies, and to learn how to forecast them. . . . For the longer you plan to meet each emergency, the greater your power to save those who have a chance of recovery . . . " (c. i). Hippocratic diagnosis and prognosis was an inference, from collections of symptoms usually present, to their probable antecedents and consequences. Thus the famous signs of death (c. 2). The possibility of predicting the course of a disease was based on a classification both of patients and of diseases, so that patients of a type would all react alike to the same disease, and diseases of a type would always run the same course, within the same general environmental conditions. But Hippocratic authors also noted considerable differences in the predictability of different ailments. Some authors were more impressed by the essential natural uniformity of human beings, indeed of men with animals, of kinds of disease, and of comparable environmental conditions. Others were more impressed by the irreducible uncertainty introduced by a variability so great, both in the human body and in external conditions, as to make each individual case virtually unique. Individual bodies differed so much in general, as well as according to sex and age and type, that except in specific ailments such as lesions prognosis seemed virtually impossible. In all cases it was essential


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to follow adequate procedures for evaluating information got from patients, and for detecting what they might consciously or unconsciously misrepresent or conceal. Most authors held that despite the uncertainty of the evidence medical prognosis was both possible and useful, just as it was possible within limits to forecast weather from likewise variable signs. For, taking due account of environmental conditions, "in every year and in every land" good and bad signs remained uniform in their indications, and proved "to have the same significance in Libya, in Delos, and in Scythia". Hence "it is not strange that one should be right in the vast majority of instances, if one learns them well and knows how to estimate and appreciate them properly". One need not trouble oneself about "the name of any disease. For it is by the same symptoms in all cases that you will know the diseases that come to a crisis at the times stated" (c. 25). We have here the recognition of a science of usual though not invariable, and not necessary, connections or regularities of events when observed in adequate numbers. It offered objective descriptive knowledge that could be established inductively, without having to know their causes, by observing and recording these stable contingent regularities. The empirical probability so established, that sequences of events already observed would likewise be observed in the future, yielded then a rational expectation. Thus on medical correlations the Hippocratic Aphorisms: "Those who are constitutionally very fat are more apt to die quickly than those who are thin" (ii.44); "Those with an impediment in their speech are very likely to be attacked by protracted diarrhoea" (vi. 32). Similarly the Aristotelian Problemata: "Why is it that the plague alone among diseases infects particularly persons who come into contact with those under treatment for it?" (i.y); "Why are people more liable to fall ill in the summer, while those who are ill are more liable to die in the winter?" (i.2,$); "Why are boys and women less liable to white leprosy than men, and middle aged women more than young?" (x.4J; "Why is it that fair men and white horses usually have grey eyes?" (x.n). Greek thinkers recognized probability essentially within the context of a search for certainty and a qualitative analysis of degrees of certainty in different subject-matters. Thus the Greek physicians might match the astronomers in aspiring to infer both

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antecedents and consequences from any present state of affairs, making past and future in effect a property of that present, but with an essential difference. The past and future expected from the mathematical postulates of the astronomers were necessary could not be otherwise, and presented no choices for decision on their outcome. But the contingent expectations from the stable but not invariable regularities found in the complex subject-matter of medicine presented a continual series of uncertain choices both about the nature of the medical situation and about appropriate action. The physicians then, ancient and modern, facing successive stages of a process of uncertain outcome, might be obliged to make a decision only to some degree likely to be proved correct. It was the same with law, but with a practical difference. Thus Plato: "in the law courts nobody cares for truth (dAnOeia, veritas) . . . but only about persuasion (neiOco, persuasio) and that is concerned with what is likely (eiKoq, verisimile)"; for "the people get their notion of the probable [piobabile] from its likeness (ouoioinc;, similitude) to truth, and . . . these likenesses can always be best discovered by someone who knows the truth" (Phaedrus 272.DE, 273D). Likeliness or probability were then to be measured against demonstration and necessity (dn68eiîq, dvdyKq), and the force of argument had to be appropriate: "If a mathematician . . . elected to argue from probability in geometry, he would not be worth anything". Mathematical questions could not be settled by "appeals to plausibility (mOavoAoyia, piobabile}" (Theaetetus i62E), but by contrast in the sciences of nature we had to be content with something less than mathematical demonstration: "We must be content then if we can furnish accounts no less probable (probabiles) than any other, remembering that I who speak and you my judges are only human, so that it is enough that in these matters we should accept the likely story (eiKoxa uu6ov, probabilia dicentur) and look for nothing further" (Timaeus ipCD). Here Plato seems to be assimilating natural science to legal persuasion, a point of great historical interest when we remember the essential part played by persuasion in the acceptance or rejection by any community of scientific as of other novelties. The whole enterprise of persuasion in ancient legal and moral and political life, the subject of Aristotle's Rhetoric and Topics and Sophistic! Elenchi, which should always be set beside the demonstrative logic of the


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Analytics and the scientific and ethical works in any account of his scientific method, was a rich and natural field for the analysis of probable arguments, of the credibility of evidence, and of the matching possibility of error. Aristotle's development of this classification was to resonate through history, just as the Latin versions of his words were to provide much of our philosophical terminology. Aristotle offered an exemplary analysis of scientific arguments appropriate to "things that come about by necessity and always, or for the most part", from which he excluded "a third class of events" attributed to chance. For "chance is supposed to belong to the class of the indeterminate and to be inscrutable to man" (Physics ii.s, ip6b 12-14), but really "chance obscure to human calculation is a cause by accident and in the unqualified sense a cause of nothing" (Metaphysics xi.8,10653 33-5). Hence: "There is no understandin through demonstration of what holds by chance. For what holds by chance is neither necessary, nor for the most part, but what comes about apart from these,- and demonstration is of one or other of these. For every deduction is either through necessary or through for the most part propositions; and if the propositions are necessary, the conclusion is necessary too; and if for the most part, the conclusion too is such" (Posterior Analytics i.3O, 8yb 18-25, trans. Barnes, 1975). He identified probability then as a descriptive regularity observable in his second class of events: those which "nature produces for the most part" lying between what nature produced "without exception" and the accidents of "fortune" which were "beyond expectation", as in the good luck of receiving some benefit or of "escaping some evil that might reasonably be expected" (Magna moralia ii.8, iO26b 38-73 4,30-33). Within reasonable expectation: "Most of the things about which we make decisions, and into which therefore we inquire, present us with alternative possibilities. . . . A probability (eiKoale: Probabilis", Revue des sciences philosophiques et theologiques, 22 (1933), 260-90, and "Probabilisme" in Dictionnaire de theologie catholique (Paris, 1936), vol. XIII.i, 417619,- V. Cioffari, Fortune and Fate from Democritus to St. Thomas Aquinas (New York, 1935), The Conception of Fortune and Fate in the Works of Dante (London, 1941), Fortune in Dante's i4th Century Commentators (Cambridge, MA, 1944); W. S. Howell, The Rhetoric of Alcuin and Charlemagne (Princeton, 1941); R. McKeon, "Rhetoric in the middle ages", Speculum, 17 (1942), 1-32; M. J. Junkersfeld, The Aristotelian-Thomistic Concept of Chance (Notre Dame, IN, 1945); R. I. Defferari, M. I. Barry and L. McGuiness, A Lexicon of St. Thomas Aquinas (Washington, DC, 1948): "Certitude", "Probabilis", "Probabilitas", etc.,- A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science 1100-1700 (Oxford, 1953; revised reprint 1971), Augustine to Galileo: Medieval and Early Modern Science, revised 2nd ed., reprinted with further revisions (London & Cambridge, MA, 1979,- 2 vols.), and Styles of Scientific Thinking, ,chs. 7-8 (note i above); .E. R. Curtius, European Literature in the Latin Middle Ages, trans. W. Tras (New York, 1953); G. Preti, "Dialettica terministica e probabilisimo nel pensiero medievale", in Le crisi dell'uso dogmatico della ragione, a cura di A. Banfi (Roma & Milano, 1953), pp. 61-97; M. D. Chenu, La theologie comme science au xiiie siecle, 36 6d. (Paris, 1957), La theologie au xii siecle, 2e 6d. (Paris, 1976); J. R. Weinberg, Abstraction, Relation and Induction: Three essays in the history of thought (Madison, Wl, 1968); E. F. Byrne, Probability and Opinion: A study in the medieval presuppositions of post-medieval theories of probability (The Hague, 1968); J. E. Murdoch, "Mathesis in philosophiam scholasticam introducta: the rise and development of application of mathematics in fourteenth-century philosophy and theology", in Arts liberaux et philosophie au moyen age (Montreal & Paris, 1969), pp. 215-54, "The development of a critical temper: new approaches and modes of analysis in fourteenth-century philosophy, science, and theology", in Medieval and Renaissance Studies, ed. S. Wenzel (Chapel Hill, NC, 1976); P. Michaud-Quantin avec . .. M. Lemoine, Etudes sur le vocabulaire philosophique

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occasions were distinguished on which it was appropriate to use demonstration or persuasion, and to appeal to the senses, reason, faith, authority, tradition, usage and so on. The central area of probability was that where an exiguous demand for action required decision that could not in the circumstances be certain. A practical problem in dealing for example with heresy and unbelief was to diagnose states of mind and to establish rules for a doubting conscience. A humane rule was to act on the most probable judgement with an inherent likelihood.4 The problem was parallel in the diagnosis of diseases, of witchcraft and magic, of the perpetrators of crimes, and so forth. The identification of a state of things depended in all such cases on antecedent assumptions about what existed and what was possible. Accepting such assumptions, theologians, lawyers, physicians and philosophers responding to a variety of practical demands developed a certain systematic precision in collecting and weighing evidence: for example in dealing with heresy and spiritual error (a basic practical question in view of their accepted consequences both for the individual person and for the order of society),5 and in dealing with leprosy, smallpox, du moyen age (Roma, 1970); A. Maieru, Terminologia logica della tarda scolastica (Roma; 1972); J.}. Murphy, Rhetoric in the Middle Ages (Berkeley & Los Angeles, 1974); The Cultural Context of Medieval Learning, ed. J. E. Murdoch and E. D. Sylla (Boston Studies in the Philosophy of Science, vol. XXVI; Dordrecht & Boston, MA, 1975); Lexikon des Mittelalters, hrg. von L. Lutz et al. (Aachen, 1977-85; 3 vols.); G. R. Evans, Old Arts and New Theology: The beginnings of theology as an academic discipline (Oxford, 1980); F. Oakley, Omnipotence, Covenant and Order: An excursion into the history of ideas from Abelard to Leibniz (Ithaca, NY, 1984). 4. Cf. Deman, "Probabilisme" (1936; note 3 above), pp. 418 ff, 431 ff, 442 ff. 5. Cf. Deman, ibid.; H. C. Lea, The Inquisition in the Middle Ages: Its organization and operation (London, 1963); J. B. Russell, Dissent and Reform in the Early Middle Ages (Berkeley & Los Angeles, 1965), Religious Dissent in the Middle Ages (New York, 1971), Witchcraft in the Middle Ages (Ithaca, NY, 1972), A History of Witchcraft: Sorcerers, heretics and pagans (London, , 1980), and J. B. Russell and C. T. Berkhout, Medieval Heresies: A bibliography (Toronto, 1981); G. Leff, Heresy in the Middle Ages (Manchester, 1967,- 2 vols.); Heresies et societes dans 1'Europe pre-industrielle (ne-i8e siecles) (Paris, 1968); H. C. E. Midelfort, Witch Hunting in Southwestern Germany, 1562-1684: The social and intellectual foundations (Stanford, CA, 1972); E. LeRoy Ladurie, Montaillou, village occitan de 1294 a 1324 (Paris, 1975); R. Kieckhefer, European Witch Trials: Their foundations in popular and learned culture (Berkeley & Los Angeles, 1976); M. Lambert, Medieval Heresy (London, 1977); G. Schormann, Hexenprozesse in Nordwestdeutschland (Hildesheim, 1977); E. M. Peters, The Magician, the Witch and the Law (Hassocks, Sussex, 1978); Heresy and Authority in Medieval Europe: Documents in transla-


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plague, and venereal and other diseases,6 and with usury.7 Rules were developed likewise for the exegesis of the Scriptural revelation.8 In all these diverse contexts the search for grounds for tion, ed. E. M. Peters (Philadelphia, 1980); G. Henningsen, The Witches'Advocates: Basque witchcraft and the Spanish Inquisition, 1609-1614 (SanRemo, NV, 1980). 6. Cf. the sections by M. McVaugh on methods of diagnosis etc. in A Source Book in Medieval Science, ed. E. Grant (Cambridge, MA, 1974), pp. 745-808, and also the preceding sections on medical theory, pp. 700 ff ; K. Sudhoff, "Pestschriften aus den ersten 150 Jahren nach der Epidemic des Schwarzen Todes 1348", Archivfur Geschichte der Medizin, 2-17 (1909-1925), Aus der Friihgeschichte der Syphilis (Studien zur Geschichte der Medizin, vol. IX; Leipzig, 1912); M. Neuburger, Geschichte der Medizin (Stuttgart, 1911), vol. II; A. C. Klebs et E. Droz, Remedes contre la peste: Facsimiles, notes et liste bibliographique des incunables sur la peste (Paris, 1925); A. M. Campbell, The Black Death and Men of Learning (New York, 1931); D. P. Lockwood, Ugo Benzi: Medieval philosopher and physician, 1376-1439 (Chicago, 1951); P. Richards, The Medieval Leper and his Northern Heirs (Cambridge, 1977); G. Baader und G. Keil, "Mittelalterliche Diagnostik: ein Bericht", in Medizinische Diagnostik in Geschichte und Gegenwart, hrg, C. Habrich, E Marguthund J. H. Wolf (Munchen, 1978), pp. 135 ff.; J. AgrimieC. Crisciani, Malato, medico e medicina nel medioevo (Torino, 1980); L. E. Demaitre, Doctor Bernard of Gordon: Professor and practitioner (Toronto, 1980); S. Jarcho, The Concept of Heart Failure from Avicenna to Albertini (Cambridge, MA, 1980); N. G. Siraisi, Taddeo Alderotti and his Pupils: Two generations of Italian medical learning (Princeton, 1981), and the next article in this volume; D. Palazzotto, The Black Death and Medicine: A report and analysis of the tractates written between 1348 and 13 so (Ann Arbor, MI, 1980); D. Williman, The Black Death: The impact of the fourteenth-century plague (Binghamton, NY, 1982). 7. Cf.}. T. Noonan, The Scholastic Analysis of Usury (Cambridge, MA, 1957),- J. W. Baldwin, The Medieval Theories of the fust Price: Romanists, canonists, and theologians in the twelfth and thirteenth centuries (Transactions of the American Philosophical Society, n.s. 49, part 4; Philadelphia, 1959); J. Gilchrist, The Church and Economic Activity in the Middle Ages (London, 1969); B. Nelson, The Idea of Usury, 2nd ed. (Chicago, 1969); R. de Roover, La pensee economique des scolastiques: doctrines et methodes (Montreal, 1971), "The scholastic attitude toward trade and entrepreneurship", in Business, Banking, and Economic Thought in Late Medieval and Early Modern Europe: Selected studies, ed. J. Kirschner (Chicago, J 974)/ PP- 336-45; J. Le Goff, Marchands et banquiers du moyen age, 2e e"d. (Paris, 1972); L. K. Little, Religious Poverty and the Profit Economy in Medieval Europe (London, 1978). 8. Cf. H. Caplan, "The four senses of scriptural interpretation and the medieval theory of preaching", Speculum, 4, part 2 (1929), 282-90; B. Spicq, Esquisse d'une histoire de 1'exegese latine au moyen age (Paris, 1944); B. Smalley, The Study of the Bible in the Middle Ages, 2nd ed. (Oxford, 1952); R. M. Grant, A Short History of the Interpretation of the Bible, revised ed. (London, 1965); R. E. McNally, "Exegesis, medieval", in New Catholic Encyclopedia (New York, 1967), vol. V, 707-12; G. W. H. Lampe, J. Leclercq, B. Smalley, E. I. J. Rosenthal, "The exposition and exegesis of Scripture", in Cambridge History of the Bible, ed. P. R. Ackroyd et al. (Cambridge, 1969), vol. II, 155-279,- The Bible and Western Culture, ed. W. Lourdaux and D. Verbalist (Louvain, 1970).

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reasoned assent or dissent, and for distinguishing the kinds of argument and authority with power to convince, were part of the style of the whole intellectual culture. Expectation: Ancient insights into probability were qualitative. For whatever reason, the Greeks never developed either the conceptions or the techniques for a mathematical mastery of chance and uncertainty in any subject-matter. The treatment of assent in the main contexts discussed by medieval philosophers was again essentially qualitative. The need to stabilize uncertain choice by quantitative measures of probable expectations was something grasped in the different practical circumstances of the commercial expansion of late medieval Europe. Moral philosophers exploring the moral context of the new enterprises met the objection that profit gained by interest on the investment of money as a loan was usury, by arguing that profit was justified by risk. Gilles of Lessines for example described, at the end of the thirteenth century, a mentality of expectation in which a business partner or a lender or an insurer could calculate a just rate of profit or interest in proportion to the risk on capital outlay assumed (De usuris... c.6, J 593/ fols. i4iv-2r). Such calculations became established practice notably in fourteenth-century Italian marine insurance, with graded premiums, estimated from accumulated experience, for distance and season and dangers from storms and pirates.9 The 9. Cf. F. E. de Roover, "Early examples of marine insurance", Journal of Economic History, 5 (1945), 175-200, R. S. Lopez and I. W. Raymond, Medieval Trade in the Mediterranean World (New York, 1955); G. Stefani, Insurance in Venice from the Origins to the End of the Serenissima (Trieste, 1958; 2 vols.); with E Hendricks, "Contributions to the history of insurance, etc.", Assurance Magazine, 2 (1852), 121-50, 222-58, 393-5, 3 (1853), 93-120, cf. 10(1863), 205-19; E. Bensa, IIcontratto di assicurazione nel medio evo (Genova, 1884); A. Chaufton, Les assurances (Paris, 1884), vol. I,- W. Gow, "Marine insurance" in Encyclopedia Britannica, nth ed. (Cambridge, 1910-1911); C. T. Lewis and T. A. Ingram, "Insurance" in ibid.,- C. E Trenerry, The Origin and Early History of Insurance (London, 1926); G. Valeri, "I primordi dell' assicurazione attraverso il documento del 1329", Rivista del diritto commerciale, 26, part i (1928), 600-41; A. Checchini, "I precedenti e lo sviluppo storico del contratto d' assicurazione", Atti dell'Istituto Nazionale delle Assicurazione (Roma, 1931), vol. Ill; T. O'Donnell, History of Life Insurance in its Formative Years (Chicago, 1936); E. Besta, Le obbligazioni nella storia del duetto italiano (Padova, 1937); I- Heers, "Le prix de 1'assurance a la fin du moyen age", Revue d'histoire economique et sociale, 37 (1959), 7-19; A. Tenenti, Naufrages, corsaires et assurance maritime d Venise 1592-1609 (Paris, 1959); H. Braun, Geschichte der Lebensversicherung und der Lebensverischerungstechnik, 2te Aufl. (Berlin, 1963); L. A. Boiteux, La fortune de mei; le besoin de securite et les debuts


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rational pursuit of profit from any of its sources required thus both personal enterprise and the habit of quantitative order, assisted technically by the new commercial arithmetic and the new financial methods of double-entry bookkeeping and the bill of exchange.10 Bernardino of Siena in the fifteenth century advised merchants, in a sermon, that if they were not assiduous in "subtly estimating risks and opportunities, they are certainly not fit for this business" (Sermo 33: "De mercationibus et artificibus . ..", art.i,c.i,i427: Opera omnia, IV, 1956, p. 142). Merchants he insisted should be honest, should sell unadulterated goods with correct weights and measures; and partners should settle up honestly at least once a year, and then go to confession (p. 143, cf. i6i-2).u A merchant wrote his younger contemporary Benedetto Cotrugli must above all estimate the future expectations guiding his actions from a systematic record of past gains or losses, for: "Mercantile records are means to remember all that a man does, from whom he must take and to whom he must give, the costs of wares, the profits and the losses, and every other transaction on which a merchant is dependent. It should be noted that knowing how to keep good and orderly records teaches one how to draw up contracts, how to do business, and how to make a profit. A merchant should not rely on memory, for that has led to many misde 1'assurance maritime (Paris, 1968); F. Melis, Origini e sviluppi delle assicurazioni in Italia (secoli XIV-XVI) (Roma, 1975), vol. i. 10. Cf. A. P. Usher, "The origins of banking: the primitive bank deposit (12001600)", Economic History Review, 4 (1932-34), 399-428, The Early History of Deposit Banking in Mediterranean Europe (Cambridge, MA, 1943); R. de Roover, "Aux origines d'une technique intellectuelle: la formation et 1'expansion de la compatabilite' £ partie double", Annales d'histoire economique et sociale, 9 (1937), 171-93, 270-98, Involution de la lettre de change (Paris, 1953), "The development of accounting prior to Luca Pacioli according to the account books of medieval merchants", in Business, Banking ... (note 7 above), pp. 119-79; E. Peragallo, The Origin and Evolution of Double-Entry Bookkeeping: A study of Italian practice from the fourteenth century (New York, 1938); F. Melis, Storia della ragioneria (Bologna, 1950); R. S. Lopez, The Three Ages of the Italian Renaissance (Charlottesville, VA, 1970), The Commercial Revolution of the Middle Ages, 950-1350 (Englewood Cliffs, NJ, 1971); Lopez and Raymond, Medieval Trade... (note 9 above), PP- 359ffn. Cf. R. de Roover, San Bernardino of Siena and Sant'Antonio of Florence: Two great economic thinkers of the middle ages (Boston, MA, 1967), especially pp. 13-14, "The scholastic attitude . .." (note 7 above), pp. 343-4; cf. M. G. Kendall, "The beginnings of a probability calculus", Biometrika, 43 (1956), 1-14 for his sermon on games of chance.

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takes" (Delia meicatum et del mercante perfetto, i. 13, 1573, fols. 37r-38r: written I458).12 All this matched the rational habit of foresighted design in the mathematical arts and sciences, in perspective painting and in engineering and architecture, and the systematic recording of techniques and results in an experimental investigation. It is surely no accident that it was in this same practical ambience that appeared the numerical estimation both of future expectations a posteriori, from the numerical regularities of past experience, and of expectations a priori, arising from the theoretical concept of an exhaustive division into equally possible outcomes in games of chance.13 Luca Pacioli14 in the fifteenth century and 12. Trans, modified from Lopez and Raymond, Medieval Trade (note 9 above), pp. 360, 375-7, cf. 416-8. 13. Cf. for the history of probability theory and statistics G. Libri, Histoire des sciences mathematiques en Italie, depuis la renaissance des lettres jusqu' a la fin du dix-septieme siecle (Paris, 1838-41; 4 vols.), II, 188 ff.; I. Todhunter, History of the Mathematical Theory of Probability (Cambridge & London, 1865); V. John, Geschichte der Statistik (Stuttgart, 1884); F. E. A. Meitzen, Theorie und Technik dei Statistik (Berlin, 1886); M. Cantor, Vorlesungen iiber Geschichte der Mathematik, 2te Aufl. (Leipzig, 1894-1901,- 3 vols.), I, 522, II 327 ff. ; The History of Statistics: Their development and progress in many countries, ed. J. Koren (New York, 1918); H. M. Walker, Studies in the History of Statistical Method (Baltimore, MD, 1929); H. Westergaard, Contributions to the History of Statistics (London, 1932); A. Wolf, A History of Science, Technology and Philosophy in the Sixteenth, Seventeenth and Eighteenth Centuries, new ed. by D. McKie (London, 1951-52; 2 vols.); M. Kline, Mathematics in Western Culture (New York, 1953); F. N. David, "Dicing and gaming (a note on the history of probability)", Biometrika, 42 (1955), 1-15, Games, Gods and Gambling: The origins and history of probability and statistical ideas from the earliest times to the Newtonian era (London, 1962); M. G. Kendall, "The beginnings of a probability calculus" (note 11 above), "Where did the history of statistics begin?", Biometrika, 47 (1960), 447-9; O. Ore, "Pascal and the invention of probability theory", American Mathematical Monthly, 67 (1960), 409-19; E. Coumet, "Leprobleme des parisavant Pascal", Archives Internationales d'histoire des sciences, 18 (1965), 245-72, "La the"orie du hasard-est elle nee par hasard?", Annales ESC, 25 (1970), 574-98; Studies in the History of Statistics and Probability, ed. E. S. Pearson, M. G. Kendall and R. L. Plackett (London & High Wycombe, 1970-77; 2 vols.); L. E. Maistrov, Probability Theory: A historical sketch, trans, from the Russian and ed. S. Kotz (New York, 1976); O. B. Sheynin, "On the prehistory of the theory of probability", Archive for History of Exact Sciences 12 (1974), 97-141, "Early history of the theory of probability", ibid., 17 (1977), 201-59, "On the history of the statistical method in biology", ibid., 22 (1980) 323-71; I. Schneider, Die Entwicklung des Wahrscheinlichkeitsbegriffs in der Mathematik von Pascal bis Laplace (Habilitationsschrift Universitat Munchen, 1972), "Die mathematisierung der Vorhersage kiinftiger Ereignisse in der Wahrscheinlichkeitstheorie von 17. bis zum 19. Jahrhundert", Berichte zur Wissenschaftsgeschichte, 2 (1979), 101-12, "Mathematisierung des Wahrscheinlichen


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Girolamo Cardano in the sixteenth dealt with both questions within the context of writings on commercial arithmetic. At any moment of time, they argued, a partner who had invested a certain amount in a company was in the same position as a player who had gained a certain number of points in a game of chance. What was the value of their investment or stake at that moment? Cardano offered a solution making the fundamental principle that of fair expectations: that there should be for all partners or players equal possible outcomes under equal conditions: "The most fundamental principle of all in a game of chance is the equality whether of players, of bystanders, of money, of situation, of the dice box, of the dice itself. To the extent that you depart from that equality, if you do so in your own favour you are unjust, if in that of your opponent you are a fool" (Liber de ludo aleae, c.6, Opera, I, und Anwendung auf Massenphanomene im 17. und 18. Jahrhundert", in Statistik und Staatsbeschieibung in derNeuzeit vornehmlich i6.-i8. Jahrhundert, hrg. von M. Rassen und J. Stagl (Paderbom, 1980), pp. 5 3-73,1. Schneider und K. Reich, "Die wirtschaftliche Entwicklung des Mittelalters im Spiegel der arithemetischen Aufgabensammlungen und ihrer Nachfolger, der Rechenbucher des 15. und 16. Jahrhunderts", Aus dew. Antiquariat, no. 52 (1978), 217-29; I. Hacking, The Emergence of Probability: A philosophical study of early ideas about probability, induction and statistical inference, covering the period 1650 to 1795 (Cambridge, I 975); I- van Brakel, "Some remarks on the prehistory of the concept of statistical probability", Archive for History of Exact Sciences, 16 (1976), 119-36; M. Ferriani, "Stori e 'prehistoria' del concetto di probabilita nell' eta moderna", Rivista di filosofta, 10 (1978), 129-53; A. Fagot, L'explication causale de la mort (Universite de Paris, these de doctoral non publiee, 1978), "Probabilities and causes: on life tables, causes of death, and etiological diagnoses", in Probabilistic Thinking, Thermodynamics, and the Interaction of the History and Philosophy of Science, ed. J. Himtikka, D. Gruender and E. Agazzi (Dordrecht & Boston, MA, 1981), pp. 41-104; K. Pearson, The History of Statistics in the ijth and i8th Centuries against the changing background of intellectual, scientific and religious thought: Lectures... 1921-33, ed. E. S. Pearson (London & High Wycombe, 1978); L. J. Cohen, "Some historical reflections on the Baconian conception of probability", Journal of the History of Ideas, 41 (1980), 219-32; D. L. Patey, Probability and Form: Philosophic theory and literary practice in the Augustan age (Cambridge, 1984); A. C. Crombie, Styles of Scientific Thinking, chs 17-20 (note 1 above). 14. Cf. Lucas de Burgo (Luca Pacioli), Summa de arithemetica, geometria et proportionalita, ix, tract. 1-2 (rules for companies), 4-6 (exchange and money), 7 (division of gains and losses), 10 (games of chance), 11 (double-entry bookkeeping) (Venice, 1494); L. Olschki, Geschichte der neusprachlichen wissenschaftlichen Literatur (Heidelberg, 1919), vol. 1,151 ff.; R. E. Taylor, No Royal Road: Luca Pacioli and his times (Chapel Hill, NC, 1942); David, "Dicing . . .", Games . . . (note 13 above), pp. 36 ff.; Coumet, "Le probleme de paris ..." (note 13 above), pp. 248 ff. ; Schneider und Reich, "Die wirtschaftliche Entwicklung ..." (note 13 above).

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1663, p. 263).15 The same applied by general agreement among all commercial and moral writers to business. Then the instantaneous saleable value of a stake whether in a business or in a game was the amount that should be risked on its future expectations of gain or loss. Thus as the Jesuit Leonard Leys (Lessius) was to put it: "The uncertain risk on capital outlay must be reduced to a price that is certain" ("Periculum sortis incertum debet reduci ad certum pretium", in De iustitia et iure... ii.iii, "De contractibus", c. 25, dubitatio 2, and c. 16, i6o6).16 Interesting attempts were made to establish the equivalence in value of an investment of money by one partner and of work by another. Moral philosophers tried also to make the equality of possible outcomes under equal conditions an explicit principle of jurisprudence for fair trial by law17 IV

In these various ways a calculus of expectation and choice was already by the sixteenth century transferring the whole experience of contingency and variability and chance from a context either of purely qualitative probability, or of irrational hazard or accident or personal luck, into one of the rational mathematical order. Mathematical expectation stabilized the future outside the uncertainty of time, by rationalizing risk and hope as a proportion of the possibilities present at every stage of any enterprise. Then an 15. Trans, modified from S. H. Gould in O. Ore, Cardano: The gambling scholar (Princeton, 1953), pp. 189 ff; cf. A. Bellini, Girolamo Caidano e il suo tempo (Milano, 1947); C. Gini, "Gerolamo Cardano e i fondamenti del calcolo della probabilita", Metron, 2* 11958), 78-96; David, Games . . . (note 13 above), pp. 55 ff.; Coumet, "Le problime des paris..." (note 13 above), 26off. ; M. Fierz, Girolamo Cardano (1501- '$76): Artz, Naturphilosoph, Mathematiker, Astronom und Traumdeutei (liasel & Stuttgart, 1977). 16. Cf Coumet, "La thôrie du hasard . . ." (note 13 above); C. Sommervogel, Bibhotheque de la Compagnie de Jesus, nouvelle ed. (Bruxelles & Paris, 1893), vol. IV, cols. 1726-51. 17. Cf. Domingo de Soto, Libri decem de iustitia et iure, iv. q.5, art. 2: "Utrum per ludum dominium transferatur", vi, q.i: "De usuris", q.6: "De contractu societatis", q.y: "De contractu assecurationis" (Lyon, 1559); Petrus a Navarra, De ablatorum restitutione in foro conscientiae, iii: "De laedente in rebus fortunae", c.2: "De restitutione rei alienae ex contractu", pars 3: "De restitutione rei alienae ex contractu societatis adquisitae"; A. Palau y Dulcet, Manuel del librero Hispano Americano (Barcelona & Oxford, 1957), vol. X, 428.


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uncertain future, and likewise an uncertain past, could be reduced to a probable expectation that was a measurable property of every present. This was the programme to be established with a new elegance and power in one aspect above all by Blaise Pascal, Christiaan Huygens, Antoine Arnauld and Pierre Nicole, Gottfried Withelm Leibniz and Jakob Bernoulli, and in another by John Graunt, Jan de Witt, William Petty and Edmund Halley. The context of this programme was a fresh awareness of the similarity in form of a variety of theoretical and practical situations requiring decision: in religion and morality, in law and politics, in gambling and commerce, in medicine and natural science. A re-examination of dependable knowledge was required first by the renewed challenge of scepticism initiated from the sixteenth century editions of Sextus Empiricus and its other Greek sources principally by Michel de Montaigne, and then by the expansion of scientific experience.18 The significant response to sceptical assertions of the undecidability of important questions, whether of just or effective action or of religious or scientific belief, was the development of a systematic new logic for the uncertain area lying between the traditional bimodality of simply true or simply false, a new logic by which the uncertainty could be stabilized in kinds and degrees of assent or of expectation appropriate to the material. Thus Francis Bacon explained that the principle of his new method of inquiry was "that we should establish degrees of certainty (cei18. Cf. H. G. Van Leeuwin, The Problem of Certainty in English Thought 16301690 (The Hague, 1963); D. C. Allen, Doubts Boundless Sea: Skepticism and faith in the Renaissance (Baltimore, MD, 1964); C. Vasoli, La dialettica e la retorica dell' Umanesimo (Milano, 1968); P. France, Rhetoric and Truth in France: Descartes to Diderot (Oxford, 1972); C. B. Schmitt, Cicero Scepticus: A study of the influence of the Academica in the Renaissance (The Hague, 1972), "The recovery and assimilation of ancient scepticism in the Renaissance", Rivista critica di storia della ftlosofia, 27 (1972,), 363-86; L. A. Jardine, Francis Bacon: Discovery of the art of discourse (Cambridge, 1974), "Lorenzo Valla and the intellectual origins of Humanist dialectic", Journal of the History of Philosophy, 15 (1977), 143-64,- C. J. R. Armstrong, "The dialectical road to truth: the dialogue", in French Renaissance Studies: 1540-70: Humanism and the Encyclopaedia, ed. p. Sharratt (Edinburgh, I 976), pp. 36-51; N. Jardine, "The forging of modern realism: Clavius and Kepler against the sceptics", Studies in History and Philosophy of Science, 10 (1979), 141-73; R. H. Popkin, The History of Scepticism from Erasmus to Spinoza, 3rd ed. (Berkeley & Los Angeles, 1979); B. J. Shapiro, Probability and Certainty in Seventeenth-Century England (Princeton, 1983); Patey, Probability and Literary Form (note 13 above); and Crombie, Styles of Scientific Thinking (note i above) for detailed discussions of what follows with bibliographical references.

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titudinis gradus}" in our knowledge of nature (Novum organum, Preface, 1620, Works, ed. Spedding et al., I, 1857, p. 151). Religious writers argued that if belief could be made neither apodeictic like mathematics or metaphysics, nor certifiable by the senses like physics, it could be given nevertheless a moral certainty beyond reasonable doubt by the accumulation of reliable testimony. The whole question provided an occasion to investigate the grounds for reasonable assent, and for distinguishing degrees of assent, both to the reliability of the evidence and to the credibility of the events and beliefs concerned. Hence Herbert of Cherbury's scale: "Of Truth, so far as it is distinguished from revelation, from probability, from possibility, and from falsehood" (De veritate . . . , 1624). Also Hugo Grotius: "so are there divers wayes of proving or manifesting the truth. Thus there is one way in mathematics, another in physics, a third in ethics, and lastly another kinde when a matter of fact is in question: wherein verily wee must rest content with such testimonies as are free from all suspicion of untruth: otherwise downe goes all the frame and use of history, and a great part of the art of physicke, together with all dutifulness that ought to be between parents and children: for matters of practice can no way else be knowne but by testimonies" (De veritate . . . ii. 24, 1633; English trans., 1632, p. 148). William Chillingworth offered the reasonable rule that we should not "expect mathematical demonstrations . . . in matters plainly incapable of them, such as are to be believed, and if we speak properly, cannot be known". It would be equally unreasonable for anyone to demand "a stronger assent to his conclusions than his arguments deserve" and to want "stronger arguments for a conclusion than the matter will bear" (Religion of Protestants, Preface to the Author, 1638). We had to be "content . . . with a morall certainty of the things" we "believe" which "are only highly credible, and not infallible" (ibid. ii. 154, p. 112). So our "judges are not infallible in their judgements, yet are they certain enough, that they judge aright, and that they proceed according to the evidence given" (ibid. iii. 26, p. 140). Something short of "truths, as certain and infallible as the very common principles of geometry and metaphysics", with "an adherence to them as certain as that of sense or science", were and had to be sufficient in many circumstances for reasonable calculated risk and prudent


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action. For "the evidence of the thing assented to, be it more or lesse, is the reason and cause of the assent in the understanding (ibid. vi. 51, p. 371). So then: "Do you think that there is such a city as Rome or Constantinople?" Properly speaking "I could not say that I knew it, but that I did as undoubtedly believe it, as those things which I did know". For while in their testimony "every particular man may deceive or be deceived, it is not impossible, though exceedingly improbable, that all men should conspire to do so". Hence with sufficient witnesses already, "my own seeing these cities would make no accession, add no degree to the strength and firmness of my faith concerning this matter, only it would change the kind of my assent, and make me know that which formerly I did but believe" ("An answer to some passages in Rushworth's Dialogues", Works, Additional Discourses ix, 1704, P. 47)In all our judgements what "we call experience", according to Thomas Hobbes, "is nothing else but remembrance of what antecedents have been followed by what consequents", in many particular observations or experiments whether natural or contrived: "Thus after a man hath been accustomed to see like antecedents followed by like consequents, whensoever he seeth the like come to pass to any thing he had seen before, he looks there should follow it the same that followed them". So "consequent upon that which is present, men call future; and thus we make remembrance to be the prevision of things to come, or expectation or presumption of the future". Conversely there was a "conjecture of the past, or presumption of the fact", when a man who "seeth the consequent, maketh account there hath been the like antecedent; then he calleth both the antecedent and the consequent, signs one of another, as clouds are signs of rain to come, and rain of clouds past". But "the signs are but conjectural; and according as they have often or seldom failed, so their assurance is more or less; but never full and evident. . . . If the signs hit twenty times for one missing, a man may lay a wager of twenty to one of the event; but may not conclude it for truth" (Humane Nature, ch. 4. 6-10, 1640, English Works, ed. Molesworth, IV, 1840, pp. 16-18). It was by reducing present judgement to an exactly calculated expectation of the future that Pascal and Huygens provided the essential mathematical model for the successive decisions that

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must be made through the uncertainties of all terrestrial existence, whether by nature or by men. This model was their calculation of expectations a priori among the closed possible outcomes of a game of dice. Thus, wrote Pascal, "what was rebellious to experience has not been able to escape from the dominion of reason. Indeed we have reduced it by geometry with so much security to an exact art, that it participates in its certainty and now boldly progresses. And so, joining mathematical demonstrations with the uncertainty of chance, . . . it justly arrogates to itself this stupendous title: the geometry of chance (aleae geometria)" ("Adresse a 1'Academie Parisienne", 1654, Oeuvres, pub. par Brunschvicg et al., Ill, 1908, pp. 307-8; presentation de Lafuma, 1963, pp. 102-3). They showed then how to calculate the present value of a stake in a game from the proportion of favourable to possible expectations exhaustively enumerated. This measured the mathematical expectation at every stage, a central principle defined by Huygens: "One's hazard or expectation (sors seu expectatio] to gain any thing, is worth so much, as, if he had it, he could purchase the like hazard or expectation again in a just and equal game" ("De ratiociniis in ludo aleae" in Schooten, Exercit. math., I 657 / pp. 52,1-2,; English trans. Arbuthnot, Of the Laws of Chance, 1692, p. 3). It was likewise to stabilize decision under uncertainty that Arnauld and Nicole at Port-Royal incorporated these insights into their analysis of judgement a posteriori among the open possible outcomes of experience. Hence their title: La logique ou Tart de penser, contenant outre les regies communes plusieurs observations nouvelles propre a former le judgement (1662). Here they delineated for the whole period the question of how to estimate the objective probability alike of historical and legal evidence for the past, and of predictions leading to action for the future. The absolute rule of impartial objectivity was that we must discount all personal motives and interests in "what we desire should be true. Nor is there any other truth than this, that ought to be found in the thing itself independent from our desires, which ought to prevail over us" (La logique . . . iii. 20.1, 5e ed., 1683; English trans., 1685 revised). When presented with accounts of two possible events: "How then shall we resolve to believe the one rather than the other, if we judge them both possible?" The rule here was that an event "must not


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be considered nakedly, and in itself, like a proposition in geometry; but all the circumstances that accompany it, as well internal as external, are to be weighed with the same consideration. I call internal circumstances such as belong to the fact itself, and external those that relate to the persons, whose testimonies induce as to believe it". Then "if all the circumstances are such that it never or very rarely happens, that the same circumstances are accompanyed with falsehood", we were persuaded to believe it as a "moral certainty", and conversely (ibid., iv. 13). With this rule La logique located the developing critique of the external reliability of evidence for historical events within the conception of their internal credibility determined by current scientific knowledge. It epitomized the common intellectual commitments alike of the rationally critical history of mankind envisaged by Jean Bodin and Francis Bacon and the rationally critical natural science of Galileo and Marin Mersenne and Descartes. Critical estimates of historical evidence, and frequencies of associations of events, yielded degrees of probability within a world of physical law eliminating myth and magic. In all reports of events "we must examine them by their particular circumstances, and by the credit and knowledge of the reporters". Hence "circumstances are to be compared and considered together, not considered apart. For it often happens, that a fact which is not very probable in one circumstance, which is ordinarily a mark of falsehood, ought to be esteemed certain, according to other circumstances", and the other way round (ibid, iv. 14). Likewise: "These rules that serve us to judge of things past, may be applied to things to come. For as we probably judge a thing to have come to pass, when the circumstances which we know are usually joined to the fact, we may as probably believe that such a thing will happen, when the present circumstances are such as are usually attended by such an effect. Thus it is that the physicians can judge of the good or bad success of diseases, captains of the future events of war, and that we judge in the world of the most part of contingent affairs". But in all cases "for that we may judge what is fit to be done, to obtain the good and avoid the evil, we ought not only to consider the good and that evil in itself, but also the probability whether it may happen or no,- and geometrically to consider the proportion which all the things hold together" (ibid, iv. 16).

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That scientific treatment of contingent expectation and uncertain choice had been transformed in concept and technique together by Pascal's aleae geometria, by Huygens's mathematical expectatio, by the measure given in La logique of "la probabilite qu'il arrive ou n'arrive pas" of an event as "geometriquement la proportion que toutes ces choses ont ensemble"; and also by the contemporary analysis in England and the Netherlands of life expectancy was noted by the historically observant Leibniz. From that viewpoint of explicit scientific recognition; the antecedent and subsequent history alike of the calculus of expectation and choice, both a priori and a posteriori, could be brought into intellectual perspective. Leibniz himself had looked independently for a logic of degrees of probability for the contingent and the uncertain first on the model of Roman jurisprudence. Turning then to mathematics he came to look for a general calculus of inquiry giving degrees of certainty according to the subject-matter, from an ars combinatoria such as Ramon Lull had invented and more recently Mersenne had used to calculate the possible combinations of a set of elements from which there could be realizations in fact, whether of musical tunes or languages or natural events. He seems to have brought together these two lines of inquiry only after he had studied, in Paris during 1672-76, the treatment of mathematical expectations a priori in games of chance by Pascal and Huygens, and a posteriori in life insurances by Jan Hudde and Jan de Witt and again by Huygens, himself then in Paris. Leibniz aimed to develop an ample scheme of human knowledge in which provision would be made for "a new logic for knowing degrees of probability", an exact "art of weighing probabilities" (Leibniz to Jean Frederic 1679, in Werke, hrg. Klopp, IV, 1865, pp. 422-23) applicable to law and politics and medicine and the study of history and so on, "where one must come to a decision and take a part even when there is no assurance" ("Nouvelles ouvertures", Opuscules, par Couturat, 1903, pp. 225-27). Technical mastery of this new style of scientific thinking was brought to its first maturity by Jakob Bernoulli in his Ars conjectandi (1713), concluding in Part iv by "setting forth the use and application of the preceding principles in civil, moral and economic affairs". In these and similar matters which we could not strictly know for certain, we had to conjecture, and: "To conjecture about something is to measure


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its probability; and therefore the art of conjecturing or the stochastic art (ars conjectandi sive stochastice) is defined by us as the art of measuring as exactly as possible the probabilities of things with this end in mind: that in our decisions or actions we may be able always to choose or to follow what has been perceived as being better, more advantageous, safer or better considered; in this alone lies all the wisdom of the philosopher and all the prudence of the statesman" (ibid. iv. 2). In this truly seminal work Jakob Bernoulli identified problems and offered solutions that were to guide inquiry for a century. The new mathematical grasp of the regularities of numerical frequencies present in adequately numerous populations gave a mastery of rational expectation and consequential action, within the limits of errors both of events and of estimations, that was to be diversified thereafter into the varied subject-matters of nature and of human society. Philosophical mathematicians and naturalists, in their search for stable knowledge and reasoned decision, established through their insights, at once into the conception and into the techniques of probable and statistical inference, both new methods of scientific exploration and in the end a new economy of nature. The term statistics appeared in this period in the traditional context of "civile, politica, statistica e militare scienza" (Ghilini, Annali di Alessandria, "A'lettori lo stampatore", 1666) as a comparative description of states, and the term was to retain also that essentially descriptive meaning after it had been applied as "statistik" as well to the numerical condition and the inferred prospects of a society (Achenwall, Abriss dei neusten Staatswissenschaft. . ., 1749). It was under the different name of "political arithemetick", supplied by William Petty (Political Arithmetick, Dedication, 1690), that the new "application of mathematics to economico-political matters" (Leibniz to Thomas Burnet i/n. ii. 1697, in Die Philosophischen Schriften, hrg. Gerhardt, III, 1887, p. 190) brought with it the first systematic collection of numerical data made explicitly for the calculation of rates of change and probabilities a posteriori, on which to base decision and action.19 From the numerical frequencies so discovered was then to come the calculation, for any given moment, both of the individual 19. Cf. W. L. Letwin, The Origins of Scientific Economics: English economic thought 1660-1776 (London, 1963).

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Science, Art and Nature in-Medievaland Modern Thought

probability of an event such as the death of a particular individual or the loss of a particular ship, and of the statistical probability of such an event occurring in the population. This kind of calculation was given a new model especially by English and Dutch writers on vital statistics and demography, who provided thereby an immediate application to social and medical policy. John Graunt in his pioneering Natural and Political Observations ... made upon the Bills of Mortality (1662,) set out explicitly the fundamental discovery that statistical regularities appeared in large numbers which were lost in small numbers. Graunt's scientific method established a new dimension of experimental medicine. From the records of births and of deaths with their symptoms kept for London for over half a century, he initiated inquiries based on the insight that stable mortality rates and sexratios and so on could be translated immediately into approximate probabilities a posteriori. This then provided for inferences in two directions: directly to the likelihood of a possible event coming about, and conversely to the likely causes of events already brought about. He insisted that records should include consistent and regular information about all diseases and other calamities, environmental and social conditions, ages and longevities, and so forth; and that account should be taken only of symptoms and other observable facts and not of opinions. In this way he made an analysis of the proportions of deaths in the population to be attributed to different causes. For example he attributed chronic diseases providing a constant proportion of the total deaths to constant conditions of the environment, and epidemic diseases providing fluctuating proportions to fluctuations in those conditions. Accepting the theory that these diseases came from alterations in the air, then: "as the proportion of acute and epidemical diseases shews the aptness of the air to suddain and vehement impressions, so the chronical diseases shew the ordinary temper of the place, so that upon the proportion of chronical diseases seems to hang the judgement of the fitness of the country for long life". Thus he observed in his numerical data for London that "among the several casualities some bear a constant proportion unto the whole number of burials; such are chronical diseases, and the diseases, whereunto the city is most subject; as for example, consumptions, dropsies, jaundice" and so on; and "some accidents, as grief,


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drowning, men's making away themselves, and being kiPd by several accidents, etc. do the like, whereas epidemical, and malignent diseases, as the plague, purples, spotted-feaver, small-pox, and measles do not keep that equality, so as in some years, or moneths, there died ten times as many as in others" (Natural and Political Observations . . . ch. 2, pp. 13-18). Among the epidemic diseases he made a detailed analysis of the supposed causes of plague by the method of comparing their "greater or less degrees" (Aristotle, Topics ii.io, ii4b 37~sa6; cf. Bacon, Novum organum, ii. 13) and eliminating those that did not match the phenomena (Natural and Political Observations... ch. 4, pp. 33-36). His rather English conclusion was that only the weather matched the plague in its sudden fluctuations. Graunt seems to have initiated here the analysis of inverse probability to be developed by Jakob Bernoulli, Abraham de Moivre and above all by Thomas Bayes, Pierre-Simon Laplace and Antoine-Augustin Cournot. Likewise his "inference from the numbers and proportions we finde in our Bills" (ibid, c.3, pp. 22-3) to the likelihood of dying from various particular diseases initiated the direct analysis of expectations developed especially by Huygens, de Witt and Halley as well as by Jakob Bernoulli. Halley provided a model for the calculation of statistical expectations a posteriori by taking Breslau, an isolated town where virtually all who died had been born, as a pure sample of mankind for pricing life annuities. The data for Breslau gave "a more just idea of the state and condition of mankind, than any thing yet extant that I know of", because virtually the whole population lived out their lives there without immigration or emigration. He showed that "the purchaser ought to pay for only such a part of the value of the annuity, as he has chances that he is living; and this ought to be computed yearly, and the sum of all those yearly values being added together, will amount to the value of the annuity for the life of the person proposed". Thus "the sum of all the present values of those chances is the true value of the annuity" ("An estimate of the degrees of mortality of mankind . . .", Philosophical Transactions, 17, 1693, pp. 600-3). The theory of decision implied here was to be elaborated by Buffon and Daniel Bernoulli into a theory of moral advantage or utility, based on the real value for our way of life of our expectations at particular times

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and in particular circumstances. Thus Daniel Bernoulli wrote: "Ever since geometricians first began to study the measurement of risks (sortes], everyone has affirmed that the value of an expectation is obtained by multiplying the values of each expected particular by the number of chances by which they can be obtained, and then dividing the aggregate of these products by the total number of chances". The chances to be considered must be "equally possible (aeque proclives)", and the "value should be estimated not from the price of a thing, but from the utility (emolumentum) which each takes therefrom. The price is estimated for the thing itself and is the same for everyone, the utility from the circumstances of the person" ("Specimen theoriae novae de mensura sortis", 1730-31, trans. Sommer, 1965). Likewise Buffon: "The mathematician in his calculation estimates money by its quantity; but the moral man must estimate it otherwise . . . ; and since the value of money in relation to the moral man is not proportional to its quantity, but rather to the advantages which money procures, it is obvious that this man ought to take a risk only in proportion to the expectation of these advantages" ("Essai d'arithmetique morale", §16,1730, Histoirenatuielle, Supplement IV, 1777, p. 80). Meanwhile from these statistical methods was to come a new statistical conception of an economy of nature generated through time by a sequence of decisions on instantaneous real values, by natural necessity as by human choice. V

An alternative to the economy of nature produced either by chance as proposed by the Greek atomists and Lucretius, or by the providential design of each separate creature preadapted to its circumstances within the whole creation, was developed by PierreLouis Moreau de Maupertuis in three essays begun before 1741 with his Essai de cosmologie and concluding with his Systeme de la nature published in 1751.20 Beyond alike those who believed 20. Cf. P. Brunei, Maupertuis (Paris, 1929; 2 vols.); E. Guyenot, Les sciences de la vie aux xviie et xviiie siecles: 1'idee de 1'evolution (Paris, 1941); A. C. Crombie, "P.L.M. de Maupertuis, F.R.S. (1698-1759), precurseur du transformisme", Revue de synthese, 78 (1957), 35-56; B. Glass, "Maupertuis, pioneer of genetics and


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that a blind mechanism could have produced all the wonderful adaptations to needs daily visible in organized bodies, and those who believed too readily that they had grasped providence in every contradictory detail, Maupertuis looked for a unifying principle truly characteristic of the Creator: a principle to be found "in phenomena of which the simplicity and universality suffered no exception and left no equivocation" (Essai de cosmologie, "Avantpropos", Oeuvres, i, 1756, p. xi). He found what he sought in his principle of least action. From this principle he claimed to deduce the general laws of all movement and change, which "being found precisely the same as those observed in nature, we can admire its application to all phenomena, in the movement of animals, in the vegetation of plants, in the revolution of the stars: and the spectacle of the universe becomes so much greater, so much more beautiful, so much more worthy of its Author. . . . These laws, so beautiful and so simple, are perhaps the only ones that the Creator and Ruler of things has established in matter in order to effect all the phenomena of this visible world" (ibid. pp. 42-45). Maupertuis approached the whole argument through the calculus of probability, applied to the political arithmetic of nature. Newton had thought that it was impossible that "a blind destiny" could have made the planets all move in the same direction in almost concentric orbits almost in the same plane. But if one supposed this "as the effect of chance", while very improbable "some probability nevertheless remains", so that one could not say that it must be the "effect of a choice" by the Creator. Likewise The argument drawn from the adaptation of the different parts of animals to their needs. . . . Does not all this indicate an intelligence and a design which presided over their construction? This argument struck the ancients as it struck Newton: and in vain the greatest enemy of providence replies to it that use has not been the goal at all, that it has been the consequence of the construction of the parts of animals; that chance having formed the eyes, the ears, the tongue, they have been used for sense, for speaking. But could it not be said that in the fortuitous combination of the productions of nature, since it would be only those that had certain adaptive relations (rapports de convenance) that could survive, it is not surprising that this adaptation is found in all the species that exist? evolution", in Forerunners of Darwin, ed. B. Glass, O. Temkin and W. L. Strauss, Jr. (Baltimore, MD, 1959), with other relevant papers therein; J. Roger, Les sciences de la vie dans la pensee fianfaise du xviiie siecle (Paris, 1963).

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Chance, it could be said, had produced an innumerable multitude of individuals; a small number were so constructed that the parts of the animal could satisfy its needs; in another infinitely greater number there was neither adapation nor order. All these latter have perished: animals without mouths could not live, others without reproduction organs could not perpetuate themselves. Only those have remained in which there was order and adaptation, and these species, which we see today, are only the smallest part of those which a blind destiny had produced (ibid. pp. 7-12; cf. Lucretius i. 1021-51, ii. 573-6, iv. 833-5, v. 56-7, 519-31, 837-77, and Empedocles in Aristotle, Departibus animalium, i. i, 6403 17-25).

Yet this could prove the perfection of providence: for "everything would be so ordered that a blind and necessary mathematics executes what the most enlightened and free intelligence prescribed" (Maupertuis, ibid. p. 2,5). Thus, extending the Cartesian mechanistic model from the biology of the individual organism to the biology of populations, Maupertuis saw in the numerical proportions and the adaptations of living species to their needs and environments, no longer the immediate operation of providence, but the necessary generation of order out of chance and chaos by the blind statistics of the least quantities required: varied birth and selective survival. The economy of nature was not then a perpetual pre-established harmony, but a shifting balance of perpetual trial for survival or exclusion. The history of living things on the Earth was a succession of states of dynamic equilibrium which had generated through time the adaptive diversity that we now observed. This simple statistical principle he combined next with a genetical hypothesis, giving to his "sketch of a system which we have proposed to explain the formation of animals . . . only the degree of assent that it deserves" (Venus physique, ii. 8, 1745, Oeuvres, II, 130-1). Then: Could we not explain by that how from only two individuals the multiplication of the most dissimilar species could have followed? They would have owed their first origin only to some fortuitous productions in which elementary particles would not have kept the order which they had in the father or mother animals; each degree of error would have made a new species; and by means of repeated deviations would have come the infinite diversity of animals that we see today: which will perhaps go on increasing with time, but to which perhaps the sequence of centuries will bring only imperceptible increments (Systeme de la nature, § xlv, Oeuvres, II, 148*49*)-


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"But should the system we propose be confined to animals?... Have not plants, minerals, and even metals a similar origin? Does not their production lead us to the production of other more organized bodies?" (ibid. § xlvii, p. 150*). All this concerned "what man has in common with the beasts, the plants, and in some way with all organized creatures". Man has in addition a principle by which he could "know God, and in which he finds moral ideas of his duties", and by which he could abstract from particular physical perceptions and "rise to this knowledge of a wholly different order" (§ Ivii, p. 160*). "To make natural history a true science", Maupertuis wrote in his Lettre sur le piogres des sciences (1752), "we must apply ourselves to researches that make us know not the particular shape of this or that animal, but the general processes of nature in its production and its preservation" (Oeuvres, II, 386). He rescued design in the history of nature, from a vision projected unmistakably from Lucretius and Empedocles, and he avoided the embarrassment of having to attribute misadaptations and adaptations alike to the individual attention of providence, by looking for the simplest and most universal principle through which, in animate as in inanimate matter: "A blind and necessary mechanics follows the designs of the most enlightened and free Intelligence" ("Accord de differentes loix de la nature", 1744, Oeuvres, IV, 21). From his approach through probabilities, Maupertuis looked, like Aristotle and like Descartes, for a world that could not be otherwise. By his highly original identification of varied birth and selective survival as the least quantities from which a blind statistics must generate progressively divergent adaptation, he brought the origination of species then within the calculus of the probability of success or failure at every stage of the process. Thus he could postulate that without any other cause progressive order, progressive genetic diversification with adaptation to variations of the environment, progressive complexity and novelty, must be generated in time with automatic necessity from unordered inherited variations (some fortuitous, some initiated by the environment) by the purely statistical process of different rates of survival. Maupertuis's speculative originality was to identify this necessary statistical process of the vectorial transformation of species by the accumulation of random changes through survivals and exclusions.

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In this whole intellectual context we can surely see in the conception of an instantaneous real value developed from Halley to Daniel Bernoulli and Buffon, with its immediate relevance to economic life, a description likewise of the situation of a biological species. It was Maupertuis who suggested to Daniel Bernoulli that he should calculate the real advantage for mankind of inoculation against smallpox. Considering the "total quantity of life" of a sample born at the same time until the death of the last individual, or the "average life" of each newborn child, Bernoulli offered a theorem by which "we should decide whether to reject or to introduce inoculation for newborn children, in so far as we wished to adopt the principle of the greatest utility for all mankind" ("Essai d'une nouvelle analyse de la mortalite causee par la petite verole, et des advantages de 1'inoculation pour la prevenir", §§12, 14, 1760, pp. 27, 33, trans. Bradley, 1971, with changes). But the relative advantage for individuals had to be weighed against the risk at every age, so that as d'Alembert pointed out "the interest of the state and that of the individual should be calculated separately" ("Sur 1'application du calcul des probabilities a 1'inoculation de la petite verole", 1761, p. 38). Again Adam Smith saw in economic society a statistical mechanism designed for an end which followed from "the order, the regular and harmonious movement of the system, the machine or economy by means of which it is produced" (Theory of Moral Sentiments, iv. i, 1759, p. 348). Businesses in competition faced the options of survival in various degrees or exclusion through the statistical accumulation of gains or losses, or of transformation to meet new circumstances. Competition stimulated structural and technical innovation and expansion into new markets : for "increase in demand" for goods "encourages production, and thereby increases the competition of the producers, who, in order to undersell one another, have recourse to new divisions of labour and new improvements of art, which they might never otherwise have thought of" (Wealth of Nations, 1776, ed. Campbell et al., V.i.e. 26, 1976, p. 748). For individual or business or state, for part or whole, advantage or disadvantage however marginal must accumulate with repetition and so with time must generate divergence. Laplace showed that regularities hidden by the complexity of phenomena could be


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revealed by the analysis of adequate numbers (Th&orie analytique des probability, ii.s, 1812). Seemingly echoing Thomas Malthus, he wrote that it was "principally by the lack of subsistence that the progressive march of the population is arrested. In all the species of animals and plants, nature tends without ceasing to augment the number of individuals until they are at the level of the means of subsistence" (Essaiphilosophique swlesprobabilites, 3e ed., 1816, p. 171). He continued: "By the repetition of an advantageous event, simple or compound, the real benefit becomes more and more probable and increases without ceasing : it becomes certain in the hypothesis of an infinite number of repetitions". Dividing it by the total number of events, "the mean benefit of each event is the mathematical expectation itself, or the advantage relative to the event. It is the same with a loss which becomes certain in the long run, however little the event may be disadvantageous". This theorem with others like it "proves that regularity ends by establishing itself in the very things most subordinated to what we call chance. When events are in large numbers, analysis gives again a very simple expression of the probability that the benefit will be confined within determined limits". The same went for loss. On the truth of this theorem "depends the stability of institutions based upon probabilities. But in order that it can be applied to them, it is necessary that these institutions should multiply the advantageous events by means of numerous transactions" (ibid. pp. 174-75). They must also base their decisions on the real value for a way of life of expectations at particular times and in particular circumstances. The real advantage expected of any event in sufficient numbers could be calculated then, for all participants alike, as a proportion of the possibilities present at every stage of any enterprise, whether the participants were biological species or varieties or commercial enterprises or players in a game, each competing for limited resources or hazardous outcomes. Thus the uncertain future could be stabilized for all alike in mathematical regularity by computing the probable expectation of gain or loss, growth or decline, as a measurable property of each participant at every instant. We know that Charles Darwin, in developing his theory of natural selection, became at some stage aware of the analysis by Malthus of the ratios of births to survivals. Perhaps the account

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given by Adam Smith of transformation as an alternative to the exclusion of a business by competition might have suggested the same for species. With natural selection Darwin in effect applied to the economy of nature the economic principle of net marginal advantage applied by Laplace to human commerce.21 He wrote in 21. Darwin referred in his "Notebooks on Transformation of Species" (transcribed by P. H. Barret in H. E. Gruber, Darwin on Man, London, 1974) to Mai thus (D 134 6-135 e, £3:1838), and to Adam Smith (M 108, 155: 1838, and N 184), and later he gave full credit to Malthus in his Autobiography, ed. N. Barlow (London, 1958), p. 120; cf. on Malthus also C. Darwin and A. R. Wallace, Evolution by Natural Selection, ed. G. R. de Beer (Cambridge, 1958), pp. 7-8 (Wallace, 1858), 46-68 (Darwin 1842), 116-9 (1844), 259 (1858), 273-9 (Wallace 1858); and on Adam Smith the reference in Darwin, Natural Selection . . . written from 1856 to 1858, ch. 6, ed. R. Stauffer (Cambridge, 1975), p. 233. Darwin wrote in the 3rd ed. of The Origin of Species, ch. 14 (London, 1861), pp. 517-8, in discussing whether life originated with one or many creations, that "Maupertuis' philosophical axiom of 'least action' leads the mind more willingly to admit the smaller number"; cf. his Variation of Animals and Plants Under Domestication, Introduction (London, 1868), pp. 12-13. He never referred to Laplace but the entomologist William Kirby (whose work Darwin knew) in the seventh of the Bridgewater Treatises, On the Power, Wisdom and Goodness of God as Manifested in the Creation of Animals and in their History, Habits and Instincts, Introduction (London, 1835), vol. I, pp. xxiv ff., xxxii ff., xl ff., accused both Laplace and Lamarck of trying "to ascribe all the works of creation to second causes; .. . without the intervention of a first" (p. xxiv). He adapted Adam Smith to argue that the Malthusian struggle brought about by the growth of populations to the limits of subsistence was the means used by the Creator to maintain the order and harmony of the system as a whole (ch. 3, vol. I, 141-4, ch. 18, vol. II, 243-4). Karl Marx wrote to Friedrich Engles on 18. vi. 1862: "It is remarkable how Darwin recognises among beasts and plants his English society with its division of labour, competition, opening up of new markets, 'inventions', and the Malthusian 'struggle for existence'. It is Hobbes's bellum omnium contra omnes . . . " (Selected Correspondence, Moscow & London, 1956, pp. 156-7). Engles commented to P. L. Lavrov on 12-17. ix. 1875: "The whole Darwinist teaching of the struggle for existence is simply a transference from society to nature of Hobbes's doctrine of bellum omnium contra omnes and of the bourgeois-economic doctrine of competition, together with Malthus's theory of population. When this conjurer's trick has been performed . . . , the same theories are transferred back again from organic nature to history and it is now claimed that their validity as eternal laws of human society has been proved" (ibid., pp. 367-8). Cf. T. Cowles, "Malthus, Darwin, and Bagehot: a study in the transference of a concept", Isis, 26 (1936), 341-8; A. Sandow, "Social factors in the origin of Darwinism", Quarterly Review of Biology, 13 (1938), 315-26; A. C. Crombie, "Darwin's scientific method", in Actes due IX e Congres International d'Histoire des Sciences: Barcelona-Madrid 1959 (Barcelona & Paris, 1960), pp. 354-62,- R. M. Young, "Malthus and the evolutionists: the common context of biological and social theory", Past and Present, no. 43 (1969), 109-45, "Darwin's metaphor: does nature select?", TheMonist, 55 (1971), 442-503; M. Ruse, The Darwinian Revolution: Science red in tooth and claw (Chicago, 1979); R. G. Mazzolini, "Stato e organismo, individui e cellule nell' opera di Rudolf Virchow negli anni 1845-1860", Annali dell'Istituto storico italo-germanico in Trento, 9 (1983), 153-293.


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his "Notebooks on Transmutation of Species" opened in July 1837 after his return in the previous year from his long voyage in the Beagle: "Seeing the beautiful seed of a bull rush I thought, surely no 'fortuitous' growth could have produced these innumerable seeds, yet if a seed were produced with an infinitesimal advantage it would have better chance of being propagated" ("Notebooks...," E 137, 1839, in Gruber, Darwin on Man, 1974, p. 460). Five year later in his Essay of 1844 he wrote that in the struggle for existence "less than a grain in the balance will determine which individuals shall live and which perish". In changing conditions "there is a most powerful means of selection, tending to preserve even the slightest variation, which aided the subsistence or defence of those organic beings, during any part of their whole existence, whose organization had been rendered plastic "(in Evolution by Natural Selection, ed. de Beer, 1958, p. 24i).22 Darwin, like Maupertuis, was making a point about the survival of even marginal advantage quite different from anything found in ancient atomism, for he was reducing the uncertain expectations of the fortuitous beloved by the atomists to the exact necessity of a statistical law. He wrote in the long manuscript of Natural Selection (18 5 7) of which On the Origin of Species (1859) was published as an abstract: "mere fluctuating variability, or any direct effect of external conditions . . . are wholly inadequate to explain the infinitude of exquisitely correlated structures, which we see on all sides of us The most credulous believer in the 'fortuitous concourse of atoms' will surely be baffled when he thinks of those innumerable and complicated yet manifest correlations". Hence: "No theory of the derivation of groups of species from a common parent can be thought satisfactory until it can be shown how these wondrous correlations of structure can arise. I believe that such means do exist in nature, analogous, but incomparably superior, to those by which man selects and adds up trifling changes" in cultivating domesticated animals and plants. This "means of selection" in nature was "that severe, though not continuous struggle for existence, to which... all organic beings are subjected, and which would give to any individual with the slightest variation of service to it (at any period of its life) a better chance of surviving, and which would almost 22. Cf. R. A. Fisher, The Genetical Theory of Natural Selection (Oxford, 1930); A. C. Crombie, "Interspecific competition", The Journal of Animal Ecology, 16 (1947), 44-73-

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ensure the destruction of an individual varying in the slightest degree in the opposite direction. I can see no limit to the perfection of this means of selection" (Natural Selection, ch. 5, ed. Stauffer, I 975> PP- 1 74~5)- Hence the fundamental efficacy of the "Principle of Divergence. . . . For in any country, a far greater number of individuals descended from the same parents can be supported, when greatly modified in different ways, in habits, constitution and structure, so as to fill as many places, as possible, in the polity of nature, than when not at all or only slightly modified". More generally "a greater absolute amount of life can be supported in any country or on the globe, when life is developed under many and widely different forms, than when under a few and allied forms". Divergence into new varieties and species was then a necessary consequence of the unlimited accumulation of marginal advantages opened into the economy of organisms by "the greatest amount of their diversification", which doctrine is in fact that of 'the division of labour'" (ibid. ch. 6, pp. 227-8, 233). With something of Adam Smith as the author of this doctrine Darwin had been familiar for many years (cf. "Notebooks . . ." M 108, 155, 1838, and N 184 in Gruber, ibid. pp. 286, 296, 351, 390). It is difficult to tell how far Darwin himself was aware of the ideas crystallized by Laplace, or of the form of argument used by Maupertuis in his identification of varied birth and selective survival or exclusion as the least statistical quantities from which the adaptive transformation of species must necessarily and automatically be generated.23 Like them both he envisaged a form of argument in which the consequences of statistical postulates followed with the certainty of a physical law, and like Maupertuis he saw in this a truer conception of the Creator than that of a series of independent creations: "how much more simple and sublime power: let attraction act according to certain law; such are inevitable consequences. Let animal be created, then by fixed laws of generation, such will be their successors . . . " ("Notebooks . . . " B= II101-2, 1837, ed. de Beer et al., 1960, p. 53). In this form he looked from the start for "laws of change, which would then be main object of study, to guide our speculations with respect to past and future" (ibid. B = II 228-9, p. 69). Like Laplace he estimated 23. See note 20 above.


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the probability of a theory by its range of predictions: "these speculations, even if partly true, they are of the greatest service towards the end of science, namely prediction; till facts are grouped and called there can be no prediction. The only advantage of discovering laws is to foretell what will happen and to see bearing of scattered facts" (ibid. D = IV 67, p. 137). For, he wrote long afterwards: "In scientific investigations it is permitted to invent any hypothesis, and if it explains various large and independent classes of facts it rises to the rank of a well-grounded theory" (Variation . . . , 1868, p. 9). He cited "the greater simplicity of the view of a few forms or of only one form having been originally created, instead of innumerable miraculous creations having been necessary at innumerable periods"; and "this more simple view accords well with Maupertuis's philosophical axiom of 'least action' " (ibid. pp. 12-13). Darwin laid out the argument of the Origin of Species itself with legal advocacy, showing why its premises should be accepted and what followed from them, stating the difficulties of his theory and demolishing them one by one: "For I am well aware that scarcely a single point is discussed in this volume on which facts cannot be adduced, often apparently leading to conclusions directly opposite to those at which I have arrived. A fair result can be obtained only by fully stating and balancing the facts and arguments on both sides of each question" (Origin, ch. i, 1859, p. 2). He had to prove that the visible order of nature was the result of an historical process, brought about by stable statistical probabilities discoverable only by careful analysis beneath the immediately observable surface of things: "Throw up a handful of feathers, and all must fall to the ground according to definite laws; but how simple is this problem compared to the action and reaction of the innumerable plants and animals which have determined, in the course of centuries, the proportional numbers and kinds" found anywhere upon the Earth (ibid. ch. 3, p. 75). He concluded: "I cannot believe that a false theory would explain, as it seems to me that the theory of natural selection does explain, the several large classes of facts above specified" (ibid., 2nd ed., ch. 14, 1860, pp. 480-1). "To my mind" Darwin wrote finally, "it accords better with what we know of the laws impressed on matter by the Creator, that the production and extinction of the past and present inhabit-

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ants of the world should have been due to secondary causes. . . . Thus, from war in nature, from famine and death, the most exalted object which we are capable of conceiving, namely the production of the higher animals, directly follows. There is grandeur in this view of life, with its powers, having been originally breathed into a few forms or into one,- and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved" (ibid., ch. 14, 1859, pp. 488, 490). But this evolution of living things, brought about by the statistical probability at every moving point of time that the decision would be success or failure, had no general direction. It was propelled only by the necessity for survival that advantage should be taken of every available opportunity: a kind of statistical principle of plentitude with in itself no evident purpose except to generate adaptive diversity and hence increase the total quantity of life. "I cannot think that the world, as we see it, is the result of chance" Darwin repeated; "and yet I cannot look at each separate thing as the result of design" (Darwin to Asa Gray 26. xi. 1860, in Life and Letters, ed. F. Darwin, II, 1887, p. 353). Each separate thing was rather the product of general laws, but the problem for him remained whether "the existence of so-called natural laws implies purpose. I cannot see this" (Darwin to W. Graham 3.vii. 1881, in ibid, i, 315). The Duke of Argyll recorded the aging Darwin's response to his remark that it was impossible to look at the many "wonderful contrivances for certain purposes in nature" discovered by Darwin himself "without seeing that they were the effect and the expression of mind". Darwin replied: "Well, that often conies over me with overwhelming force; but at other times . . . it seems to go away" (ibid. p. 316). Thomas Henry Huxley in his treatment of Evolution and Ethics (1893) placed the question of design and purpose firmly within the horizon of human responsibility. He described "attempts to apply the analogy of cosmic order to society" (CollectedEssays, IX, 1894, p. 82) as simply "reasoned savagery" (ibid. p. 115): "The history of civilization details the steps by which men have succeeded in building up an artificial world within the cosmos. Fragile reed as he may be, man, as Pascal says, is a thinking reed" (ibid. p. 83;


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Pascal, Pensees 2oo^Lafuma =347 Brunschvicg). That was his true expectation. Surely all this points to the fundamental logic of evolutionary and of moral expectation and choice alike. For we can place the biological theory of the evolutionary transformation of living organisms by varied birth and selective survival, that is by natural selection, within a theory of decision, whether made impersonally in nature or voluntarily by man, in its most general form. This was a distant outcome of the analogy of economic expectation and of choice according to real value and their quantification. The quantified concept of future things, formed in the mind from numerical data collected in rational anticipation of action, introduced into business and games, as it was to do into politics and war, the style of a mathematical rational art. The mathematical science of statistics, developed with the calculus of probabilities in the seventeenth and eighteenth centuries, offered something beyond the traditional descriptions of the natural and human resources of states. It was transposed, especially in eighteenth-century France and Britain, into a new statistical economy at once of human society and of nature. The essential concept of the instantaneous real value of a stake in a game or a commercial enterprise, measured by the amount that should be risked on its future expectations of gain or loss, was transferred to the formally identical situation of a biological species. We may see then a formal identity between the economic concept of net marginal advantage, which Laplace showed must with repetition generate an ever increasing divergence between enterprises or states, and Charles Darwin's biological concept of natural selection generating an evolution of species. The measure of the instantaneous value of a variety or species as a contributor to the total quantity of life, like that of a commercial enterprise or of a player for stakes, was its expectations in the circumstances of that instant. The same applies to a decision fittest for the occasion, whether in a choice of action or a choice of theory. The difference is that men in their decisions may be free and responsible, may by free choices accelerate or retard or reverse a process of gain, whether in things or in knowledge, and may beyond the quantity choose the quality of life. The conformity of logical style so discovered in scientific think-

400

Science, Art and Nature in Medieval.and Modern Thought

ing, through different historical periods and over a wide variety of subject matters, provides an illuminating insight into very deep characteristics of our intellectual culture. It also raises the question of the limits of a scientific style, and of the motivation of scientific change. It is an insight that can come only from a comparative historical analysis. It is only through such philosophical history that we can see how problems and their solutions came to be formulated, promoted, and accepted or rejected. As historians of a movement through the past we can only interpret the signs we have now in the present, and the signs seem to indicate that what I call the intellectual and moral commitments of any major culture have a very tenacious life. In that sense we may conclude indeed: Veritas ftlia temporis.


401

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Everything would be so ordered that a blind and necessary mathematics executes what the most enlightened and free intelligence prescribed. (Maupertuis, Essai de Cosmologie i)

18 P.-L. Moreau de Maupertuis, F.R.S. (1698-1759). Precurseur du Transformisme I

Pierre-Louis Moreau de Maupertuis, fils de Ren6 Moreau, seigneur de Maupertuis, naquit a Saint-Malo en 1698; mort a Bale en 1759, il est bien connu comme un des grands mathematicians francais de la premiere moitie du xvme siecle et comme Fauteur du principe physique qui porte le nom de principe de moindre action. II est important aussi dans Phistoire de la science comme le premier protagoniste en France des idees newtoniennes, et comme le createur effectif et le premier president de 1'Academic de Frederic le Grand a Berlin. Un aspect de son ceuvre scientifique qui n'est certainement pas moins important que ceux susmentionn^s, aspect qui, jusqu'ici, n'a pas attire beaucoup 1'attention, c'est sa contribution a la th£orie du transformisme organique. II est, en effet, 1'auteur du premier essai systematique en vue de formuler une th6orie des causes du transformisme, et c'est cette contribution qui forme le sujet de cet expose. Maupertuis etait, en effet, comme le demontra feu Pierre Brunet par son etude eclaire1© et interessante J, une personne de vitalite etonnante. Avant de discuter le probleme de 1'origine des especes selon les ide"es de ses contemporains, et la solution qu'il y proposa, je devrai dire quelques mots de sa vie. Cette vie ne manque certainement pas d'interet, tenant en effet quelque chose de ce caractere bizarre du si 1. P. BRUNET, Maupertuis, Paris, 1929, 2 parties Cf. [J.-H.-S. FORMEY], «Eloge de M. de Maupertuis», Histoire de I'Academie royale des Sciences, annee 1759, Berlin, 1766, pp. 464-512; see A. C. Crombie, Styles of Scientific Thinking in the European Tradition, ch. 20 (London, 1994) for up to date bibliography.

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souvent a des incidents qui surviennent a des personnes de bonne volonte et d'intelligences perspicaces, mais qui ne sont pas entierement affermies par le bon sens. On dit que la mere de Maupertuis Fidolatrait plutot qu'elle ne Faimait; enfant, il semble bien avoir 6t6 quelque peii gate et pendant toute sa vie il continua de manifester son esprit independant dans la plupart des circonstances. Jeune homme, 11 passa deux ans a Farmee comme officier de cavalerie. Puis, apres avoir acquis en France un certain renom comme mathematicien, le premier grand tournant dans sa vie — tournant dans lequel il entraina bientot la science franâise tout entiere — fut sa visite a Londres en 1728, Fannee qui suivit la mort de Newton. II passa six niois a Londres, et fit la connaissance de Samuel Clarke — partisan de Leibniz dans la polemique celebre a propos de la conception de Newton sur Pespace absolu et de la theologie naturelle — et celle d'autres membres eminents de la Royal Society. Peu de temps apres, le contraste entre la physique cartesienne et celle de Newton se trouva caracterise d'une facon spirituelle par Voltaire dans cette lettre bien connue, numero 14 des Lettres philosophiques (1734), qui dit 2 : « Un Franâis qui arrive a Londres trouve les choses bien changees en philosophic comme dans tout le reste. II a laisse le monde plein, il le trouve vide. A Paris on voit FUnivers compose de tourbillons de matiere subtile; a Londres on ne voit rien de cela. Chez nous c'est la pression de la lune qui cause le flux de la mer; chez les Anglais c'est la mer qui gravite vers la lune... Chez nos Cartesiens tout se fait par une impulsion qu'on ne comprend guere; chez M. Newton, c'est par une attraction dont on ne connait pas mieux la cause. A Paris vous vous figurez la terre faite comme un melon; a Londres, elle est aplatie des deux cotes. La lumiere, pour un Carte'sien, existe dans Fair; pour un newtonien, elle vient du soleil en six minutes et demie... Voila de serieuses contrarietes! » Maupertuis etait convaincu que le point de vue de Newton sur ces questions etait correct et celui de Descartes faux, et des son retour a Paris, il se mit a encourager un mouvement en faveur du systeme newtonien. C'est lui qui persuada Voltaire de la valeur scientifique de la theorie, avancee par Newton, de Fattraction universelle — nous verrons comment 2. VOLTAIRE, (Euvres completes, «d. Beuchot, Paris, 1879, XXII, 127-8.

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il adapta cette derniere a sa propre th6orie g^neiique — et de I'lnferiorite de tout systeme rival de la physique et de la cosmologie de Newton. Comme dit d'Alembert au sujet de Maupertuis, « le premier qui ait os^ parmi nous se declarer ouvertement newtonien », dans son Discours preliminaire a I'Encycloptdie 3 : « Maupertuis a cru qu'on pouvoit etre bon citoyen, sans adopter aveuglement la physique de son pays [le cart^sianisme]; et pour attaquer cette physique, il a eu besoin d'un courage dont on doit lui savoir gre\ » Par un des premiers et des plus heureux essais de vulgarisation scientifique, Voltaire introduisit dans le grand public en France le systeme newtonien. Apres quelques annees passees a 1'etude de Fastronomie, Maupertuis attira Tattention du public par un voyage audacieux, en 1736-1737, en Laponie, destine a resoudre la question de la forme de la terre en mesurant un arc de m^ridien situ£ le plus au nord possible. On avait fait en 1735 des mesures semblables vers le sud, au Perou. Maupertuis ecrivit une description du voyage a travers les montagnes et les forets; la gene epouvantable causee par les mouches, qu'on ne pouvait pas ^carter meme en s'entourant d'une £paisse fumê; les cataractes qu'il fallait franchir sur les bateaux tres lagers des Lapons. Par son sang-froid, sa bonne humeur, sa tenacite, il semble avoir maintenu I'unit6 de Texp^dition. Ses Observa~ tions... faites par ordre du Roy au Cercle Polaire 4, qui d^crit leurs aventures, est un des livres de voyages les plus captivants. En 1738, peu apres son retour, Voltaire — ami aussi bon que-pouvait 1'etre une personne toujours disposed k sacrifier 1'amitie a la vanite et a Fambition personnelle — recommanda a Frederic de Prusse d'appeler Maupertuis pour former a Berlin une Academic des Sciences, ecole newtonienne qui d^passerait en importance 1'Academic de Paris. En 1740, 1'annee de son accession au trdne, Fre"d6ric invita Maupertuis a Berlin pour mettre ce projet a execution; mais il fut bientot arr^te, temporairement, par un incident bizarre. Au moment de Tarrivê de Maupertuis a Berlin, la Prusse etaft en eiat de guerre avec TAutriche, pour la possession de la Sil&sie. En Janvier 1741, Maupertuis ecrivit a Frederic, 3. D'ALEMBERT, (Enures philosophiques, historiques et litteraires, Paris, 1805, I, 281. Cf< R. DUGAS, La m&canique OB XVII" sietle* Nettchitel, 1954, pp. 586-92. 4. (Euvres de M. de Maupertuis, Lyon, 1756, III, 69 sqq.

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lui demandant la permission de venir au camp royal pour lui soumettre des plans pour 1'Academic. Frederic envoya cette reponse laconique : « Venez ici, Ton vous attend avec impatience » 5. Mais le tableau charmant des conversations sur le front entre le Roi-Philosophe et son philosophe particulier n'allait pas durer. Quelques jours apres son arrivee, Maupertuis se trouva pris dans la bataille de Molwitz; son cheval s'emballa et Fentraina derriere les lignes de 1'ennemi. Pendant quelques jours, on crut au camp prussien qu'il etait mort. « Nous en sommes touches aux larmes », £crivit Voltaire, en apprenant les nouvelles; « Mon Dieu! Quelle fatale destinee! » 6. Mais un peu plus tard, Voltaire re$ut de nouveaux details. « J'apprends dans le moment, ecrivit-il, que Maupertuis est a Vienne, en bonne sante. II fut depouill£ par les paysans dans cette maudite Foret-Noire, ou il etait comme Don Quichotte faisant penitence. On le mit tout nu; quelques housards, dont un parlait franc.ais, eurent pitie de lui, chose peu ordinaire aux housards. On lui donna une chemise sale, et on le mena au comte Neipperg [Neuperg]. Tout cela se passa deux jours avant la bataille. Le comte lui preta cinquante louis avec quoi il prit sur-le-champ le chemin de Vienne, comme prisonnier sur sa parole : car on ne voulut pas qu'il retournat vers le roi, apres avoir vu 1'armee ennemie, et on craignit le compte qu'en pouvait rendre un geometre... » 7 On permit a Maupertuis d'aller de Vienne a Paris, ou le roi attendit qu'il retournat a Berlin. Mais Frederic, comme Voltaire, avait traite 1'afFaire avec un manque de serieux qui offusqua Maupertuis, et ce n'est, en effet, qu'en 1745 qu'il oublia definitivement son ressentiment et s'etablit a Berlin, ou il se fixa vite par son mariage avec une Prussienne. L'arrivee de Maupertuis a 1'Academie de Berlin fut un vrai succes; il y attira Euler, Meckel, Condillac, La Mettrie, Lalande, et d'autres savants et ecrivains distingues8. Tout alia a merveille jusqu'a ce que Voltaire, dont Maupertuis trouvait deja quelque peu ennuyeux les sarcasmes perânts, decidat en 1750 que lui aussi se fixerait a Berlin. Une querelle 5. BRUNET, op. cit., I, 90. 6. VOLTAIRE, Lettre A M. l'Abt>6 de Valori, 2 mai 1741. (Euvres completes, 70 vol. (Paris, 1785-89), XXXVI, 46. Cf. ibid., I, 20; BRUNET, op. cit., I, 91. 7. VOLTAIRE, (Euvres, XXXVI, 46-47. 8. BHUNET, op. eft., I, 110, 123, 137.


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eclata entre les deux philosophes, ostensiblement au sujet de ce que Voltaire qualifia de tentative ridicule de la part de Maupertuis, c'est-a-dire de son essai de se servir du principe de moindre action comme argument pour prouver 1'existence de Dieu 9, mais querelle envenimee par une hostility personnelle de plus en plus profonde. Voltaire y parait sous un jour des plus defavorables. Maupertuis essaya de s'en tenir au fait; le but de Voltaire, c'eiait de gagner dans cet echange de polemique et de faire paraltre son ennemi a la fois cretin et canaille. Pour ce qui est de ses ecrits, il y reussit. Dans sa Diatribe du Docteur Akakia (1752), il repr^sente Maupertuis comme « un homme qui aurait, par exemple, douze cents ducats de pension pour avoir parle1 de mathematique et de metaphysique, pour avoir disseque deux crapauds, et s'etre fait peindre avec un bonnet fourr6 » 10. (On avait peint le portrait de Maupertuis en costume lapon.) II dit aussi qu'il etait un « ignorant » ayant « en recompense une imagination singuliere », et un « Arlequin d^guise en archeveque » u. Le roi fut choque de ces critiques sur le president de son Academic, et Voltaire dut quitter la Prusse, rendant son Ordre de Merite et sa clef de Chambellan, selon sa propre expression : « au Salomon du Nord, pour ses etrennes, les grelots et la marotte » 12. Voltaire ne pardonna jamais a Maupertuis; de sa nouvelle demeure en Alsace, il continua de Tattaquer13 et, dans L'Homme aux quarante 4cus, il le ridiculisa meme apres sa mort en 1759. L'interet que Maupertuis prit a la biologic date des premiers temps de sa carriere scientifique. Dans une des premieres conferences 14 qu'il soumit a 1'Academic des Sciences, en 1727, il fit crouler la vieille croyance que les salamandres etaient spontanement combustibles — sujet singulier de recherches a cette epoque; mais la conference contient aussi une description d'experiences prouvant que la salamandre est ovovivipare (c'est-a-dire que les oeufs peuvent 6clore dans 9. Ibid., I, 128-58. Cf. E. MACH, La Mecanique, traduction franâise, Paris, 1925, IV, § 2, p. 425 sqq. 10. VOLTAIRE, CEuvres, XXIII, 562; BHUNET, op. cit., I, 148. 11. VOLTAIRE, (Euvres, XXIII, 563, 565. Cf. « Vie de Voltaire par Condorcet », ibid., I, 231 sqq. 12. BRUNBT, op. cit., I, 152. 13. Dans Histoire du Docteur Akakia et du natifde Saint-Malo (1753). 14. Histoire de I'Acadtmie royale des Sciences, annte 1727, Mtmoires, pp. 27-32.

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et hors de la mere). En 1731, il publia un autre article excellent sur les differentes especes de scorpions15. II £tait, en effet, naturaliste de pure race, chose rare pour un math^maticien. Un ami decrivit sa maison a Berlin comme etant « une veritable menagerie, remplie d'animaux de toute espece, qui n'y entretenaient pas la proprete. Dans les appartements, troupes de chiens et de chats, perroquets, perruches, etc. II fit venir une fois de Hambourg une cargaison de poules rares avec leur coq. II etait dangereux quelquefois de passer a travers la plupart de ces animaux, par lesquels on etait attaque... M. de Maupertuis se divertissait surtout a creer de nouvelles especes par 1'accouplement de differentes races; et il montrait avec complaisance les produits de ces accouplements, qui participaient aux qualites des males et des femelles qui les avaient engendres. J'aimais mieux voir les oiseaux, et surtout les perruches qui etaient charmantes » 16. Le meme ecrivain a decrit aussi comment « M. de Maupertuis rassemblait avec beaucoup de peine et a grands frais des animaux etrangers ou singuliers, pour observer leurs allures et etudier en quelque sorte leur caractere ». II

Maupertuis ecrivit sa premiere oeuvre importante sur la production de nouvelles especes pendant le sejour qu'il fit a Paris pour reprendre des forces, apres le malheureux incident de Molwitz; d'autres ceuvres suivirent, a Berlin. Avant d'en parler, il faut etudier en raccourci 1'etat du probleme de 1'origine des especes a cette epoque, c'est-a-dire 1'etude dans toute son ampleur de la raison pour laquelle tous les animaux et toutes les plantes connus en sont venus a assumer leurs formes actuelles. II est utile de distinguer deux aspects de la question gen6rale. Par exemple, quand on donnait des explications dans le sens du transformisme, deux problemes principaux se trouvaient engages : 1° la preuve, d'apres la morphologic comparative, la paleontologie et les experiences de reproduction, qu'un processus historique de transformisme avait, en effet, eii lieu; 2° les theories sur les causes de ce processus, une s6rie de lois a 1'aide desquelles on pouvait d&luire, et 15. Tbid., 1731, pp. 223-9. 16. BRUNET, op. cit., I, 179-80.


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ainsi expliquer a la maniere classique, le processus evolutionniste, de meme que Ton explique les mouvements des planetes par la mecanique newtdnienne. En effet, pendant un siecle environ, avant que, dans la deuxieme moitie du xixe siecle, la theorie du transformisme ne soit generalement acceptee, beaucoup de biologistes se rendirent compte que bien des elements militaient en faveur du processus historique, mais ils n'etaient pas satisfaits des essais contemporains faits pour 1'expliquer17. Dans un sens tres general, sans application particuliere a la biologic, les explications evolutionnistes sont parmi les plus anciennement connues de la science. Les premiers cosmologistes grecs ont cherche a montrer que toute la complexite du monde que nous observons derivait d'un etat plus simple. Mais, pour une raison ou pour une autre, de telles explications avaient passe de mode et une grande partie de 1'evidence de base par laquelle la theorie du transformisme organique s'etait renouvelee au xvnr siecle, fut, en effet, rassemblee par des biologistes qui ne la consideraient aucunement en termes de transformisme. Au xvn* siecle et aux premieres annees du xviii", le probleme le plus important pour les botanistes et pour les zoologistes, c'6tait d'elaborer un systeme efficace de classification. Cela occupa tout biologiste d'importance (a part les physiologistes), depuis Belon et Cesalpino au xvi' siecle, en passant par John Ray, Tournefort, Tyson et d'autres, jusqu'k Linne, dont le Systema Naturae en 1735 resuma toute la serie des essais anterieurs 18. Dans le Syst&me de Linne, les lignes principales de la classification moderne des plantes avec la nomenclature binome se trouvaient etablies; la classification zoologique de Linn6 reussit moins bien et il fallut la modifier considerablement plus tard. Mais ce qui nous concerne le plus, ce sont les principes. Linne montra comment mettre precisement en rapport logique avec tous les autres, chaque espece, genre, ordre et classe, et comment identifier un organisme inconnu, lui donner un nom, et le mettre dans le Systeme de la Nature. 17. Cf. E. GtrrfNor, Les Sciences de la vie aux XVII" et XVIII" siecles, Paris, 1941; P. G, FOTHERGILL, Historical Aspects of Organic Evolution, Londres, 1952; et pour1 une bibliographic excellente voir C.-C. GILUSPIE, Genesis and Geology, Cambridge, Mass^ 1951, pp. 23 sqq. Cf. aussi J.-T. MERZ, A History of European Thought in the Nineteenth Century, Loadres, 1903, II, et E.-S. RUSSEL, Form and Function, Londres, 1916. 18. Cf. H. DAUDIN, Etudes d'histoire des sciences naturelles, Paris. 1926, I.

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Le but immediat des tentatives de Linne, c'etait de resoudre le probleme pratique de ramener £ 1'ordre un monde divers et chaotique; mais, comme ses contemporains, il pretendait que la classification devait montrer non settlement un ordre commode, mais le vrai ordre de rapports entre les individus. C'est-a-dire que la classification devait etre non settlement un systeme artificiel, mais aussi ce qu'on appelait un systeme « naturel », qui exprimat ce que Linne appelait « 1'ordre souverain de la Nature » 19. Get « ordre souverain de la Nature », selon les conceptions du xvn* et du xviii" siecle, possedait plusieurs caracteristiques qui sont importantes, car elles formaient Farriere-plan des theories evolutionnistes du xvme siecle. D'abord, c'etait un ordre essentiellement immuable, dans lequel toute chose et toute substance dans 1'univers, les astres et les planetes dans leurs mouvements, les elements chimiques, les etres vivants, avaient chacun leur place et leur role definis. Galilee et Descartes avaient detruit la conception particuliere de 1'ordre naturel derivee d'Aristote, mais la croyance qu'il y avait un ordre stable dans 1'univers physique, ordre qui etait reste sans changement depuis la creation, persistait largement. De notre point de vue, la chose la plus importante en rapport avec cet ordre fixe de la nature, c'est qu'on considerait que les especes biologiques etaient fixes et avaient des limites definies. L'opinion de Linne etait que toutes les especes d'organismes avaient et6 creees par Dieu des le commencement, et n'etaient pas susceptibles de changement sauf en des deiails non essentiels20; a son avis, cette thôrie se trouvait appuyee par roeuvre de Harvey, de Redi et de Swammerdam, d^montrant que des organismes se reproduisaient par des reufs. Dans la reproduction, c'etait la nature specifique qui etait transmise : toute difference remarquee entre parent et rejeton devait etre accidentelle et temporaire 21. Un deuxieme trait de « 1'ordre souverain de la Nature » de Linne, c'etait qu'il estimait que les organismes formaient une echelle, s'etendant de 1'etre vivant le plus primitif, a peine 19. Caroli LINNAEI, Systema naturae, 13s ed., Vienne, 1767, I, 13. 20. Plus tard, comme resultat d'experiences avec 1'hybridation, Lannd admit la possibilite de mutations limitês des especes dans nn genre particulier, qui avait ele cree par Dieu. Sur toute cette question, ses disciples Etaient beaucoup plus dogmatiques que Linne m£me., 21. Caroli LINNAEI, Philosophia botanica, Stockholm, 1751, p. 99. Cf. DAUDIN, op. cit., I, 65. Cf. ARISTOTE, De generatione animalium, I, 21-22; II, 1, 731 b 33-35; III, 3-4.

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susceptible de se distinguer de la matiere inorganique, au degr£ le plus bas de 1'gchelle, en passant par les plantes, les zoophytes (Sponges, etc.), les animaux, jusqu'a 1'homme, au degr£ le plus £lev&22. Cette idee d'une £chelle de la nature organique derivait, en premier lieu, d'Aristote 23. Tout d'abord, on supposa l'6chelle lineaire; puis, lorsqu'on connut mieux le probleme, on assigna aux plantes et aux betes des rameaux diffgrents, y ajoutant des groupes subordonn^s ou des rameaux plus petits, et ainsi de suite, tout comme s'il s'agissait d'Un arbre24. Get arbre devint les « donn£es > que les theories de transformisme devaient expliquer. Cela peut se voir dans la notion de « gradation » traitSe par 1'anatomiste anglais, Edward Tyson, en 1699, dans son e"tude bien connue du chimpanzS. Tyson dit qu'en faisant « une elude comparative de cet animal et d'un singe, une guenon et un homme..., on peut mieux observer les gradations de la nature dans la formation des corps animaux, et les transitions faites entre un animal et un autre » 25. Une troisieme caracteristique de 1'ordre de la Nature, c'elait la croyance qu'il y avait dans 1'univers une harmonic. On supposait qu'il y avait adaptation parfaite des parties d'un organisme avec son ensemble, et aussi des organismes avec leur milieu physique et de 1'un a 1'autre : par exemple, que les plantes s'alimentaient du sol, les insectes des plantes, les oiseaux des insectes, les oiseaux plus grands des oiseaux plus petits, et ainsi de suite, le tout maintenant un gquilibre parfait de population26. Tous les savants se trouverent impressionne's par cette harmonic; Newton regarda la structure de 1'ceil de la mouche comme extant une preuve thôlogique sMeuse; John Ray d^crivit « la sagesse de Dieu, manifested dans les CEuvres de la creation » 27; la soi-disante preuve des 22. Cf. A.-O. LOVEJOY, The Great Chain of Being, Cambridge, Mass., 1936. 23. Cf. ARISTOTE, Historia animalium, VIII, 1, 588 b 4; De gen. animal, II, 1, 733 b 1-17. 24. Cf. DAUDIN, op. cit., I, 159-73. 25. Edward TYSON, Orang-Outang, sive Homo Sglvestris, Londres, 1699, preface, p. vn. Cf. M.-F. Ashley MONTAGU, « Edward Tyson, M.D., FJR.S., 1650-1708, and the rise of human and comparative anatomy in England » (Memoirs of the American Philosophical Society, XX). Philadelphia, 1943, pp. 240-1. 26. LINN£, Systema naturae, 6d. cit, I, 10-11, 17-18, 535. Cf. DAUDIN, op. cit., pp. 174-5. 27. The Wisdom of God manifested in the Works of the Creation, Londres, 1691.

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causes finales, raisonnant de la montre a 1'Horloger Divin, devint un des lieux communs de la thSologie naturelle, comrae, par exemple, dans I'Analogy of Religion de Bishop Butler, et dans les ecrits de Paley. Les moralistes du xvur siecle firent appel a rharnionie de 1'univers physique pour appuyer leurs vues sur la « gouvernance » morale du monde. Une voix dissidente fut celle du docteur Johnson, martyre de la goutte, qui ne trouvait aucune explication rationnelle de la douleur physique. Cette conception de 1'ordre, de Pharmonie dans le monde biologique devint un probleme important pour les protagonistes d'explications evolutionnistes, car ils essayaient essentiellement de demontrer comment du chaos pourrait sortir Pordre. Avant que Maupertuis et d'autres evolutionnistes eussent mis a jour leurs idees, on trouvait cela impossible. Cela se voit clairement dans le fameux « discours de degr^s », prononce par Ulysse dans le Troilus and Cressida de Shakespeare. Apres avoir decrit comment « The heavens themselves, the planets and this centre « Observe degree, priority and place » et ainsi de suite, en descendant par Pordre naturel et social tout entier, Ulysse dit : « Take but degree away, untune that string, « And, hark, what discord follows! each thing meets « In mere oppugnancy. » 28 S'il n'y avait pas un ordre exterieur a observer, la vie se trouverait reduite a un chaos de lutte entre les individus. On verra de quelle maniere Maupertuis, dans sa theorie du transformisme, se servait d'une telle lutte comme moyen pour developper Pordre. Cette comparaison entre les mondes social et naturel vient bien a propos, car, a partir de la fin du xvne siecle, Popinion sur la question d'un ordre fixe commencait a donner partout des signes de modification. II est impossible d'examiner ici le developpement de Pidee de progres historique, mais on peut citer quelques evenements significatifs 29. La controverse entre « les Anciens et les Modernes > ouvrit toute la question 28. Troilus and Cressida, I, 3. 29. Cf. F. BRUNETI&RE, « La formation de 1'idSe de progres au xviiie siecle », Etudes critiques sur I'histoire de la litterature frangaise, 5« serie, 2« ed., Paris, 1896, pp. 183-350; J.-B. BURY, Th« Idea of Progress, Londres, 1920; R.-F. JONES, « Ancients and Moderns » (Washington


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de savoir si la pense'e et la civilisation s'etaient ameliorees; et, en grande partie grace aux triomphes de la science, elle se termina par une victoire retentissante pour les Modernes. L'opinion elait an changement historique. Ceux qui e"crivaient sur 1'histoire — les « sociologues », comme on les appelle aujourd'hui — eherchaient a formuler les lois du developpement social inspire'es directement par le modele des lois de la meeanique de Newton. Us prenaient en consideration 1'influenee de P ambiance, de la nourriture, de la geographic, des etudes, et ainsi de suite. Les ecrivains les plus influents en matiere de progres historique et de transformisme biologique se connaissaient tous tres bien; en effet, la plupart d'entre eux dtaient des Francais. Voltaire, qui par son Siecle de Louis XIV (1752) et son Essai sur les mceurs et I'esprit des nations (1756), produisit les premiers essais valables dans le domaine de Fanalyse des causes de 1'histoire, « histoire philosophique » comme il la nommait, connaissait particulierement Maupertuis (comme nous 1'avons vu) et aussi Buffon 30. Diderot, qui traita de la sociologie et de la biologic, engagea une controverse contre Maupertuis31. Le developpement parallele des idees de progres social et de transformisme biologique est un des aspects les plus se*duisants de toute 1'affaire et fournit en me'ine temps un exemple frappant de Tinfluence dans plusieurs spheres differentes d'une forme particuliere de la pensee ou de la maniere de regarder les choses, a un moment donne. Pour ce qui regardait la biologic, en meme temps que Linne pr^parait son tableau magnifique d'un « ordre souverain de la Nature » immuable, d'autres biologistes rassemblaient en differents endroits les faits evidents qui s'opposaient a cette conception des choses, surtout a 1'idee que toutes les especes connues avaient et4 creees a la fois et que jamais aucuii changement ne s'etait produit. Par exemple, la vraie nature des fossiles dtait connue de certains ecrivains depuis Fepoque University Studies, N. S., Language and Literature, VI), Saint-Louis, 1936; W. K. FERGUSON, The Renaissance in Historical Thought, Boston, Mass., 1948, pp. 68-112. 30. Cf. Thomas PENNANT, Tour on the Continent 1765, 6d. G. R. de Beer, Londres, 1948, pp. 38-39 : « Madame de Buffon told me that Voltaire was worth 113.000 livres a year and 700.000 in cash, that he traded in cattle, insured ships, etc.; that his original estate was only 500 £ pr Annum. » 31. Cf. MAUPERTUIS, (Enures II, 169-84, Cf. A. VARTANIAN, Diderot and Descartes, Princeton, 1953.

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classique &*, et Robert Hooke, ail xvir siecle, avait signal^ que 1'histoire des fossiles montrait, selon son expression, « qu'il y a eu aux epoques anterieures beaucoup d'autres especes de creatures, dont nous ne pouvons trouver aucun exemple actuellement; et il se peut qu'il y ait actuellement beaucoup de nouvelles especes, qui n'existaient pas au commencement » S3. Buff on donna un premier compte rendu de la succession de formes differentes dans les couches geologiques, dans son Histoire de la Terre (1744), et une description plus etendue, dans les Epoques de la Nature (1778). L'evidence experimentale que des changements he're'ditaires pouvaient avoir lieu dans 1'organisnie eiait attested par les horticulteurs, en particulier par ceux qui cultivaient la fraise et la tulipe (1'industrie des oignons hollandais commenc,ait a. se developper), et par les eleveurs de pigeons et de chiens, comme aussi par les anomalies humaines, telles que 1'albinisme chez les negres (un cas fut cite par Tyson34) et la polydactylie. Se basant sur tout cela, Buff on, en 1753, dans 1'article bien connu de son Histoire Naturelle au sujet de « L'Ane », donnait un aperû brillant d'une conception ^volutionniste de 1'origine d'une meme souche de tous les animaux. Linne avait classe le cheval (Equus cauda undique setosd) et 1'ane (Equus cauda extreme setosa) comme deux especes du meme genre (ou famille); pour Buff on, cela impliquait qu'ils devraient avoir le meme parentage. Car, « si Ton admet une fois qu'il y ait des families dans les plantes et dans les animaux •», ecrivit-il, « que 1'ane soit de la famille du cheval, et qu'il n'en differe que parce qu'il a degdnere, on pourra dire egalement que le singe est de la famille de 1'homme, que c'est un homme degenere, que l'homme et le singe ont eu une origine commune comme le cheval et 1'ane, que chaque famille, tant dans les animaux que dans les vegetaux, n'a eu qu'une seule souche, et meme que tous les animaux sont venus d'un seul animal, qui, dans la succession des temps, a produit en se 32. Cf. P. DUHEM, Etudes sur Ldonard de Vinci, II, Paris, 1909, pp. 289, 307-8, 316-7, 323-4, 336-9; A.-C. CROMBIE, « Avicenna's influence on the medieval scientific tradition », dans Avicenna: scientist and philosopher, 6d. G. M. Wickens, Londres, 1952, pp. 97-99. 33. Robert HOOKE, « A Discourse of Earthquake », Posthumous Works, ed. R. Walter, Londres, 1705, p. 291. 34. Ashley MONTAGU, Edward Tyson, pp. 212-3.


419

perfectionnant et en ddg£n6rant, toutes les races des autres animaux » 35. Si tous les organismes sent ainsi censes tirer leur origine d'ancStres communs, et avoir subi des modifications dues au climat, & 1'alimentation, etc., au cours de 1'histoire gSologique, ceci expliquerait le fait, sur lequel se basalt la classification, que, par exemple, un groupe comme les vertelwe's £tait une s6rie de variations sur un plan de base commun. De ce point de vue, conclut Buffon, on peut regarder tous les animaux comme appartenant a la meme famille, ce qui n'empeche pas que « dans cette grande et nombreuse famille, que Dieu seul a conûe et tirSe du ndant, il y ait d'autres petites families projete"es par la Nature et produites par le temps... ». De par ces passages tire's hors du contexte, « L'Ane » se trouve souvent citd en t&moignage de I'Svolutionnisme de Buffon. Mais a lire 1'article tout entier, il est evident que, quelles que fussent ses ide~es plus tard M, tout le but de la discussion dans « L'Ane », c'elait d'attaquer la conception de families d'ou suivaient ces consequences radicales. En effet il ne pr6sente la possibility du transformisme que pour la detruire. Quant aux families de Linn6 — premier objet de son attaque37 — il ecrivit : « Ces families sont notre ouvrage ... la Nature ... ne connait point ces pr^tendues families, et ne contient en effet que des individus. » Le seul terme de classification qui r^pondait a quelque chose de rêl, c'6tait 1'espece, la succession d'individus susceptibles de se reproduire par croisement, engendrant ainsi un rejeton fecond. L'usage d'expressions telles que « la famille » pour toute autre chose que la commodity leur emploi pour signifier une parente de descendance, etait reprehensible. Malgr§ la presence chez les plantes, les animaux et les hommes, de variations hereditaires, il n'y avait aucune Evidence, declarait Buffon, pour que ces dernieres aboutissent a de nouvelles especes, tandis qu'il y avait des difficultes considerables a supposer que tel e"tait le cas, par exemple, le fait que la plupart des variations observers etaient des monstruosites, 1'absence d'especes intermMiaires, et I'lmprobabilite qu'une variation se produisit chez des individus de 1'autre sexe de 35. Histoire naturelle, Paris, 1753, IV, 381-2. 36. Cf. « De la degeneration des animaux », ibid., 1766, XJV, 311-74. 37. Ibid., IV, 378; cf. « Maniere d'eludier et de trailer 1'histoire naturelle », ibid., 1749, 1-20 sqq.

420


sorte qu'elle put se reproduire38. « Quoiqu'on ne puisse pas demontrer que la production d'une espece par la degeneration soit une chose impossible a la Nature, conclut-il, le nombre des probabilites contraires est si enorme, que philosophiquement meme on n'en peut guere douter. » « L'Ane » occupe ainsi une position curieuse dans 1'histoire de la theorie du transformisme, car quoique Buffon avance la theorie expres pour 1'attaquer, il donne neanmoins la le premier apercu systematique de la possibility qu'un procede historique du transformisme ait pu avoir lieu. Mais ce n'est pas a Buffon qu'il faut attribuer 1'honneur d'avoir ete a 1'origine de la theorie moderne du transformisme, c'est plutot a Maupertuis, que cite Buffon et dont les vues sur ]a variation genetique se trouvaient indubitablement le but d'attaque par Buffon dans « L'Ane ». Maupertuis semble avoir ete le premier qui trouva I'idee que tous les organismes tirent leur origine, avec modification, d'ancetres communs; on trouve cela dans son Essai de Cosmologie, ecrit avant 1741 quoique public seulement en 1750. II avait public entre temps un autre livre a ce sujet, avec le titre charmant, pour un traite scientifique, de Venus physique (1745). Dans ces O3uvres, Maupertuis presenta le premier une explication - systematique et causative du processus transformiste. Maupertuis abordait le probleme de 1'origine des especes entierement du cote de la genetique, et il ecrivit la Venus physique en premier lieu pour donner Fexplication d'un phenomene specifique, et ensuite, en generalisant, de tout phenomene semblable. Le phenomene specifique, c'etait un garcon negre, albinos, amene a Paris de TAmerique du Sud, qu'il avait vu dans le salon d'une dame a la fois elegante et intellectuelle, en 1744. Vu que 1'ambiance dans laquelle la curiosite intellectuelle s'exprime est aussi importante a 1'histoire de la science qu'a 1'histoire de la pensee en general, il vaut la peine de rappeler qu'a cette epoque la science naturelle etait tres a la mode dans la haute societe frangaise. Voltaire a decrit cette periode comme une epoque ou tout honnete homme devait etre philosophe, ou une dame pouvait 38. Ces difficultes sont tout a fait suffisantes pour expliquer le rejet, de la part de Buffon, dans « L'Ane », du transformisme. On ne devrait pas attribuer trop d'influence, comme par exemple le fait Guyenot (op. cit., p. 397), a son exclamation : « Mais non, il est certain, par la revelation, que tous les animaux ont egalement participe a la grace de la creation.... »


421

oser 1'etre sans ambages. II existe une histoire de deux dames qui contracterent la passion de Peiude de 1'anatomie, ce qu'on regardait comme extravagant, me'me en ces temps de pensee avanc6e. Une certaine dame gardait dans son boudoir un cadavre qu'elle disse'quait pendant ses heures de loisir; tandis qu'une autre avait un dispositif special, fixe dans sa voiture, de fagon a pouvoir diss&juer tin cadavre pendant de longs voyages, tout comme d'autres dames d'un gout plus conventionnel auraient pu s'adonner k la lecture. Maupertuis donna dans sa Vdnus physique une description du petit negre, qui commence, en temoignant d'une sympathie tout humaine : « J'oublierais volontiers ici le phenomene que j'ai entrepris d'expliquer : j'aimerais bien mieux m'occuper du reveil d'Iris, que de parler du petit monstre dont il faut que je vous fasse 1'histoire. » 39 II continue : « C'est un enfant de 4 ou 5 ans qui a tous les traits des negres, et dont une peau tres blanche et blafarde ne fait qu'augmenter la laidenr. Sa tMe est couverte d'une laine blanche tirant sur le roux : ses yeux d'un bleu clair paraissent blesses de I'^clat du jour : ses mains grosses et nial faites resscmblent plutot aux pattes d'un animal qu'aux mains d'un homme. II est n6, a ce qu'on assure, de pere et mere africains, et tres noirs. » 11 fait ensuite mention de m^moires au sujet d'autres negres albinos, de ralbinisme parmi les merles, les corbeaux et les poules, et d'autres changements hereditaires dans les plantes acclimatees et chez les animaux apprivoises 40. Son but immediat est, done, de trouver une theorie de Theredite susceptible d'expliquer ces ph6nomenes, tout aussi bien que 1'heredite normale 41. Pendant la premiere moitie du xvnr siecle la theorie dominante de la generation et de 1'heredite 42, c'etait celle de la « pr^formation », qui existait sous deux formes : dans 1'une, on supposait rembryon derive entierement de 1'ceuf, la fonc39. MAUPERTUIS, (Euvres, II, 115-6. 40. Ibid., pp. 118-9. 41. Gf. C. ZIRKLE, « The early history of the idea of the inheritance of acquired characters and of pangenesis », Transactions of the American Philosophical Society, Philadelphia, XXXV (1946), 139-40, 131. 42. Cf. GuvfiNOT, op. cit., pp. 208-312 ? E.-J. Ck)LE, Early Theories of Sexual Generation, Oxford, 1980.

422


tion du male n'etant que de stimuler 1'ceuf a commencer a se developper; dans 1'autre, avancee apres la decouverte par Hartsoeker et Leeuwenhoek, en 1674-1677, du spermatozoide — resultat direct du nouveau microscope — c'etait le germe male seulement qui se transformait en embryon, la femelle se bornant a fournir la nourriture 43. La theorie de 1'heredite etait la meme, quelle que fut la forme de « preformation » qu'on preferat. Considerons 1' « ovisme », comme s'appelait la premiere. On soutenait que chaque partie de 1'adulte contribuait a 1'ceuf par une particule, 1'oeuf etant ainsi un adulte en miniature; pendant le developpement embryologique, les particules ne faisaient que se dilater jusqu'a devenir des parties a dimensions adultes. On supposait le premier individu de chaque serie — la femelle — avoir ete cr£e avec toutes les generations subsequentes dedans, 1'une a I'int^rieur de 1'autre, telle une boite chinoise; dans le cours du temps, les generations ne faisaient qu'eclore et se developper, 1'une apres 1'autre. Selon 1' «ovisme », les males de chaque generation ne faisaient naitre aucun autre individu. L'autre forme de !a theorie preformationiste, connue sous le nom de « animalculisme », etait exactement pareille, sauf que le germe male etait I'element operateur. Maupertuis fit remarquer que ni 1'une ni 1'autre des formes de la theorie preformationiste ne pouvait expliquer certaines observations : la ressemblance avec les deux parents, ou avec des ancetres eloignes mais pas avec les ancetres immediats, les hybrides, et les nouvelles caracteristiques qui se montraient de temps en temps dans des plantes, des animaux et des hommes44. Pour expliquer ces phe"nomenes, il dit, en premier lieu, qu'il fallait supposer que 1'embryon se formait de 1'union des germes des deux parents, le male et la femelle 43. A cette epoque-la, le role des cellules dans la repro43. Cf. MAUPERTUIS, (Euvres, II, 21-24. 44. Ibid., pp. 64-71, 80-85, 93, 109-10. Cf. Lettres, XIV, ibid., pp. 267-82; Lettre sur le progr&s des sciences, ibid., pp. 385-90. Cf. B. GLASS, « Maupertuis and the beginnings of genetics », Quarterly Reviews of Biology, Baltimore, XXII (1947), 196-210; P. OSTOYA, Maupertuis et la biologic », Revue d'Histoire des Sciences, VII (1954), 60-78. 45. « II me semble, ecrivit-il, que Pidee que nous proposons sur la formation du foetus satisfairoit mieux qu'aucune autre aux phenomenes de la generation; a la ressemblance de 1'enfant, tant au pere qu'a la mere; aux animaux mixtes qui naissent des deux especes differentes; aux monstres, tant par exces que par defaut : enfln cette idee paroit la seule qui puisse subsister avec les observations de Harvey. » MAUPERTUIS, (Euvres, II, 93. Sur Harvey, cf. pp. 36-50.


423

duction etait mal connu, et il supposait que le germe etait un produit fluide. II dit que chaque liquide seminal se composait de particules, chacune desquelles derivant d'une partie donnee du parent. Par 1'union entre les parents, les deux liquides se melangeaient et les particules se combinaient en paires, une de chaque parent; la serie entiere de paires faisait naitre 1'embryon. II y avait beaucoup plus de particules qu'il n'etait necessaire pour former 1'embryon, par consequent, il y avait un degre de largeur considerable dans la serie particuliere de caracteristiques actuellement heritee par le rejeton. Maupertuis soutenait que c'etaient les membres normaux de 1'espece, dans un leger degre de variation, qui se reproduisaient, parce que chaque particule avait « un plus grand rapport d'union » avec les particules habituellement voisines, qu'avec d'autres. Ces « rapports d'union », dit-il, pouvaient s'expliquer en supposant qu'il y avait une force d'attraction qui fonctionnait entre eux, force analogue £ la gravitation de Newton et a I'attraction suggeree comme explication de la combinaison chimique 46. Mais on ne peut pas concevoir cette attraction comme etant simplement une force physique. II y a un instinct des animaux, dit-il, « qui leur fait rechercher ce qui leur convient, et fuir ce qui leur nuit », et « n'appartient-il point aux plus petites parties dont 1'animal est forme? Get instinct, ... ne suffit-il pas cependant pour faire les unions necessaires entre ces parties? » 47. Plus tard, dans son Systeme de la Nature (1751), Maupertuis etait encore plus net. « Les elements propres a former le foetus, dit-il, nagent dans les semences des animaux pere et mere : mais chacun extrait de la partie semblable a celle qu'il doit former, conserve une espece de souvenir de son ancienne situation; et 1'ira reprendre toutes les fois qu'il le pourra, pour former dans le foetus la meme partie. » 48 S'il se produit un defaut d'attraction, de sorte que des combinaisons anormales de particules se fassent, le resultat dans ces circonstances est une variation ou un monstre en quelque sorte. D'abord, les particules venant d'ancetres normaux, avec le plus d'affinite pour 1'union normale, sont plus nombreuses, dans le fluide seminal de la variele, que celles 46. Ibid., pp. 88-92; cf. pp. 139-41. Cf. NEWTON, Opticks, 4e ed. 1730. Query, 31. 47. MAUPERTUIS, GRuvres, II, 31. 48. Ibid., pp. 158-9.

424


de la disposition nouvelle, de sorte qu'apres quelques generations, la variete peut retourner au type normal49. Mais si les facteurs qui produisent la variety continuent a f onctionner pendant plusieurs generations, alors les particules donnant de nouveaux assemblages, avec des souvenirs des nouvelles situations, en viennent peu a peu a surpasser en nombre celles propres a faire les traits originaires, de faôn que la variete soit etablie. Maupertuis suggera qu'on pouvait verifier cette theorie par 1'experience simple de trancher la queue a des souris pendant plusieurs generations, pour voir s'il serait possible de produire une race de souris sans queue. Les particules de queue dans les liquides seminaux seraient peu a peu reduits en nombre et finiraient par disparaitre. Selon Maupertuis, les causes de ces nouvelles dispositions de particules sont de deux sortes. D'abord, il y a des recombinaisons dans les liquides seininaux, produites par « le hasard », c'est-a-dire par certaines circonstances inconnues fonctionnant dans les fluides m£mes, « dans lesquelles les parties elementaires n'auroient pas retenu 1'ordre qu'elles tenoient dans les animaux peres et meres » 50. D'autre part, des changements peuvent se produire du fait du milieu, par exemple, par le climat, la nourriture, la mutilation. Etant donn6 la theorie de Maupertuis, les variationsvenant de ces deux causes seraient heritees. Parce que des enfants negres nes de parents blancs se trouvaient incomparablement plus rares que des negres albinos, Maupertuis soutenait que le blane etait la couleur humaine primitive, et que la chaleur de la zone torride fomenta « les parties qui rendent la peau noire » 51. Un negre albinos etait ainsi un retour au type primitif. Cette theorie tout entiere soulevait toutes les difficult^s qu'il pouvait y avoir a accepter le recit de la Genese sur la descendance de toute la race humaine £ partir de deux parents originaux52. Dans son Essai de Cosmologie et son Syst&me de la Nature, Maupertuis se servit de cette theorie de Theredit^ pour donner une explication generale de 1'origine des especes. Fai&ant la supposition que de nouvelles dispositions des particules elementaires avaient eu lieu par le pass6 sans interruption, alors dit-il : « Chaque degr£ d'erreur aurait fait une nouvelle 49. 50. 51. 52.

Ibid., Ibid., Ibid., Ibid.,

pp. 119-21. p. 148*. p. 123. p. 128.


425

espece : et a force d'ecarts repetes, seroit venue ia diversity infinie #es anhaaux que nous Toyons aujourdlrai. » *• Mais comment les nouvelles Tarietes s'adaptaient-eHes mi miheu? Maupertuis n'etait plus a meme d'accepter la vieille notion que Diea avail cre£ les organismes en adaptation parfaite a leurs conditions et a leurs besoms, et de plus, il dit que Ton avait beaueoup abuse de la preuve des causes finales. II y avait dans la nature une Evidence considerable de gaspillage et de mal-adaptation; et, tout en admettant que la gouvernance des choses se trouve eventuellement sous la gouverne de la Providence, les causes qu'on est a meme d'observer immediatement semblent etre de pur hasard. I/explication de 1'adaptation de Torganisme est a la fois une anticipation remarquable de la theorie de la selection naturelle de Charles Darwin, et la reflexion de Finfluence dÊmpedocle et de Lucrece. 4 Mais ne pourroit-on pas dire, ecrit-il, que dans la combinaison fortuite des productions de la Nature, comme il n'y avoit que celles ou se trouvoient certains rapports de convenance, qui pussent subsister, il n'est pas merveilleux que cette convenance se trouve dans toutes les especes qui actuellement existent? Le hazard, diroit-on, avoit produit une multitude innonabrable d'individus; un petit nombre se trouvoit construit de maniere que les parties de ranimal pouvoient satisfaire a ses besoins; dans un autre infiniment plus grand, il n'y auroit ni convenance, ni ordre; tous ces derniers ont peri; des animaux sans bouche ne pouvoient pas vivre, d'autres qui mamquoient d'organes pour la generation ne pouvoient pas se peipetuer : les seuls qui soient restes sont ceux ou se trouvoient Fordre et la convenance; et ces especes, que nous voyons aujourd*hui, ne sont que la plus petite partie de ce qu*un destin aveugle avoit produit. » M En faisant valoir cette explication de la diversification des organismes comme un processus qui avait eu lieu dans le temps, Maupertuis tourna sens dessus dessous tout le probleme de Tadaptation. Ray et Linne" avaient essaye1 de pr6senter une image du monde organique tel qu'il avait et6 cree par Daeu dans un etat d'harmonie autoregulatrice, chaque creature s'adaptant parfaitement a son mode de vie; ceci entraina la consequence que des cas de mal-adaptation cons53. Ibid., p. 148 *. 54. Esscri de Cosmologie, (Euvres, I, 11-12.

426


tituaient un embarras theologique et biologique considerable. Pour Maupertuis, au contraire, Tadaptation ne s'achevait que par un processus de lutte et d'elimination, en commeânt par un monde en chaos, quand, comme dans le discours d'Ulysse, « each thing meets in mere oppugnancy ». L'ordre fut retabli par la loi de la jungle. Un autre probleme que Maupertuis devait confronter, c'etait d'expliquer 1'apparition d'innovations pendant le processus du transformisme dans le temps, de telle faôn que les organismes montrassent non seulement une diversification dans des milieux differents, mais formassent aussi une Echelle de perfection ou d'amelioration. Tel est le sujet principal de son Systeme de la Nature. Maupertuis s'interessait particulierement a 1'emergence de nouvelles facultes intellectuelles que Ton pouvait observer en montant I'^chelle, depuis les creatures tres modestes telles que les vers, jusqu'au chien, au singe et a rhomme. Son probleme 6tait d'expliquer Emergence de facultes intellectuelles en termes de sa thôrie de 1'heredite, a Taide de nouvelles combinaisons de particules elementaires. II decida tout de suite qu'il etait possible de faire deriver des qualites telles que la m^moire, rintelligence ou le desir, d'une conception de particules, et de forces telles que 1'attraction, destined seulement a manier la matiere inorganique; des caracteres intellectuels de ce genre ne trouvaient absolument aucune place dans cette conception 55. Sa solution du probleme suivit les lignes ^tablies par Leibniz 56. 11 fit remarquer que Descartes avait rendu insoluble le probleme, en etablissant une separation absolue entre les intelligences qui pensent et les corps qui s'etendent dans 1'espace. Mais 1'existence d'animaux et d'hommes demontrait que la pensee et 1'etendue pourraient etre toutes les deux des qualites de la meme substance de base. Les phenomenes intellectuels observes dans certains organismes pouvaient s'expliquer, dit-il, en dotant les particules elementaires d'un degre de « perception » — selon son expression57. Ensuite, tout comme de nouvelles combinaisons des particules memes produisirent de nouveaux organes et fonctions du corps, de meme les nouvelles combinaisons concomitantes de perceptions Elementaires donnerent lieu a de nouvelles facultes intellects. (F.uvres, II, 152-5. 58. Cf. BRUNET, Maupertuis, II, 391-408. 57. MAUPERTUIS, (Euures, II, 155M61; Cf. pp. 147-9, 157-49*.

P.-L. Moreau de Maupertuis 427

427

tuelles, car toutes etaient unies dans une seule et nouvelle perception, qui etait quelque chose d'autre que la totality de ses parties. En faisant usage de cette theorie, Maupertuis chercha a expliquer le caractere hereditaire de qualites intellectuelles, telles que le talent pour les mathematiques dans la famille Bernoulli et pour la musique chez les flls de J.-S. Bach. II chercha aussi a expliquer I'origine d'organismes (la vie) venant des combinaisons de la categorie la plus simple de particules elementaires en des molecules plus complexes, et 1'evolution de 1'intelligence depuis les creatures les plus humbles jusqu'a rhomme. La seule exception qu'il fait au processus general, c'est chez 1'homme la connaissance de Dieu, le sens du devoir moral, et le raisonnement abstrait, tous, a son avis, d'un ordre different de « 1'intelligence qui resulte des perceptions reunies des Elements » 58. II n'offrit pas d'expliquer 1'origine chez rhomme de ces facultes superieures, mais se contenta de faire remarquer leur existence. II serait absurde d'exiger de la theorie de Maupertuis qu'elle soit plus qu'une analyse formelle remarquable de quelquesuns des problemes de base par rapport au transformisme. Si Ton compare la richesse d'observations et d'exemples qu'on trouve dans VOrigine des Especes de Charles Darwin, aux ecrits de Maupertuis, ceux-ci paraissent bien na'ifs et un peu minces. Mais dans 1'histoire du probleme, son travail est de la plus haute importance. II n'est nullement exagere de dire qu'il reorienta toute la question de I'origine, de la diversification, de 1'adaptation, et du transformisme emergeant des etres vivants. Ses idees furent le point de depart des discussions de Buff on et de Bonnet sur ces problemes; elles influencerent Lamarck59, quelques-uines meme d'entre elles se retrouveront, ayant sans doute parcouru une route indirecte, dans la theorie genetique de pangenese de Charles Darwin, et dans sa theorie de la selection naturelle, comme dans la theorie de rhereditS par le souvenir, de Samuel Butler. En dehors de la sphere immediate de la biologie, sa notion d'ordre sortant du chaos et ses contributions a la « theologie naturelle » du transformisme, se trouvaient discutees avec acharnement par Voltaire, Diderot et d'autres 6crivains associes a 58. Ibid., p. 160*. 59. Cf. BRUNET, op. cit., pp. 166, 288-9, 326-36, et « La notion d'6volution dans la science moderne avant Lamarck », Archewn, Rome, XIX (1937), 37-43.

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1'Encyclopedic franchise 60. Des questions semblables devaient ressusciter lors de la potemique sur le darwinisme, an xix" siecle. Certes, Maupertuis ne trouva pas la solution du probleme, il ne decouvrit pas une thôrie satisfaisante du transformisme. II fallait toutes les preuves detaille'es de Charles Darwin pour convaincre les biologistes de 1'operation de la selection naturelle; et il fallait Mendel et la geneiique moderne pour eviter les difficult^ de Buffon et pour montrer comment les variations h&reditaires — les mutations — pouvaient etre preserves dans la race, et ne pas etre fusionnees de nouveau dans le type normal. Et on ne peut pas dire d'ailleurs que nous ayons encore trouve la solution de tous les problemes suscites par Maupertuis. Done, si nous pouvons retenir une des insultes de Voltaire, et admettre la description qu'il fait de son ancien ami comme « un vieux capitaine de cavalerie travesti en philosophe » 61, nous pouvons aussi voir le Philosophe du Roi, maintenant le chef de la cohorte evolutionniste, chevauchant avec une volonte plus tenace, et d'une maniere plus Elegante, que lors de Tattaque malencontreuse qu'il fit seul a la bataille de Molwitz.

60. La pensê de Maupertuis sur la theologie naturelle arrivait a exercer une influence importante. Dans son Examen de la preuve de I'existence de Dieu employee dans I'Essai de Cosmologie (Histoire de I'Academic des Sciences, Mtmoires Ann6e 1756, Berlin, 1758, pp.389-424), Maupertuis avait discute le caractere relatif des assertions mathe"-* matiques et metaphysiques, et avait refuse" k ces dernieres tout caractere de necessite. En consequence de ce m^moire, les Acaddmiciens de Berlin mirent au concours le probleme : « Les rente's metaphysiques sont-elles susceptibles de la m£me Evidence que les rente's mathematiques, et quelle est la nature de leur certitude? » Le prix alia a Moi'se Mendelsohn et Kant eut un accessit. C'est dans ce me"moire, ou 1'influence de Maupertuis apparait nettement, que Kant faisait pour la premiere fois sa distinction entre analyse et synthese, et il en resta toujours au point de vue critique y adopte. Voir MOSES MENDELSOHN, Abhandlung fiber die Evidenz in metaphysischen Wissenschaften..., Berlin, 1764. Le memoire de Kant suit, sans no,m d'auteur, pp. 67-99 : Untersuchungen iiber die Dentlichkeit der Grundsatze der naturlichen Theologie und der Moral, zur Beantwortung der Frage welche die Konigl. Akademie der Wissenschaften zu Berlin auf das Jahr i763 aufgegeben hat. Cf. Kant, Sammtliche Werke, &d. G. Hartenstein, Leipzig, 1867, II, pp. vii-vm, 281-309. 61. L'Art de Men argumenter en philosophic reduit en pratique par un vienx capitaine de cavalerie travesti en philosophe (1753), dans VOLTAIRE, (Euvres, XXIII, 581; cf. BRUNET, op. cit., I, 153.

19

The Public and Private Faces of Charles Darwin When Charles Darwin's elder brother Erasmus read The Origin of Species, he wrote off a letter of congratulations saying : «the d priori reasoning is so entirely satisfactory to me that if the facts won't fit in, why so much the worse for the facts is my feelings.1 Charles's response to this compliment is not recorded, but he must have been surprised. He had tried in his book to overwhelm the reader with facts. But his unscientific brother had been struck by one characteristic that indeed gave power to Darwin's argument : its highly theoretical form. A second characteristic that now strikes us ishe kind of explanation used. This cut through all the qualitative diversity that was making biological theory so unmanageable and aimed to be strictly quantitative and mechanistic. The fact that The Origin of Species succeeded in making evolution accepted while previous writers on the subject had failed has raised a problem for historians of science. Neither the idea of evolution nor the theory of natural selection to explain it was original with Darwin. How did he alone manage to convince his contemporaries? Some unsympathetic critics, in the nineteenth as well as the twentieth century, have looked for the answer in external circumstances. They have said that Darwin was lucky with his timing, that his book appeared just at the moment when his fellow scientists and the public were ready to accept it. They have also accused Darwin of playing up to public opinion, and of being unfair to precursors who had anticipated all his main ideas. To these unsympathetic explanations of his success Darwin himself made the obvious and just reply that scientists had been persuaded to accept evolution for good reasons and that it was in the main he who had persuaded them. He had spent over twenty years, virtually since his return to England in the «Beagle» in 1836, collecting evidence to test his theories. His organisation i. The Life and Letters of Charles Darwin, ed. Francis Darwin, London, 1887, ii. 234; see A.C. Crombie, Styles of Scientific Thinking in the European Tradition, ch. 24 (London, 1994).

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of the evidence was immensely superior to that of any of his precursors. He might have added that the history of science is littered with precursors — including many of those that became attached to himself — who became interesting only when someone after them succeeded where they failed. He could also have said thad effective originality consists not only in having ideas but also in knowing how to exploit their scientific consequences to the full. Darwin is one of the most interesting of all scientific authors for the modern reader because, in addition to his pleasant style, he was himself intensely interested in all these questions of scientific method and scientific originality that were involved in his work. For example he wrote to one of his sons in 1871 that he had been speculating about «what makes a man a discoverer of undiscovered things, and a most perplexing problem it is». He went on : aMany men who are very clever — much cleverer than discoverers —, never originate anything. As far as I can conjecture, the art consists in habitually searching for causes or meaning of everything which occurs. This implies sharp observation and requires as much knowledge as possible of the subject investigated*.2 Darwin did not formulate any systematic philosophy of science, any more than Newton did. Practising scientists rarely do. But both left a trail of informal evidence, especially when forced to justify particular scientific conclusions, showing how they actually used ideas and why they believed their explanations to be scientifically satisfactory and the alternatives unsatisfactory. The materials for studying these questions in Darwin's case are all available in his correspondence, note books and diaries as well as his published works. They throw considerable light not only on how his mind in fact worked, but also on how he came to make evolution scientifically acceptable. One of Darwin's main criticisms of his predecessors — not an entirely just one — was that they had relied too much on indirect evidence simply for the occurrence of evolution, without looking for an adequate explanation. So their conclusions remained superficial. He proposed a different approach : first to look for an adequate cause of evolution, and then to see whether this was able to account for the various different phenomina concerned. In the introduction to the Origin he made public a description of how 2. The Autobiography of Charles Darwin, ed. Nora Barlow, London, 1958, p. 164

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he ad set about this process of discovery. This leads us into the central problems of his intellectual biography and scientific method. In the famous opening paragraph of the Origin, Darwin presented himself as a thinker not at all corresponding to his brother's praise, but, on the contrary, slow to use ideas until forced to do so by patiently accumulated facts. He described how he ad been struck while on the «Beagle» by the geographical distribution of related animals in South America and the relation of living to fossil forms ; how he thought these facts might throw light on the origin of differences between species ; how, when he got home, he collected still more facts. Eventually, he wrote, «"After five years" work I allowed myself to speculate on the subject*. He added : «I have not been hasty in coming to a decision*. The picture built up is repeated elsewhere. «I worked on true Baconian principles*, he wrote in the Autobiography, «and without any theory collected facts on a wholesale scale*.8 To Joseph Hooker he wrote in 1844 that he was «determined to collect blindly every sort of fact* bearing on the problem. But, he admitted, «At last gleams of light have come, and I am at last convinced (quite contrary to the opinion I started with) that species are not (it is like confessing a murder), immutable*.* Now this was written in the same year that Darwin wrote the long Essay on evolution by natural selection of which part was to be read at the Linnean Society in 1858 together with A. R. Wallace's paper on the same subject. The Essay was based on an even earlier sketch. In many ways it is the clearest and most attractive presentation of Darwin's ideas. The Origin follows its argument closely, simply adding much more supporting evidence. So when Darwin wrote disingenuously to his friend Hooker about «gleams of light* having come, he had in fact already worked out his theory in full detail. No doubt Darwin chose to present this picture of his progress as a shield against the accusation that evolution was merely speculative. Certainly this was the usual current view of the idea. His published self-portrait also fitted in with some contemporary ideas on scientific method, especially those of J. S. Mill. It was a picture of a great discoverer that gave public satisfaction. But it 3. Ibfd., p. 119.

4. Life and Letters, ii. 23.

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was largely false. In his private thoughts Darwin was a very different character. Darwin's correspondence is notorious for the number of contradictory statements it contains. But from his letters together with the other evidence it is possible to build up a well-documented intellectual biography. One thing becomes immediately certain. ((Collecting facts to give us ideas*, as Buffon had once put it, was the reverse of Darwin's method. «How odd it is*, he wrote to a correspondent in 1861, «that anyone should not see that all observation must be for or against some view if it is to be of any service!*5 In 1857 he wrote to Wallace: «I am a firm believer that without speculation there are no good and original observations*.8 «Let theory guide your observations*, he wrote with pleasant candour to another correspondent, «but till your reputation is well established, be sparing in publishing theory. It makes persons doubt your observations*.7 His son Francis, who worked as his assistant during his last years, confirms this picture. He wrote that his father «often said that no one could be a good observer unless he was an active theoriser. This brings me back to what I said about his instinct for arresting exceptions : it was as though he was charged with theorising power ready to flow into any channel on the slightest disturbance, so that no fact, however small, could avoid releasing a stream of theory, and thus the fact became magnified into importance. In this way it naturally happened that many untenable theories occurred to him ; but fortunately his richness of imagination was equalled by his power of judging and condemning the thoughts that occurred to him*.8 To be overflowing with ideas is surely the basis of all great originality, whether in the sciences or the arts. Darwin's main problem was not to get ideas, but to give his ideas effective scientific form in which they could be tested. The autobiography of Darwin's discoveries shows that he was driven to them all by his gifts for active speculation. Without those gifts he might have remained simply an inspired naturalist, a collector of unexplained information. He describes in his Autobiography his intense satisfaction as a boy with Euclid's clear 5. More Letters of Charles Darwin, ed. Francis Darwin and A. C. Seward, I/ondon, 1903, i. 195. 6. Life and Letters, ii. 108. 7. More Letters, ii. 323.

8. Life and Letters, i. 149,

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geometrical proofs and later with the logical form of Paley's Evidences for Christianity. Shortly before he sailed in the «Beagle» he was much struck by an incident with Adam Sedgwick, Professor of Geology at Cambridge, with whom he went on a geological investigation in North Wales. A labourer at Shrewsbury had shown Darwin a typically tropical shell found in a local gravel pit. He told Sedgwick, but Sedgwick merely said that someone must have thrown it there. He added that if it really did belong to the area «it would be the greatest misfortune to geology, as it would overthrow all we know about the superficial deposits in the midland counties*.9 Nothing before, Darwin wrote, had ever made him so thoroughly realise that science consists of a structure of laws and generalisations. Another experience on the same trip struck him later. Sedgwick was looking for fossils. Neither of them noticed the evidence of glaciation that is so characteristic of the area — a striking instance, as he said, of how easy it is to overlook phenomena, however conspicuous, if you don't expect them. It was in geology that Darwin first learnt to be a scientist. When he sailed in the «Beagle» in December 1831 he had had no proper formal training in any scientific discipline. This was not unusual at the time but it was at first a considerable disadvantage. The piles of papers he brought back describing rough dissections made on the voyage were almost useless. But he describes how having to work out the geology of an unknown area taught him the necessity of reasoning in advance and using predictions to guide his observations. He worked out his whole theory of coral reefs, which cleared up the whole question, on the west coast of South America before he had ever seen a true coral reef. Only when the «B eagle* crossed the Pacific was he able to test the theory by examining actual reefs. Darwin's note books show that his work on evolution began in the same highly speculative spirit. Like many great innovators, like Kepler and Galileo with the new cosmology, he became convinced himself long before he had enough evidence to convince others. He first considered the question at the very beginning of his serious work as a biologist, when the «Beagle» called at the g. Autobiography, pp. 69-70. 10. Charles Darwin and the Voyage of the Beagle, ed. Nora Barlow, London, 1945, pp. 246-7.

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Galapagos Islands in 1835." He was then twenty six. His attention, as he said later, was aroused by the way the animals and plants varied slighttly from island to island of this group. In 1837 he opened his first note book on atransmutation of species*,11 and wrote that the Galapagos species and the South American succession of fossils related to living forms were the origin of all his views. In this note book he speculated optimistically on the unexplained phenomena evolution would be able to explain, and described the form of theory that would give the explanatory power he was seeking. He shows that he was looking for a theory in which the whole production of all past and present organic forms could be shown to follow from given laws on the model of Newton's theory of gravitation. This was before he had any clear idea of what the laws of evolution might be. Thus he wrote : «let attraction act according to certain law, such are inevitable consequences — let animals be created, then by the fixed laws of generation such will be their successors*.12 These «laws of change* would then become «the main object of study, to guide our speculations*. Again and again in his writings he was to take Newtonian mechanics as the model for a scientific explanation. He had already by 1837 connected the problem of extinction with that of adaptation. Then in 1838 he read Malthus on the pressure of population against the means of subsistence. So, he concluded a famous autobiographical passage, «it at once struck me that under these circumstances favourable variations would tend to be preserved, and unfavourable ones to be destroyed. The result would be the formation of a new species. Here, then, I had at last got a theory with which to work*.13 For the public he was writing at this time, in the Journal of Researches, in terms of old concepts such as the uniformity of action of the «creative power* in producing similar organisms in a given area.14 The prodigious labours in collecting facts to which Darwin dedicated the rest of his life all stemmed from this new theoretical source. Far from working ablindly*, «without any theory* — as 11. Life and Letters, ii. 5-8, i. 276; CHARLES DARWIN, Journal of Researches, London, 1839, pp. 474-5; Autobiography, p. 118; CHARLES DARWIN and A. R. Wallace, Evolution by Natural Selection, ed. Sir. Gavin de Beer, Cambridge, 1958, pp. 5-6, 25-26. 12. Life and Letters, ii. 9. 13. Autobiography, p. 120. 14. Journal of Researches, pp. 212, 469, 474,

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if that were possible! — all his observations bore on very precise questions. The whole point of the vast labour he undertook in collecting facts about the selection of domesticated varieties of animals and plants by breeders was in order to explore the hypothesis that tnatural selection* had produced natural species and evolution by an extension of the same process. As he wrote : tl assume that species arise like our domestic varieties with much extinction ; and then test this hypothesis bv comparison with as many general and pretty well-established propositions as I can find made out — in geographical distribution, geological history, affinities, etc. ...».15 And «this seems to me the only fair and legitimate manner of considering the question — by trying whether it explains several large and independent classes of facts*.1" Far from being the classical example of a «Baconian» he tried to paint himself, Darwin appears as an almost extreme exponent of speculative thinking. In modern jargon the form of his thought might be called «hypthetico-deductive» or «retrodictive». He became puzzled by various observations and always used hypotheses to probe the question with further observations. The test of his hypothesis of evolution by natural selection was its range of application. He laid it out in the Origin like a legal argument, showing why its premisses must be acceped and what followed from them, stating the difficulties of the theory and demolishing them one by one. He concluded that a theory that explained so much could not be false. Besides the form of Darwin's argument, the second characteristic that strikes the modern reader is liis conception of the kind of material explanation of evolution that would de scientifically satisfactory. This aspect of his discussion of evolution was a contribution to biological thought as important as natural selection itself. Biology at that time was a field of confused issues. Natural theology and untestable ad hoc notions about innate organic drives towards improvement were mixed up with testable, analytical science. Darwin, and Wallace independently, made explicit the criteria of scientific explanation by which they judged all attempts to account for the facts. They took their stand on the model of physics and aimed to be strictly mechanistic. In contrast with 15. Life and Letters, ii. 78-9. 16. CHARLES DARWIN, Variation of Animals and Plants under Domestication, and ed., London, 1875, i, 9.

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biology, physics consisted of theories and laws that were testable, allowed no discontinuities in their field of explanation, and eliminated mysteries. Darwin comparied his treatment of natural selection with contemporary physicists' treatment of theories of gravitation, light and the ether. The theory of evolution by natural selection required two sets of laws : laws of heredity and variation, and laws of survival. Darwin and Wallace contributed the second, and for their law of natural selection they took an idea from the social sciences and organised it on the phvsical model. Natural selection was a statistical law of the redistribution of matter and energy among competing consumers. It showed how increasing order would be automatically generated from unordered variations by the operation of purely mechanistic principles. Wallace compared its action to that of the governor of a steam engine. Thus the built-in responses of a Cartesian mechanism would lead it to multiply, evolve and inhabit the earth. Darwin and Wallace each argued that natural selection, like a physical law, offered a sufficient and testable explanation of all the facts. Thus if it were confirmed no other kind of explanation would be necessary. Darwin has recently been criticised because in face of one large difficulty, concerning the first set of laws required by his theory of evolution, he later retreated from this position. According to the views on heredity and the best reasoning then available the mathematical odds against successful variations being transmitted were overwhelming. He felt himself forced to admit that hereditary variations might be produced by the direct action of the environment, thus giving evolution a direction independent of natural selection. Perhaps it was weak of him to make this retreat. But it is asking a lot to expect him to have guessed that the theoretical solution to his problem lay behind an innocent-looking title in the Royal Society Catalogue of Scientific Papers : «Experiments in Plant Hybridization» by Gregor Mendel. When we remember the state of biological theory, in the first half of the nineteenth century, it is easy to appreciate the force of Darwin's remark that the chief obstacle to the new ideas was that «of looking at whole classes of facts from a new point of view». Yet he also admitted that biologists were waiting for a theory in which all the diverse facts that were being accumulated would fall into place. oLooking backs, he wrote to Sir Charles Lyell on reading the last proof sheet of the Origin, «I think it was more

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difficult to see what the problems were than to solve them». 17 The problem as he saw it was to make evolutionary theory quantitative and predictive. Natural selection is still supported by far less direct evidence than most contemporary physical theories. But few biologists would deny its potential explanatory power. Not the least part of Darwin's intellectual success was that he knew what he was doing. Perhaps the most deceptive thing about his intellectual biography is that he reached his main conclusions so early. He was fifty when the Origin was published, but he knew the kind of evolutionary theory he wanted by the age of twenty-eight and wrote out his first sketch of it at thirty-three.

17. Life and Letters, ii. 170,

The best part of human language, properly so called, is derived from reflection on the acts of the mind itself. (Coleridge, Biographia literaria xvii)

20

The Language of Science

May I say first how honoured I am to be invited to participate in this Forum, and at the same time how alarmed I feel at doing so 'dans 1'espace francophone', with all the accompanying hazards for someone whose native tongue is English. I should like to say also that I am, as for myself, entirely in sympathy with the aim of the Forum 'de montrer la vitalite de la science dans 1'espace francophone', except that I should put the question differently. The vitality of scientific thought in French is after all evident to all the world. The practical problem is rather that of maintaining the language as a medium of communication in a world increasingly, and it seems unstoppably, dominated by English. This has great dangers for English itself, which risks becoming disintegrated into a diversity of dialects scattered round the globe, as classical Latin was disintegrated after the fall of the Roman empire into the different Romance languages of Europe. The beauty and sophistication achieved by these languages, pioneered by Italian and reaching a new dominance with French, may seem to offer some hope for a disintegrated English; but only after many, many generations. I hope that at least in Europe we will find a different solution which will maintain our languages more or less as they are. I believe that a monoglot Europe would be a cultural disaster, and that thought of all kinds, including scientific, would be enormously impoverished by having effectively only one language. A language after all embodies and expresses a way of thinking, the perspective of a whole cultural experience. To translate that perspective from one language into another requires far more than knowledge simply of the languages themselves, as anyone who tries to translate even between English and French very soon discovers. There are of course great practical problems, in the world as it is becoming, both for French and for English and indeed for other major languages. Events tend to go the way of least resistance. We must keep our nerve. Concerning more specifically the subject of this Table ronde, I shall comment briefly, and inevitably impressionistically, on some historical relations between language and scientific thinking and their changes. History illuminates the present and no doubt the future, and we must take a long view. When we speak today of natural science we mean a specific vision, created within Western culture, at once of knowledge and of its object, at once of

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science and of nature. We can trace this vision to the commitment of the ancient Greek philosophers, mathematicians and physicians, for whatever reason, to the decision of questions by argument and evidence as distinct from custom, edict, authority, revelation, rule-of-thumb or whatever else. In this way they developed the notion of a problem as distinct from a doctrine, and they initiated the history of science as the history of argument in a search for principles at once of nature and of argument itself. They discovered two fundamental principles from which the essential style of Western scientific thinking has followed: those of exclusive natural causality, and matching that of formal proof. The marvellous and fascinating scholarship which during recent decades has so much enriched our knowledge of other major ancient cultures has not, so far as I can see, revealed there a grasp of these principles, whether in Babylon or Egypt, India or China, or Central America. They had impressively ingenious and inventive technologies, including highly original mathematical technologies as in Babylonian arithmetic and astronomy, in an ambience of myths scarcely related to technical knowledge. In Western terms they had no system of rational science. The idea that the style of thinking arises from the intellectual and moral commitments which provide the expectations, dispositions and memories of a culture in an invitation to treat the history of science as a kind of comparative historical anthropology of scientific thinking. This must be concerned before all with people and their vision; we must learn to look at once with and into the eye of the beholder. Styles of thinking and making decisions, established with the commitments with which they began, habitually endure as long as these remain. Hence the structural differences between different civilisations and societies and the persistence in each of a specific identity, continuing through all sorts of changes. It is an important question, as we look at the westernisation of the globe, to ask at what levels general moral and intellectual commitments are altered, and what remains the same. Restricting the question to an historical anthropology only of Western science, language is an indispensable guide both to theoretical ideas and to real actions. Any language embodies a theory of meaning, a logic, a classification of experience, a conception of perceiver, knower and agent and their objects, and an apprehension of existence in space and time. We need to ask how language conditioned scientific thinking and was in turn altered by it. We may distinguish three levels: those of the structure of a language itself, of general conceptions of the nature of things expressed in it, and of particular theories. The language of causality for example is closely related to conceptions of causality. It is hard to say which came first, but there is an obvious structural conformity between the grammar of subject and predicate found in all European languages, and the ontology of substance and attribute developed most systematically by Aristotle. Aristotle's logic imposed on Western science for many centuries a form of demonstration, relating cause to effect as premise to conclusion, expressing this grammar and ontology of subject-predicate, substance-attribute. His conception of causality was structural and non-

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temporal and was focused on the definition, which explained both the behaviour and the existence of something by its defining attributes. Parallel to this the Greek mathematicians exploited the speculative power of geometry by imposing upon the phenomena at once its deductive logic and an appropriate geometrical model delineating for each its form in space. Thus they reduced the phenomena of visual perspective to the properties of the straight line and the angle, of astronomy to the properties of the sphere, of mechanics to the relations of weights determined by the properties of the straight line and the circle. They could then develop their immediate research into the phenomena purely theoretically within the model itself. The geometrical conception of causality was again structural and nontemporal, focused on space and place, not on the sequence of events in time. These conceptions, and specifically Aristotle's logic of subject and predicate, were to become a major obstacle to the medieval and early modern natural philosophers and mathematicians of Latin Christendom who, in a different intellectual context, came to develop a new conception of causality based not on static structure by on rates of change. They came to express causality in the language not of subject and predicate but of algebraic functions, and they devised a new Latin terminology to express such fundamental quantities as velocity, acceleration, instantaneous velocity, and so on. These quantities were defined in the fourteenth century by mathematicians in Paris and Oxford, and their terminology was to be used by Galileo and Newton. This new functional causality of classical physics related events as sequences in time brought about only by contact or through a medium or field; the disputed choice between these was based on wider ontological beliefs. Starting with Roger Bacon causality came to incorporate a theology of laws of nature laid down by the Creator: for as Dante put it 'dove Dio senza mezzo governa, la legge natural nulla rileva (where God governs without intermediate the natural law has no relevance)' (Paradiso xxx. 122-3). Created law reestablished the stable predictability of nature within Hebrew-Christian doctrine. Newton was to combine this theology with Euclid in calling his fundamental dynamical principles 'axioms, or laws of motion' (Principia mathematica). Such language clearly arises not from the interior of natural science but from its intellectual context. Must science in different linguistic cultures always acquire differences of logical form, and must a language always impose its ontological presuppositions on the science developing within it? The technical language of science has often been developed partly to escape from just such impositions, and to detach a specific scientific meaning from misleading analogies coming from its source in common vocabulary. The word current', wrote Michael Faraday, 'is so expressive in common language that, when applied in the consideration of electrical phenomena, we can hardly divest it sufficiently of its meaning, or prevent our minds from being prejudiced by it' (Experimental Researches in Electricity, i, London, 1839, p. 515). With the aid of William Whewell he devised a new terminology to fit the exact context of electro-chemistry, for

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example replacing the word 'pole', inconveniently suggesting attraction, with the neutral 'electrode'. From the fourteenth century radically new technical languages were gradually built up, precisely symbolised first for mathematics and music. From the end of the fifteenth century the mathematical symbols +, — , x, -f-, > , < , , / , = etc. came into use to represent operations or relations previously written out in words. Later in the seventeenth century Francois Viete began to systemise the essential general principle of modern algebra by designating quantities by letters, distinguishing knowns, unknowns, powers and so on. Thus was launched the universal numerical language of mathematics, and during the same period that of music, both transcending all national boundaries and transparently comprehensible within their explicit limits. Their message was precision and economy, but of course precision alone is useless without content, which comes from scientific or artistic imagination. This depends on vision beyond such limits, and it is vision controlled by a precise critique that establishes, usually in advance of any particular research, the kind of world that is supposed to exist. This in turn established the kind of explanation in science, and presentation in art, that will give satisfaction because the supposedly discoverable has been discovered. But all this needs to be expressed in our natural languages, and that leaves our problem there just as I indicated at the beginning of these brief comments. Note: see my Styles of Scientific Thinking in the European Tradition (London, 1994).

21

Some Historical Questions about Disease

Under this very general title I want to talk briefly about the relations between medical science, the medical art of healing, and conceptions of disease. But first it may be helpful to put this question within a much larger context of what we may call a comparative historical anthropology of science and medicine, focusing on people and their vision, and their circumstances both human and physical.* The central history of science as I see it is the history of argument: an argument initiated in the West by ancient Greek philosophers, mathematicians and physicians in their search for principles at once of nature and of argument itself. Of its essence have been periodic re-assessments, varying considerably in different historical contexts, of its presuppositions about the nature of what exists, about scientific cogency and validity, and about the intellectual, practical and moral justification of the whole enterprise. Of its essence also have been its genuine continuity, even after long breaks, based on education and the study by any generation of texts written by its predecessors; and its genuine progress both in scientific knowledge and in the analysis of scientific argument with its various logical, experimental and mathematical techniques. It has been a subtle historical question to assess what has continued through different periods and societies and what has changed. We can characterise the vision and the circumstances of people at different times and places by what we may call their commitments. It is their intellectual and moral commitments, involving their expectations, dispositions and memories, that give to people their vision and their style of thinking and of making decisions. We can distinguish two kinds of intellectual commitment in the history of science: 1 Commitments to conceptions of nature and its knowability to man, within the context of general beliefs about the nature of existence, and of man in See A.C. Crombie, Styles of Scientific Thinking in the European Tradition (London, 1994) with 'Historical Commitments of biology', The British Journal for the History of Science, iii (1966) 97-108, 'Historical Commitments of European Science', Annali dell'Istituto e Museo di Storia delta Scienza di Firenze, vii. 2 (1982) 29-51, 'Pari sur le hasard et choix dans 1'incertain' in Medecine et probabilities, ed. A. Fagot (Paris, 1982) 3-41; and for various questions indicated below Hippocrates, ed. W.H.S. Jones, i (London and New-York, 1923), P. Lain Entralgo , Mind and Body: Psychosomatic Pathology (London, 1955), La Historia Clinica, 2nd ed. (Barcelona, 1961), O. Temkin, 'The Scientific Approach to Disease: Specific Entity and Individual Sickness' in

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mental and bodily health or disease: such conceptions tend to be strongly conditioned by language. 2 Commitments to conceptions of science, that is of scientific methods of argument, inquiry and explanation. From the interaction of these two intellectual commitments come the perception of problems, as distinct from doctrines; conceptions of acceptable questions to put to a subject-matter as well as of acceptable answers; and to a considerable extent the direction of attention and inquiry towards certain types of problems and of solution and away from others. They establish in advance the kinds of problem that will be seen and so they foster certain kinds of discovery, and at the same time they establish the kinds of explanation that will give satisfaction because the supposedly discoverable has been discovered. Scientific change comes from a combination of scientific experience, especially of failure, with rethinking of basic principles, again with a deep involvement of language. Any language itself embodies a theory of meaning, a logic, a classification of experience in names, a set of presuppositions about exists or seems to exist behind experience. Language mediates man's experience of nature and of himself; hence philology, both of traditional languages and of the technical languages of the sciences and arts (given precision in symbols first in mathematics and music), can be an indispensable guide to theoretical ideas and real actions. 3 A third kind of commitment giving people their vision is to conceptions of what is desirable and possible, in view of evaluations of the nature, purpose and circumstances of human life. Such commitments concern right human action, what should and can be done, both morally, and scientifically and technically in the sense of being capable of achieving their ends. To this kind of commitment are linked dispositions, both of individuals and of societies, generating habitual responses to events: dispositions to expect to master or to be mastered by events, to change or to resist change both in ideas and in practices, to accept or to reject the possibility of truth within supposed error and hence to integrate within reasoned argument both agreement and disagreement. Here education and experience can furnish options for the choice of a different future. 4 Besides these three kinds of intellectual and moral commitment giving people their vision there is a fourth kind of commitment involving their circumstances. This is the commitment to the physical and biological environment in which they find themselves: they may try to change it, but first it is given. A comprehensive comparative historical anthropology of science and medicine would address itself to questions at the different levels indicated by Scientific Change, ed. A.C. Crombie (London, 1963) 629-58, T. McKeown, The Rise of Modern Population (London, 1976), W.H. McNeill, Plagues and Peoples, (Oxford, 1977), M.D. Grmek,

Some Historical Questions About Disease

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these commitments, some given by nature, some made by man. Thus at the level of nature there is historical ecology: the reconstruction of the physical and bio-medical environment and of what people made of it, from both written records and physical remains, as in striking recent work on palaeopathology, palaeodemography, palaeobotany, and the history of climate. Reconstruction at the levels of people and their vision requires the exegesis of evidence including in its scope religion, law, politics and so on far beyond simply scientific thought. At all levels historical questions demand in the historian exact scientific and linguistic knowledge (as well as much else of the intellectual, visual and other sorts of culture that mediate human experience) to enable him to control the view of any present recorded through the eyes and language of those who experience it. It does not have to be demonstrated here that the road to understanding of our human condition at any time, including the present, lies as much through the study of history as through that of the nature and people immediately in front of us. This is as true of scientific and medical thinking and practice as it is of any other of our activities and habits. Styles and forms of thinking and behaving become established with the commitments with which these began and they persist as long as they remain. Hence the structural differences between different civilisations, cultures and societies. Of course there is development, change and occasionally revolution, but more often than not retaining a structural similarity throughout from habit and education. One may cite the persistent differences between China and Europe, and the persistent similarities between Russia before and after 1917. Hence the need for an historical dimension for a true perception of ourselves as human beings in all our cultural diversity, and for an educated understanding of change itself. This, like most human behaviour, begins in the mind. I come now to medical science, medical art, and conceptions of disease. We may start with the definition of medicine given in the Hippocratic Epidemics (i. 11): The art consists of three things: the disease, the patient and the physician. The physician is the servant of the art. The patient must help the physician to combat the disease'. The historian must study all three. They present the subtle question of the relation of medical science to medical art, with goals that are different, but intricately tied together. Medical science aims through the analysis of its subject-matter at theoretical understanding to be expressed in general statements. Since antiquity it has been concerned with two main activities: (1) the observation and recording of regularities of symptoms and their course through the duration of diseases: this is found in the case-histories developed by Egyptian and Babylonian physicians; but the whole method was transformed by (2) the search for causes, introduced by the Greeks under the name of Hippocrates. The Greek

Les Maladies a I'aube de la civilisation occidentale (Paris, 1983), A. Fagot-Largeault, L'homme bio-tthique (Paris, 1985).

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physicians, in accordance with their general habit of mind, madephysiologia, knowledge of nature, essential to the science and art of medicine. There was really no general conception of nature before the Greeks, anyhow in the Western ancient world. There was an often detailed discernment of empirical connections and regularities, in medicine as in astronomy (which involved sophisticated mathematical predictions), but no conception of nature as a system of exclusive natural causality, and no associated form of argument for demonstrating causal connections by an explicit logic. 'Each disease has a natural cause' wrote the author of the Hippocratic Airs, Waters, Places (§ 22), 'and nothing happens without a natural cause'. With the Greek search for causes in medicine came the concept of the natural norm (e.g. the balance of the four Galenic humours), after all an abstraction, and of disease as deviation from that norm. Causes of disease came to be conceived of as of two kinds: (1) physiological disturbances of the body or psychological disturbance of the soul arising from within; and (2) effects on the patient of external agents. Conceptions of these two kinds of cause, whether of internal disturbances or of agents that may invade the body as specific entities, have provided the substantial programme for Western medicine ever since. Diseases are identified and distinguished by the regular appearance of specific symptoms, given names, and allocated causes within current medical theory. This raises historical questions of its own in the identification of diseases recorded from the past. Some like Thucydides's plague of Athens correspond in symptoms to no known current disease, while others like diptheria, bubonic plague and smallpox have persisted through the centuries with recognisably the same diagnostic symptoms, which became attributed to persisting specific microbial pathogenic agents. Medical art by contrast with science aims not at generalities by at restoring and preserving the health of particular individuals. To do that of course it has used the results of medical science, but it cannot treat an individual patient as simply an example of general phenomenon. It is concerned with an individual person who is unique and irreplaceable by any other person. It shares this concern rather with the traditional religions than with analytical science. Where it differs is in the means. Its relation to medical science is like that of other practical arts, aiming at the composition of an effect, to their corresponding sciences: of painting for example to optics, or of the gaining of political ends to the analysis of rhetorical manipulative skills. Here the complexities begin. A politician acting with no regard to truth may still provide for the public good; a physician acting on his best understanding of scientific theory may propel his patients to disaster; while desired effects may be produced with what may seem to be no real understanding of causes, as for example by traditional Chinese or Indian medical practices and by Western psychiatry. Theories of disease have obviously affected treatment and are not neutral or innocent, whether physicians looked like Thomas Sydenham for specific drugs to act on specific diseases as Cinchona acts on malaria or for specific remedies as did Edward Jenner and Louis Pasteur, or they insisted as


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did others like Francois Broussais and some modern physicians dealing with degenerative disorders and neuroses that diseases are abstractions and that it is the patient who has to be treated. It is the perception of the unique and responsible human individual that has given rise to the ethical questions of Western medicine. People who saw their lives within at once a physical and a moral cosmology took corresponding attitudes to disease and calamity and choice of all kinds, stressing natural causation or moral responsibility according to their beliefs. Job saw his ailments within an entirely moral context and complained because, as a just man, he should be so unjustly afflicted. In the ancient world there was an immediate contrast between Greek medical thinking, which might reduce sin to sickness, and Hebrew moral thinking reducing sickness to sin. This contrast continued through the Christian middle ages, and it persists in some legal attitudes to crime, and in the whole conception of diminished responsibility as a pathological as distinct from a moral phenomenon. Boundaries have been drawn differently in different periods and circumstances between the normal and the abnormal: for example deaf-mutes were classified as imbeciles until it was discovered by science in the seventeenth century that they were dumb because they could not hear. Again personal attitudes to suffering and death through illness, as to hard decisions like that of Thomas More which could lead only to martyrdom, have differed fundamentally according to general beliefs about human existence and its purpose. It made a difference whether the prospect was Christian hope or simply extinction, and whether ultimate death was of the body or of the soul. It was through the form of argument and procedure developed through the Hippocratic case-history, then the recognition of statistical regularities, and eventually the clinical trial, that medical art and science found a way to come together to relate individual illnesses to the general explanations reached by scientific analysis. The Greeks remained purely qualitative in the regularities they observed and the prognoses made from them. It was in the different practical circumstances of the commercial expansion of late medieval Europe that mainly Italian mathematicians began to grasp the idea of quantitative expectation for such purposes as insurance and the division of profits. In the seventeenth century Blaise Pascal, Christiaan Huygens and Jakob Bernoulli showed with great mathematical sophistication how, from the regular numerical frequencies present in adequate numbers of things, to stabilise uncertain expectations as probabilities. This offered a new mastery of rational choice and action in a whole range of subject-matters, from the sciences of nature to commerce and politics. In medicine John Graunt in his Natural and Political Observations . . . made upon the Bills of Mortality (1662) set out explicitly the fundamental discovery that statistical regularities appeared in large numbers of things which were lost in small numbers. This was a phenomenon new to science whose recognition came to transform scientific thinking. Starting from the records of births and of deaths with their symptoms kept for London for over half a century, Graunt arranged for a further regular recording of

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information about all diseases and related data in the area, insisting that his helpers should record only observed symptoms and other facts and should ignore opinions, medical or otherwise. He saw that stable mortality rates, sexratios etc. could be translated immediately into approximate probabilities a posteriori. This then provided for inferences in two directions: directly to the probability of a possible event coming about, and conversely to the probable causes of events already brought about. In this way he made an analysis of the proportions of deaths in a population to be attributed to different causes, distinguishing chronic or endemic diseases from epidemic diseases, and so on. The next century and a half witnessed through the work of Buff on, Daniel Bernoulli, Thomas Bayes, Laplace and many others an elaboration and sophistication of statistical analysis and theory of probability without which the quantitative study of disease would scarcely have been possible. This began seriously with the institutional facilities provided by the modern hospitals of the nineteenth and twentieth centuries. Here, by means of new techniques of medical examination, quantitative data were accumulated for describing individual illnesses in new and precise detail; by observing many cases of the same disease standards and limits of normality were established; clinical symptoms were related to physiology and pathology; a scientific taxonomy of disease was developed. All this followed from a statistical approach to the normal and the abnormal, and it led eventually to an experimental approach to clinical science. The science and art of medicine would scarcely be what they are now without the controlled therapeutic trial for exploring the actions of drugs, and the statistical methods that have revealed such hitherto obscure connections as that between smoking and cancer. The essential scientific insight came here from R.A. Fisher's book The Design of Experiments (1935). I will conclude with three final historical questions. (1) The appearance of disease as recorded historically must always depend on the eye of the beholder: we must then examine the credentials, beliefs and methods of observation of the witnesses who describe and identify diseases, as well as the symptoms they describe. Likewise we must examine the eye of the modern historian: we are inevitably alerted to phenomena of the past by current interests, and that also we must monitor critically. The same applies to high modern technology: could quantitative epidemiology itself invent diseases existing only it its own results? (2) Our enthusiasm for medical science, with its fascinating intellectual problems, can blind us to more mundane aspects of medical history. For example the death rate in England, where full records have been kept from the beginning of the eighteenth century, declined steadily from that time, but the discoveries of causes of disease and the therapies introduced over two centuries had no general effect on that steady decline before the general use of sulphur drugs and antibiotics about fifty years ago. The cause of the decline was not medical science but hygiene (town drains, water supply), improved general nourishment, and public health. This might have some bearing on some developing countries and groups in industrialised


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counties now afflicted with AIDS. Like most aspect of human behaviour, the problem begins in the mind. There is a case for making intensive studies both of the historical ecology and of the historical anthropology of Africa, which presents special problems for historical investigation because of the relative lack of documentary evidence. (3) Lastly this: the self-critical European tradition, which includes science and is unique among the cultures of the world, has generated a capacity, albeit often uncertain, to see Western values through alien eyes and all in comparison with each other. Hence Western anthropology, and historiography of thought of many kinds and in many contexts and periods. To do this is of course an immensely difficult exercise in critical imagination, empathy and reasoning. We may the more easily grasp other mentalities by exploring the scientific origins and development of our own from the Greek search for principles at once of a subject-matter and of argument about it. A true comparative intellectual anthropology must look not only with, but also into the eye of the beholder.

The choice: to be conscious participants in, or victims of, historical tradition.

22

Historians and the Scientific Revolution

To a generation made more aware than any previous one of the division between science and the humanities, there is a particular interest in the treatment of the ' Scientific Revolution' by the earliest modern historians who discussed the history of science!. As observers living during or just after the event, writers of ' philosophical history' from Francis Bacon to Voltaire set out to give a systematic account of the meaning, for an educated person, of the scientific movement as a revolution in ideas, methods and attitudes. They had inherited the techniques and conceptions of the historical discipline that had been developed by scholars since the fifteenth century, contemporaneously with modern science itself, and they used them to show how science had emerged in the history of civilization. In doing so, they gave analyses both of the nature of scientific thought itself, as they saw it, and also of the conditions that favoured or discouraged its progress, that have left their mark on subsequent conceptions of the history of science down to the present day. The writer who summed up the whole of this early conception of the scientific revolution as an historical event was Voltaire2. A product of the 1 An earlier version of this paper was published in «Endeavour», xix (1960) 9-13. On the historiography of science, cf. also O. Temkin, An essay on tbt usefulness of medical history for medicine, ^Bulletin of the History of Medicine*, xix (1946) 9-47, The study of the history of medicine, «Bulletin of the Johns Hopkins Hospital*, civ (1959) 99-106, and Scitntfic medicine and historical research, ^Perspectives in Biology and Medicine*, iii (1959) 70-85; F. N. L. Poynter, below, n. 28; H. Butterfield, below, n. 20; A. C. Crombie, Science, Optics and Music in Medieval and Early Modern Thought, chs. 1-2 (London, 1990) and Styles of Scientific Thinking in the European Tradition, chs. 1-2, 22 (London, 1994). 2 Cf. J. H. Brumfitt, Voltaire Historian (Oxford, 1958); G. Lanson, Voltaire, 5eme ed. (Paris, 1924).

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age in which both modern science and modern historiography reached maturity, Voltaire was not only the first systematic historian of civilization and the first to make extensive use of the comparative method, but also the first historian to treat the history of science systematically as part of the history of civilization. In this, his conception of history stands in striking contrast with that of nineteenth-century historians, who concentrated their attention almost entirely on political and constitutional events, a limitation from which historians have by no means yet entirely freed themselves. Voltaire became known on the Continent as the most influential popularizer of Newtonian physics and of English empirical philosophy. He interpreted the scientific movement to educated Europe and projected it in a conception of history that, in spite of criticisms to which it is open both in general and in particular, still forms a recognizable part of the historical outlook of a large part of the educated Western world. The view of the scientific movement that Voltaire incorporated into his systematic reconstruction of history came in the first place largely from the publicists of contemporary science, especially Francis Bacon and Fontenelle, and from the great scientists themselves. But he also made use of a view of history that had originated with the humanist historians of fifteenth-century Italy and had become modified by science, during the seventeenth century, in the controversy between the Ancients and Moderns. Voltaire presents a picture of the historical consciousness of an age in which all educated people shared a common background in the humanities and in which the ' new philosophy', of experimental and mathematical science, had recently become established as an essential part of general culture. He gave expression to what many thought, or were ready to think. The view of history into which all the early modern historians fitted the origins of modern science was based on a specific conception of a great revival in European civilization between the fifteenth and the seventeenth centuries. This conception not only established a periodization of history, into Ancient, Medieval and Modern, that has become conventional; it made value judgements and offered explanations of the course of events that carried with them formulae for future advance. By Voltaire's time the conception had gone through three main stages of development: humanist, religious, and scientific. The concept of a renaissance in the fifteenth century, after a thousand years of ' dark ages' following the fall of Rome, was developed during the period of the Renaissance itself3. In the fourteenth century Petrarch, 3 See W. K. Ferguson, The Renaissance in Historical Thought: Five centuries of interpretation (Cambridge, Mass., 1948); H. Baron, The Crisis of the Early Italian Renaissance, 2nd ed., i (Princeton, 1966).


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inspired by a romantic admiration for pagan Latin literature, the city of ancient Rome, and the ideal of republican virtue, had divided history into 'ancient' (antiqua) — before Constantine's adoption of Christianity, and ' modern ' (nova) — the long succeeding period of barbarism and ' darkness ' (tenebrae) that had continued to his own time. From the end of the fourteenth century, humanist historians of art and of the Italian city states, especially of Florence, added to this periodization the notion of a recent revival, the beginning of which they often placed in the thirteenth century. The term ' middle age' (media tempestas) was introduced in the fifteenth century in Germany in reference to Nicholas of Cusa4. From the first, this conception of antiquity, a middle period of barbarism, and a recent revival was far from merely descriptive; it made an historical judgement that influenced contemporary action. For example, the fifteenth-century Florentine historian Leonardo Bruni, who first explicitly used this periodization in political history, made the recent political progress of his city an explicit revival of the model of republican Rome. In 1483 Flavio Biondo, a papal secretary and student of the monuments of ancient Rome, defined the chronological boundaries of world history, with A.D. 410 to A.D. 1410 as a period different from those preceding and following it. Other Italian historians, especially Machiavelli, were even more precise in their use of history for contemporary political purposes. Similarly, historians of the arts, in presenting the contemporary development of painting, sculpture and literature as a revival of classical models, wrote to encourage the new styles. They knew little and cared less about medieval Latin literature and the Gothic art beyond the Alps. For example Filippo Villani, writing at the end of the fourteenth century, mentions no poets for nine centuries before Dante and no artists before Cimabue, who recalled art to nature, and Giotto, «who not only can be compared with the illustrious painters of antiquity but surpassed them in skill and genius» 5 . Practising artists like Ghiberti and Alberti were content to accept this account of their relation to the past, and in the sixteenth century it became finally established in Vasari's phrase for the new style, la rinascita. The whole movement was crowned, he wrote, by «that excellence which, by surpassing the achievements of the ancients, has rendered this modern age so glorious» 6 . The humanist historians made the conception of a revival, leading on to new conquests, an explicit part of their historical thinking, but half4 P. Lehmann, Vom Mittelalter und von der lateinischen Pbilologie des Mittelalters, «Quellen und Untersuchungen z. lateinischen Philologie des Mittelalters», v. i (1914); G. Gordon, Medium Aevum and the Middle Age (Society for Pure English Tract No. xix; Oxford, 1925); M. L. McLaughlin, «Humanist concepts of renaissance and middle ages in the tre- and quattrocento*, Renaissance Studies, ii (1988) 131-42; Crombie, Styles. . . Ch. i above n. i. For Petrarch see Ferguson, op. cit., p. 8. 5 Quoted by Ferguson, op. cit., p. 21; see pp. 9-21. 6 Ferguson, op. cit., p. 64; see pp. 59-67.

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consciously it had for long been an element in the restless mentality of the ' barbarians' who had entered into the lands and heritage of the western Roman Empire. It began to find expression by writers in the twelfth and thirteenth centuries who could observe the effects on intellectual life of the translations being made, from the Greek and Arabic into Latin, of scientific and philosophical works, and who were witnessing also a modest technical revolution in the development of machinery for harnessing the power of wind, water, and draught animals, and in building, glassmaking, metallurgy, warfare, .surgery, navigation and other activities. According to John of Salisbury, in the twelfth century, the French scholar «Bernard of Chartres used to compare us to dwarfs perched on the shoulders of giants, so that we see more and farther than they can, not because we have keener vision or greater height, but because we are lifted up and borne aloft on their gigantic stature» 7 . A century later, Roger Bacon could assert the progress of knowledge more confidently : « We of later ages should supply what the ancient lacked, since we have entered into their labours, by which, unless we are asses, we can be aroused to better things; because it is most miserable always to use old discoveries and never to be on the track of new ones Christians should ... complete the paths of the unbelieving philosophers, not only because we are of a later age and should add to their works, but so that we may bend their labours to our own ends » 8.

The activist attitude that is essential to the research mentality, prepared not simply to contemplate knowledge gained from past writers but to use it as a base for further advance, can already be seen in formation in the writings of scholastic natural philosophers and mathematicians such as Robert Grosseteste, Roger Bacon, Albertus Magnus, Thomas Bradwardine or Nicole Oresme. It was the motive behind the numerous proposals for scientific method already characteristic of the thirteenth and fourteenth centuries, as they were to become more abundantly of the seventeenth. Moreover, Roger Bacon anticipated (with differences) his namesake Francis in offering an analysis of the «causes of error» 9 and of the stagnation of science in contemporary Christendom, including among the most important the neglect of mathematics and «experimental science» 10 and the under-valuation of true learning. The low opinion of 7 loannes Saresberaensis; Metalogicon libri iv, iii-4, recognovit... C. C. J. Webb (Oxford, 1929). The same remark is quoted by Alexander Neckam, De naturis rerum libri duo, i. 78, ed. T. Wright (London, 1863); cf. R. Klibansky, Standing on the shoulders of giants, « Isis », xxvi (1936) 147-98 Roger Bacon, Opus Majus, ii. 15, ed. J.H. Bridges, iii (London, 1900) 69-70. » Ibid., i. 10 Opus Majus, vi, « De scientia experimental!», ed. Bridges, ii. On this cf. A. C. Crombic, The relevance of the middle ages to the scientific movement, in « Perspectives in Medieval History », ed. K. F. Drew and F. S. Lear (Chicago, 1963) 35-57, and with }. D. North, Bacon, Roger, in « Dictionary of Scientific Biography » (New York, in press); M Schramm, Aristotelianism • basis and obstacle to scientific progress in the middle ages, « History of Science », ii (1963) 104-9.


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medieval culture held by the humanists was based on literature and Gothic art rather than on science and philosophy, in which at first they took little interest. But both the scholastic and the humanist reformers applied the same activist formula to history, taking an attitude to the past determined by the needs and aspirations of the present and providing a programme for future action. Such an attitude seems to be a deeply persistent element in modern European historical thinking. To the humanist doctrine of the Renaissance, the religious controversies of the sixteenth century added a new interpretation that was to become a second important element in later accounts of the rise of modern science. To justify their own position, both humanist and Protestant writers agreed in seeing the immediate past as a revolting spectacle of ignorance, superstition and corruption, polluting the pure stream of style or doctrine that had existed in an earlier, ideal period of their choice. «Throughout the first two centuries of Protestant historiography», Wallace K. Ferguson has written in his recent study, The Renaissance in Historical Thought11, a medieval culture meant scholasticism, and scholasticism meant a peculiarly pernicious state of ignorance». The Catholic Erasmus attacked medieval education, to which he attributed the decline. The English Protestant Bishop John Bale, in 1548 described the great scholastic writers as «that obscure and ignoble breed of sordid writers of sentences and summulae, the mere recording of whose names should move generous and well-born minds to nausea» 12 . Ferguson continues: «Taking over the Erasmian conception of the close causal relation between the revival of learning and that of religion... the Protestant historians blandly assumed that any improvement in learning must have led to a clearer perception of truth and therefore must have aided the acceptance of Protestant doctrine» 13 . The connection between humanism, Protestantism, and the rise of modern science became established in historical doctrine at the end of the seventeenth century, when each movement was seen as part of a common revolt against authority — the authority of scholastic education which still dominated the universities, the authority of Aristotle and Galen. In each case the reformers appealed from authority accepted in the immediate past, to an earlier state of things which they held belonged to a tradition that had been broken. The humanists turned from the ' dog' Latin and barbarous jargon of the scholastics to the pure style of classical literature, especially of Cicero. The Protestants appealed from the institutionalized sacerdotal guidance of the medieval Church to the 11 12

P. 51.

Quoted by Ferguson, ibid., p. 51 " Ibid., p. 54.

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plain text of Scripture and private judgement of its meaning, such as they held had existed in the primitive Church. The humanist-trained scientific reformers appealed first from medieval ' corruptions' to the pure Greek text of Aristotle, Galen or Ptolemy, and later from these texts to direct observation of nature such as had been practised in Greek times. The complete doctrine was succinctly expressed by the American writer Cotton Mather in his American Tears upon the Ruines of Greek Churches published in Boston in 1701: «Incredible darkness was upon the Western parts of Europe, two hundred years ago: learning was wholly swallowed up on barbarity. But when the Turks made their descent so far upon the Greek churches as to drive all before them, very many learned Greeks, with their manuscripts, and monuments, fled into Italy, and other parts of Europe. This occasioned the revival of letters there, which prepared the world for the Reformation of Religion too; and for the advances of the sciences ever since» 14 . The same form of the doctrine making a close connection between the literary revival, the Reformation, and the rationalism of modern science is found in Pierre Bayle's Dictionary, published in 1697 and a source of many of Voltaire's historical opinions. The need of the innovating parties in the literary and religious controversies to define their position in relation to the immediate past affected the historiography of science rather by their general attitude to the past than by an special interest they had in science. Humanist editors of Archimedes, Hippocrates or Aristotle were more interested in establishing a good Greek text or making a good Latin translation than in the mathematics or biology the texts contained. There are cases of literary scholars such as Conrad Gesner being led by by the text to the study of nature, and in Gesner's case to becoming a first-rate observer and naturalist. Similarly, the sixteenth-century reconstructions of the original text of Archimedes required mathematical as well as linguistic skill, and in this tradition the young Galileo himself was led to reconstruct Archimedes' methods before extending them to new scientific problems15. But humanist interest in Greek science, as in other aspects of ancient literature, had its origin in a backwards-looking admiration for antiquity; before it looked forwards it had to become something more than merely literary. Early in the seventeenth century, a new group of scientific commentators upon history arose with a completely different outlook upon the past and the future. These writers, Campanella, Francis Bacon, Descartes and their followers, mark the third major stage in the conception 14 15

Pp. 42-3; Ferguson, op. cit., p. 55. Galileo Galilei, La Bilancetta (1586), « Opere » ed. naz., i (Firenze, 1890) 211-6.


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of history that was to find full expression in Voltaire. They combined a full measure of contempt for the medieval past with an entirely new estimation of the importance of the scientific revival. Like their predecessors, they made their interpretation of history in the interests of a contemporary movement of which they were spokesmen. But, except in so far as these had prepared the ground for science, they were in general unsympathetic towards the humanist and religious reformers, whose controversies they were inclined to find either uninteresting or unintelligible. They turned their eyes to the future and saw a favourable prospect. They held that the new science was something essentially different from anything found in classical antiquity, let alone the barbarous middle ages; something which they themselves were adding to civilized life. Their attitude was similar to that taken by some sixteenth-century artists to the relation of their own work to classical models. Writing more and more in the vernacular, the new scientific propagandists stressed the material benefits brought by science and rational technology, most famously by the invention of printing, gunpowder, and the mariner's compass16, and by the general advance of industry, commerce, geographical discovery and medicine. The source of power over nature, as Francis Bacon was most emphatic in pointing out, was knowledge. The age began to bristle with works on scientific method and with schemes for scientific Utopias such as Campanella's City of the Sun (1623) and Bacon's New Atlantis (1627). Explanations of the past stagnation and present progress of science were used to provide the formulae for future advance. Common to them all was the stress laid, in varying degrees, on experiment, mathematics, and the usefulness of science. All were optimistic about the success that could be expected from the right organization and methods. This optimism about the progress of humanity through natural knowledge was accompanied by a renewed hope in nature itself. In its light the sixteenth-century doctrine that the powers of nature and mankind were in decay was rejected, later to be replaced by the eighteenth-century belief in their limitless perfectibility17. The most influential of the early seventeenth-century analyses of the history of science and of contemporary science were undoubtedly those by Francis Bacon and Descartes. Their accounts were comple16

Cf. R. F. Jones, Ancients and Moderns, and ed. (St. Louis, 1961). See J. B. Bury, The Idea of Progress (London, 1920); Jones, op. cit.; H. Baron, Towards a more positive evaluation of the fijteenthcentury renaissance, « Journal of the History of Ideas », iv (1943) 21-49, The ' Querelle ' of the Ancients and Moderns as a problem for renaissance scholarship, « ibid. », xx (1959) 3-22; V. I. Harris, All Coherence Gone (Chicago, 1949). Cf. G. Hakewill, An Apologie of the Power and Providence of God in the Government of the World, or An examination and censure of the common errour touching natures perpetuall and universall decay, 3rd ed., revised and augmented (Oxford, 1635). 17

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mentary and comprehensive, and they became the starting points for disagreement as well as for development. Bacon stressed experiment and utility; Descartes stressed mathematics and utility. This combination provided the standard two-fold formula for future progress. Both writers used history, according to the commonplace repeated in Sir Walter Ralegh's phrase, «to teach by examples of times past, such wisdom as may guide our desires and activities» 18 . In both, the key to their conceptions of scientific method can be found in their view of the history of science. In his peremptory references to the history of philosophy, Descartes described how he found that only in mathematics, pure and applied, had there been any grasp of truth 19 . His analysis of scientific method was aimed at realizing the ideal of a «universal mathematics» embracing all the sciences. Bacon went into the history of science much more thoroughly than Descartes and offered the first detailed modern sociological and historical analysis of the conditions for, and causes of, scientific progress and decline. In the Advancement of Learning (1605) Bacon divided the study of human history into three kinds, civil, ecclesiastical, and literary, each with its own sources and problems. In his discussion of the third kind, he set out a remarkable design for an intellectual history that would not only include the origin and development of scientific thought in different societies, but would also relate scientific progress and decay to the disposition of the people and their laws, religion and institutions. Bacon had called for something which he found lacking in his time, a history of «the general state of learning to be described and represented from age to age, as many have done the works of nature and the state civil and ecclesiastical; without which the history of the world seemeth to me to be as the statua of Polyphemus with his eye out; that part being wanting which doth shew the spirit and life of the person». He wanted something more than the « small memorials of the schools, authors, and books» in the « divers particular sciences» and «barren relations touching the invention of arts or usages». What he wanted from intellectual history, he wrote, was «a just story of learning containing the antiquities and originals of knowledges, and their sects; their inventions, their traditions; their diverse administrations and managings; their flourishings, their oppositions, decays, depressions, oblivions, removes; with the causes and occasions of them, and all other events concerning learning, throughout the ages of the world; I may truly affirm to be wanting. The use and end of which work I do not so much design for curiosity, or satisfaction of those that are the lovers of learning; but chiefly for a 18 19

History of the World, book ii, ch. xxi, § 6 (London, 1614) 537. Descartes, Regulae ad directionem tngfftii, iv; Discours de la methods, i.


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more serious and grave purpose, which is this in few words, that it will make learned men wise in the use and administration of learning» 20 . This was in effect a plea for the study of the history of science, and characteristically, its conclusions were to be applied in contemporary problems. Bacon complained in the preface to The Great Instauration that in the intellectual sciences there was no search for new knowledge. They «stand like statues, worshipped and celebrated, but not moved or advanced)). The mechanical arts had shown some progress, just because they were by their nature in close touch with experience and practice. Experiment, as he said famously, was essential for the a inquisition of nature» 21 ; it was the essential method of discovery; but in the past it had not been properly conceived. In the Novum Organum (1620) he described how, on the one hand, philosophers and men of learning had failed to test their theories critically by a comparison with systematic experiments and observations; whereas, on the other hand, the large number of experiments made in the course of technological practice provided few «of most use for the information of the understanding»22. Philosophers had spun out general systems with too little reference to facts, while «mechanics» were only interested in particular technical problems and did not search for causes. Bacon believed that they should combine their interests. His new experimental science was a method of acquiring knowledge of causes, tested by designed experiments, that would provide both explanations of nature and a rational basis for technology. Bacon's analysis, in the Advancement of Learning and the Novum Organum, of why science had not progressed in the past provided later historians in the seventeenth and eighteenth centuries with their basic views on the subject. He said that the sciences had fluorished during only three short periods of history: among the ancient Greeks, among the Romans, and, recently, among the nations of Western Europe. But even in those relatively favourable periods scientific progress had not been as great as it should have been. He gave several reasons for this. Besides the lack of understanding of the experimental method and of an effective approach to the ' inquisition of nature ', he emphasized the lack of opportunity for a proper scientific education, of a scientific profession commanding proper respect and position, and of government 20 Francis Bacon, Advancement of Learning, book ii. See P. Smith, A History of Modern Culture, i (London, 1930) 255-7; H. Butterfield, The history of science and the study of history, « Harvard Library Bulletin », xiii (1959) 329-47; P. Rossi, Francis Bacon: From magic to science (London, 1968). 21 Instauratio magna, in Francis Bacon, Worlds, collected and edited by J. Spedding, R. L. Ellis and D. D. Heath, i (London, 1864) 126, 132, iv (1860) 14, 20; cf. Novum organum, i. 98. 22 Novum organum, i. 99; see i. 78-105.

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interest in science. Scholars had concentrated their main attention on other disciplines, the Greeks and Romans on moral philosophy and the moderns on theology. There were no full-time scientists, except perhaps for «some monk studying in his cell, or some gentleman in his country house » 2 3 . In the universities « natural philosophy» was studied only at an elementary level as a preparation for some other profession; there was no proper scientific education, including the essential training in experiment, and there was no scientific profession in which men could specialize in particular sciences and earn a proper living. This state of affairs « hath not only had a malign aspect and influence upon the growth of sciences, but hath also been prejudicial to states and governments» 24 . In fact, Bacon's blunt appraisal remained largely applicable down to the university reforms and the development of a scientific profession in the nineteenth century. He said that the goal of natural science had not been appreciated: to enrich human life with new discoveries and powers. The right method of discovery had not been understood: designed experimentation, ordered in relation to «axioms». There had been too great a respect for « antiquity»: but true antiquity belonged to «our own times a 2 5 , with all the experience of earlier centuries behind them. There was too much complacency with existing knowledge and technical achievements, and too great a readiness to assume that nature was inscrutable and could not be mastered or understood. There was the fear that progress in science and philosophy would « end in assaults on religion » 2 6 . Above all there was a lack of rational optimism. Bacon's attitude to the history of science, his claim that his analysis had not only exposed the mistakes of the past but also provided the means of avoiding them in the future, above all his emphasis on the past neglect of experiment and the dangers of philosophical systems and his optimism for the future of scientific discovery and its applications, all deeply influenced the outlook of the founders of the Royal Society and contributed to the emotional energy behind their enterprise. They criticised Bacon for his neglect of mathematics, but they soon remedied that themselves; they also respected Descartes. The same combination of beliefs and attitudes can be found in the Academic royale des Sciences. In the literary war between the Ancients and Moderns, by the end of the seventeenth century the Moderns were able to use the recent progress of science to gain total victory over the humanist rearguard and to convince the educated public of the superiority of modern over ancient achieve23 24 25 26

Ibid., i. 80; see i. 78-79. Advancement of Learning, book ii; cf. book i, and Novum organum, i. 90-91. Nov. org., i. 84; cf. i. 80-81, 85, 103-5. Ibid., i. 89; cf. i. 92-94.


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ments in the arts and sciences. The scientific revolution was seen as the most important part of the recent revival of the West. «Is it not evident», John Dryden wrote in 1668, not in a scientific work but in his Essay of Dramatic Poesy, «in the last hundred years (when the study of philosophy has been the business of all the Virtuosi of Christendom), that almost a new Nature has been revealed to us? — that more errors of the school have been detected, more useful experiments in philosophy have been made, more noble secrets in optics, medicine, anatomy, astronomy, discovered, than in all those credulous and doting ages from Aristotle to us? — so true it is, that nothing spreads more fast than science, when rightly and generally cultivated»17. During the second half of the seventeenth century and the first half of the eighteenth, the new science radically changed the type of culture of educated Europeans. It had been demonstrated that experimental and mathematical analysis could solve interesting problems with useful applications. Theology and literary culture began to give way as dominant interests to a concern with the aims, methods, achievements, applications and consequences of science. Science began to develop as one of the learned professions, earning respect and sometimes reward, especially in France where the government gave direct support. Scientists acquired a new sense of solidarity among themselves. This is evident both in Thomas Sprat's History of the Royal Society, published in 1667 partly to justify the policy of the Society,- and in the Eloges, obituary biographies of great scientists of all nations, which Fontenelle wrote in the exercise of the office of permanent secretary of the Academie des Sciences, which he held from 1699 till 1741. Fontenelle popularized the scientific movement; books on botany were written for young ladies and on mathematics for the general public; Voltaire created literary events with his exposition of English empirical philosophy and science in his Lettres philosophiques, or Lettres sur les Anglais (1734), and with his exposition of Newton's natural philosophy. Leading writers on many subjects — Locke, Hume, Vico, Montesquieu, Rousseau, Diderot, Condorcet, Goethe —• studied science seriously and explored the possibility of extending its methods, the only sources of certain knowledge, to all aspects of human life, behaviour, and history. Just as science had discovered the fixed laws of nature, so they would try to discover those governing human behaviour and the progress and decline of civilizations. And just as scientific knowledge could be applied in technology, so they wrote history not simply to interpret society but also to change it. 27 See P. Smith, A History of Modern Culture, 2 vols. (London, 1930-34); L. M. Marsak, Bernard de Fontenelle: the idea of science in the French Enlightenment, « Transactions of the American Philosophical Society », n. s. xlix. 7 (1959); above n. 17. Cf. W. Wotton, Reflections upon Ancient and Modern Learning (London, 1694).

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It was these interests and attitudes that initiated the first detailed studies of the history of science, and of science as part of civilization. A history of medicine by Daniel Le Clerc published in 1696 is an early example of the Baconian analytical approach to intellectual history in a particular science. «There is», he wrote, «abundance of difference between a History of Physick, that is, a collection of all that relates to their persons, the titles, and number of their writings, and a History of Physick, that is, to set forth the opinions of the Physicians, their Systems, and Methods and to trace step by step all their discoveries.... This History ... is obliged to penetrate into the very soul of every age, and every Author; to relate faithfully and impartially the thoughts of all, and to maintain everyone in his right, not giving to the Moderns what belongs to the Antients, nor bestowing upon these latter what is due to the former; leaving every body at liberty to make reflections for himself upon the matters of Fact as they stand related"28. Leibniz followed Bacon in proposing the writing of a history that would include science, literature and religion as well as politics29. In 1751, in the Preliminary discourse of the Encyclopedic, D'Alembert wrote: «The metaphysical exposition of the origin and of the liaison of the sciences has been of great use to us in forming the encyclopaedic tree; the historical exposition of the order in which our sciences have followed one another will be no less advantageous in enlightening us on how to transmit these sciences to our readers» 30 . The next year, 1752, saw the publication of Voltaire's Siecle de Louis XIV, followed in 1756 by his Essai sur les moeurs et I'esprit des nations, written to convince his friend Madame du Chatelet, the translator of Newton's Principia into French, that the study of history could be as interesting as that of mathematics and natural science and could give rise to principles of equal importance31. In these works Voltaire set out to give an example of history written en philosophe, to discover the causes of progress and decline and to teach by the results. One of his greatest achievements was to replace the picture of world history guided by the hand of providence, as presented by Bossuet, by one in which events were explained by natural causes. His contemporaries Maupertuis and Buff on were doing the same 28 D. Le Clcrc, The History of Physic^, Author's preface (London, 1699); ist ed., Histoire de h medecine (Genevre, 1696). See F. N. L. Poynter, Medicine and the historian, « Bulletin of the History of Medicine », xxx (1956) 424; cf. W. Pagel, Aristotle and seventeenth-century biological thought, in « Science, Medicine and History », essays in honour of Charles Singer, i (Oxford, 1953) 509. 29 G. W. Leibniz, Sdmtliche Schriften, hrg. von der Preussischen Akademie der Wissenschaften, I Reihe, i (Darmstadt, 1923) 91, 103 (1670). 30 Cf. Smith, op. cit., ii, 250 sqq. 31 See Voltaire's introduction to the Siecle de Lotus XIV; his « La philosophic de 1'histoire », printed as an introduction to the Essai; and his « Remarques pour servir de supplement a 1'Essai », i-iii, xvii.


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for the history of nature, of the earth and its plant and animal inhabitants through geological time32. Voltaire's basic theme was a survey of European civilization from the time of Charlemagne to his own day, but in pursuing his analytical objective he cast the civilization of Europe against the background of world history. His account included a description of the history of the arts and sciences, religion, politics and commerce, populations and social structure, geography, climate and natural resources of ancient Egypt, Babylon, Greece and Rome, India and China, and of the life of savages, for comparison with the history of Europe. Science had provided him with a model of analytical and comparative methods of investigation; in return, he included in his comparative history of civilization a description of the history of science and technology. Other historians in the second half of the eighteenth century, notably Hume, Robertson, Gibbon and Condorcet, gave similar recognition, albeit sometimes peremptory, to the influence of science and technology in history. The same period saw the appearance of specialized histories of particular sciences. The publication of J. E. Montucla's great Histoire des mathematiques, in fact a history of the physical sciences, in 1758 was followed by other works of varying value including Joseph Priestley's histories of electricity and optics and J. S. Bailly's history of astronomy33. At the end of the century and in the early nineteenth century the succession continued with the historical writings of Laplace, Cuvier, Thomas Young, Delambre and, later, of Guglielmo Libri and William Whewell. Auguste Comte now succeeded Francis Bacon as the formative influence on the historiography of science34. But by this time the general character of historiography had changed: it had become more accurate, but also more restricted. The eighteenth-century historians whose outlook had been formed by the intellectual revolution of early modern times may have seen history in the mirror of their own aspirations. They drew from the new science their model of rational investigation; in repaying their debt, by making the history 32 See Bury, above n. 17; A. O. Lovejoy, The Great Chain of Being (Cambridge, Mass. 1936); A. C. Crombie, P. L. Moreau de Maupertius, F. R. S. (1698-1759), precurseur du transformisme, « Revue de synthese », Ixxviii (1957) 35-56; B. Glass, O. Temkin, W. L. Straus, jr. (editors), Forerunners of Darwin: 1745-1859 (Baltimore, 1959); J. Roger, Les sciences de la vie dans la pensee franfoise du XVIII* siecle (Paris, 1963). For the parallel interest in the history of nature and the history of mankind cf. R. Hooke, « A Discourse of Earthquakes », Posthumous Worfa, ed. R. Waller (London, 1705) 291, 334, 426-7, 433-6; Fontenelle, Histoire de I'AcadSmie Royale des Sciences, Annee 1710 (Paris, 1731) 22; Button, Les Epoques de la nature, ed. critique, par J. Roger (Paris, 1962); A. C. Crombie and M. A. Hoskin, The scientific movement and the diffusion of scientific ideas, in « New Cambridge Modern History », vi (Cambridge, 1969) 60-71. 33 Cf. Bailly, Lettres sur I'origine des sciences, et sur celles des peuples d'Asie, addresses a M. dt Voltaire (Londres et Paris, 1777). 34 Cf. A. Comte, Cours de philosophic positive, i, Premiere lec.on (Paris, 1830); W. Whewell, Philosophy of the Inductive Sciences, 2nd ed., ii (London, 1847) 320 sqq.; J. S. Mill, Auguste Comte and Positivism, 2nd ed. (London, 1866) 6-8; Bury, op. cit., ch. 16.

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of science and technology part of the history of civilization, they may have written polemically in order to extend the reign of ' reason' in their own day. The political and constitutional historians who dominated nineteenth-century historiography no longer felt that debt and they made history into the history of government. One reason for this may have been the influence of the classical seminar in German universities on the nineteenth-century conception of historical research. At the same time there was a hardening of the division in university education between science and the humanities. Classically trained historians excluded from their consideration all aspects of life not conventionally included among the 'humanities'. Also, during this formative period of nineteenth-century historiography, the general upset in the structure and concepts of government following the revolutionary wars in Europe, and the business of acquiring and governing empires, gave constitutional and political history an immediately topical and practical interest. Historiography must perhaps always reflect the problems of its own time. The character of life in our own day gives a new relevance to the eighteenth-century historians whose view included the whole of civilization. The present interest in social, intellectual and scientific history and in the comparative method are in a sense a return to the ideas with which mature modern historiography began in the age of Voltaire. Once more, historians in their analysis of human behaviour and human society are seeking enlightenment from all aspects of civilized life. Historiography is again becoming the study of civilization as a whole, with the potentiality of providing a bridge, instead or reflecting a division, between the scientific and humanistic sides of our education.

23

The Origins of Western Science'

The purpose of this book, according to the preface, seems to be to replace earlier accounts of ancient and medieval science, rather prominently for the latter my Augustine to Galileo, first published in 1952 but revised and greatly enlarged in 1959. Bruce Eastwood concludes in his generous but valedictory essay on my book and its influence in Isis (Ixxxiii, 1992, pp. 84-99): 'We can now reasonably hope for an up-to-date textbook on medieval science in David Lindberg's forthcoming survey'. Mine 'has completed its useful life' but as 'an old friend' it 'remains a connection to historical controversies and philosophical commitments of our disciplinary past'. Perhaps so, perhaps not, but it may be worth mentioning that the latest edition in English published by Harvard (1979) is still on the market and that of the eight editions in foreign languages, that in Italian (reprinted in 1982) remains especially active, and that in Spanish has been reprinted five times since its first publication in 1974. The Greek edition was handsomely reprinted in 1992, and others are in prospect. A book like The Beginnings of Western Science needs a vision of its subject, with the main lines of its perspective illustrated by telling details. Instead we have here a survey, written in an elementary style seemingly for a popular public knowing very little. 'My concern' Dr Lindberg writes, 'will be with the beginnings of scientific thought1 (p. 3), not with technology or methodology or anything else, but with the ideas and contents of science, or less ambiguously, natural philosophy. Some very brief indications or prehistoric attitudes to nature and of ancient Babylonian and Egyptian mathematics and medicine lead him to the true beginnings of scientific theory with the Greeks. The history of scientific thought, as I put it (History of Science, xxvi, 1988, pp. 1-12; above, ch. 1) is the history of a vision explored and controlled by argument. It is a vision and an argument initiated by ancient Greek philosophers, mathematicians and physicians in their search for principles at once of nature and of argument itself. By natural science we mean then a

David C. Lindberg, The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600 B.C. to A.D. 1450 (The University of Chicago Press, 1992).

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specific vision, created within Western culture, at once of knowledge and of the object of that knowledge, at once of natural science and of nature. We may trace the characteristically Western tradition of rational science and philosophy to the commitment of the ancient Greeks, for whatever reason, to the decision of questions by argument and evidence, as distinct from custom, edict, revelation, authority or whatever else. Of course all people as rational beings may decide questions by argument and evidence. It was the Greek style of rationality to make this explicit by the analysis of the reasoning involved, in the manner of Socrates. The Greeks developed thereby the conception of a problem as distinct from a doctrine. At the same time by deciding that, among the many possible worlds as envisaged in other cultures, the one existing world was a world of exclusively self-consistent and discoverable rational causality, they committed their scientific successors exclusively to this effective direction of thinking, and closed to them elsewhere still open visions of things. They introduced in this way the conception of nature, comprising a rational scientific system, in which formal reasoning matched natural causation, so that natural events and reasoned conclusions must equally follow exactly from true principles. Hence the two fundamental conceptions from which the characteristic style of all Western rational thinking has followed: causal demonstration and formal proof. The Western scientific movement has been concerned with man's relations with nature as perceiver, knower and agent. It can be identified most precisely among the great historical cultures as an approach to nature effectively competent not only to solve problems, but also to determine what counts as a solution, whether in particular cases or in general systems of theoretical explanation. Thus it offers rational control of subject-matters of all kinds, from mathematical to material, from ideas to things. A similar rational style is evident over the whole range of Western intellectual and practical enterprise, in ethics and metaphysics, in law, government and commerce, in drama and music, in the visual and constructive arts, and in technology and manufacturing. Of the essence of the scientific movement as a tradition have been its genuine continuity, even after long breaks, based on the study by any generation of texts written by its predecessors; its progress equally in scientific knowledge and in the analysis of scientific argument, for innovation is a product of continuity; and its recurrent critique of its practical and moral justifications. A subtle question then is what continued and what changed through different historical contexts, in the scientific argument and in the cultural vision through which experience is mediated, when education, experience and innovation could furnish options for a different future. The scientific argument comprises both the form and the subject-matter. It is obviously absurd, in analysing how a particular problem or phenomenon has been treated at a particular time, to consider the one without the other. But the same phenomenon may be treated in different forms or styles of argument, and a common form of argument may unite an assembly of diverse though cognate subject-matters. The Western scientific movement brought together

The Origins of Western Science

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within a common restriction to answerable questions a variety of forms or styles of scientific inquiry, demonstration and explanation, diversified by their subject-matters, by general conceptions of nature and the expectations they entail, by presuppositions about scientific cogency and validity, and by scientific experience of the interactions of creative thinking with testing, of programmes with their realisation, modification or rejection. The diversification and testing of these different forms of argument was the highly intellectualised product of many generations. A scientific style identifies certain regularities in the experience of nature which become its object of inquiry and define the questions put to the subject-matter within that style. The interactions between style and subject-matter then generate appropriate methods of inquiry and kinds of argument and evidence for finding acceptable answers. We can establish in the scientific movement a taxonomy of styles, distinguished by their objects of inquiry and forms of argument. Three were developed in the investigation of individual regularities, and three in the investigation of the regularities of populations ordered in space and time. The primary style invented by the Greeks was what I call postulation, in two different forms, mathematical and syllogistic. The former exploited the demonstrative power of geometry and arithmetic and eventually united all the mathematical sciences and dependent arts, from optics and music to mechanics, astronomy and cartography, under a common form of proof. The latter exploited the demonstrative power of logic as established by Aristotle in all the natural sciences as well as other subject-matters of philosophy. The second style I call the experimental argument, both to control postulation and to explore by observation and measurement the observable relations of more complex subject-matters in the search for their principles. Ptolemy used well designed experiments to control the postulations of optics and Galen did likewise to explore the operations of the ureters, the spinal cord, and other physiological phenomena. The experimental argument, in its various forms arid contexts, was logically designed to bring in experiment, with the necessary apparatus and instrumentation, at the relevant points of decision. The third style, hypothetical modelling, proceeds by exploiting the properties of a theoretical or physical artifact, which we know because we designed it ourselves, and with which we can simulate and thus explore and explain the phenomena of nature. Perhaps the most striking original model of all was Eudoxus's geometrical model of the cosmos, which transformed astronomy as developed with great arithmetical sophistication by the Babylonians into an entirely new style of scientific thinking. Hypothetical modelling was developed in a mature form by its transposition from art to science in early modern Europe: perspective painting was a perceptual model of the natural scene; Kepler solved the problem of the formation of the retinal image by using the camera obscura as a model of the eye; Descartes generalised the whole style. Taxonomy as the fourth style was again developed by the Greeks, notably Plato, Aristotle and Theophrastus, as a logical method of ordering variety in any subject-matter by comparison and difference, raising the question of

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discovering natural affinities. The fifth style, probabilistic analysis of contingent expectation and uncertain choice, was also broached qualitatively by Greek logicians and physicians and Roman lawyers faced with making decisions with incomplete but probable evidence, and it reappeared in medieval treatments of similar cases. It was quantified practically in the fifteen and sixteenth centuries in dealing with insurance and other commercial questions, and theoretically in its two forms, analytic and synthetic, in the seventeenth century. At the same time came the explicit discovery of a new kind of regularity, the statistical regularities in adequately numerous populations of economic, medical and other events. Lastly, the method of historical derivation, or the analysis and synthesis of genetic development, was again used first by the Greeks in application to human cultures and civilisations, before being appropriated in early modern Europe for the evolution of languages, of the Earth, and then later of living organisms. The subject-matter of historical derivation was defined by the diagnosis, from the common characteristics of diverse existing things, of a common source earlier in time, followed by the postulation of causes to account for the diversification from that source. Each style then defines the questions to be put to its subject-matter, and those questions yield answers within that style. A change of style changes the questions put to the same subject-matter, as the Aristotelian analysis of motion in a qualitative taxonomy of causes was replaced, from the fourteenth to the seventeenth century, by its analysis into quantitative functional relations. Thus each style of questioning can exclude others, a point made vigorously in this example by Galileo. But usually different styles are combined in any particular research. Each style introduces a specific conception of causality, and hence the fundamental differences in the physical worlds envisaged by geometrical postulation, but qualitative taxonomy, and by the quantified mechanistic and the probabilistic conceptions of nature. Each style again introduces new questions about the existence of its objects in nature as distinct from their being products of its methods of abstraction, classification, measurement, sampling and so on, or of its language. Lindberg's survey is very different from the kind of intellectual analysis just outlined. He begins his sketch of ancient science, occupying about a third of the book, with a rapid conventional run through Greek ideas from Homer and Hesiod to Plato and Aristotle. He rightly indicates that the fundamental questions for Greek philosophy were those of the nature of the identity persisting through change, causality, the structure of the cosmos and its relation to its first cause, and the nature and knowability of that cause. No sensible historian is likely to disagree with the statement that the 'proper measure of a philosophical system is not the degree to which it anticipated modern thought, but its degree of success in treating the philosophical problems of its own day.' (p. 67), but similar remarks dotted through the book seem to anticipate a fairly uneducated audience. Next come a brief account of Hellenistic natural philosophy with some interesting references to ancient


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schools and education, followed by a sketch of the Greek mathematical sciences, essentially of astronomy, optics, and the science of weights. He indicates correctly that both Euclid in his optics and Archimedes in his analysis of the balance exploit the demonstrative power of geometry to develop experimental sciences without experiments. An illustration of scientific style not mentioned is the Babylonian source of Ptolemy's tables correlating planetary positions, which became the model for those correlating angles of incidence and refraction. The science of optics was later substantially developed by astronomers. After this comes an account of Greek and Roman medicine, dealing with both clinical diagnosis and physiology from Hippocrates to Galen. The case histories and rational diagnostic procedures in the Hippocratic corpus (with their more primitive antecedents in the very different contexts of Egyptian and Babylonian medicine) matched the sophistication of the mathematical sciences, while the systematic physiological theory culminating the Galen matched in the microcosm of man the theory of the macrocosm. No mention is made of Galen's well designed experimental investigations which were to become a model for William Harvey. The narrative of ancient science concludes with the Roman popularisers and encyclopedists, most substantially Pliny, Latin translations and epitomes of Greek science notably by Calcidius with his version of the Timaeus, and Boethius, with a brief account of Roman and early Latin medieval education. There is no mention of the basic importance of Cicero as the author of the essential Latin philosophical terminology translated from the Greek, from which came that of modern European languages. It would have been useful also to include some account of the development of technical language and terminology, a subject pioneered in philosophy by Etienne Gilson and Alfonso Maieru and in science and mathematics notably by students of fourteenth-century kinematics and dynamics. No mention is made either of the development of vernaculars for science and philosophy, in which Dante, Geoffrey Chaucer and Nicole Oresme played so prominent a part. Another important omission, in a brief discussion of the role of Christianity, is the confrontation of Greek philosophy with the Hebrew and Christian theology of creation over the fundamental nature of God's relation to the world and to mankind. The confrontation began systematically in the first century B.C. with Philo Judeaus of Alexandria, the last great thinker in the line of Hellenised Jews. Directly and indirectly, through Lactantius, Augustine of Hippo, and other routes, Philo affected profoundly later Jewish, Christian and Moslem thought on this question and with it on natural philosophy. Philo accepted the Greek conception of the order of nature determined by unchanging causes, but the source of that order was not the Platonic god of the Timaeus, who made the world by a necessary act of his own perfection out of pre-existing matter, nor the eternal divine reason of Aristotle from which the world emanated as a necessary consequence of causes discoverable by human reason, nor the material divinity of the Stoics. The God of Abraham was in no way necessitated, but acted with an entirely free

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omnipotence to create ex nihilo a world entirely separate from himself, for reasons unknowable by man apart from divine revelation. Philo used the term logos for the principles on which God modelled his creation, like a city fashioned within the mind of an architect, from which followed with invariable regularity all the operations of this universe. But God could overrule these regularities just as he could have created another kind of universe had he so chosen. Philo saw in Scripture both literal and underlying meanings, from which he could apply the analogy of law to God's actions. In the Christian context the created world was then reduced to a mechanism operating according to a system of laws. Lactantius likened God's creation to Archimedes's modelling of the cosmos with his brass armillary sphere. Basil of Cappadocia likened it to a spinning top. The most pervasive route through which these ideas passed into Latin medieval thought was Augustine, for whom the naturales leges which God had ordained were the laws of measures, numbers and weights. He applied the concept of natural laws, or laws of nature, to the motions of the heavenly bodies, the generation of living things, and the development of the world itself pregnant with things to come. God could then be discovered in the great open book of nature, as well as in the revealed book of Holy Scripture. These ideas were to become fundamental principles of Western medieval and early modern natural philosophy. See my 'Infinite Power and the Laws of Nature: A Medieval Speculation' in L'infinito nella scienza, a cura di G. Toraldo di Francia (Roma, 1987) 223-43 (reprinted above, ch. 6); and with J.D. North, 'Univers' in Les caracteres originaux de I'Occident medieval, ed. J. Le Goff et J.-C. Schmitt (Paris, forthcoming). A brief and inadequate chapter on Byzantinum and Islam skips through Hellenistic commentaries on Aristotle, the translation of Greek science into Arabic, and the Islamic scientific achievement and decline, on which it raises some interesting questions but does little to explore them. No reference is made to the fundamental work of Roshdi Rashed and GUI Russell on Arabic optics and on the cultural situation of Islamic science in general. Next we have a standard account of the revival of learning in the West from the Carolingian reforms to the development of education in the schools of the eleventh and twelfth centuries, natural philosophy with its expansion through the translations from Greek and Arabic into Latin during the twelvth and thirteenth centuries, and the assimilation of this new learning in the universities. The confrontation of Aristotelian metaphysics with the Christian theology of creation again led to a vigorous defence of divine omnipotent freedom and human moral responsibility against determinist interpretations of Aristotle. On these central issues in the condemnations of 1270 and 1277 the recent work of Luca Bianchi (not cited here) has thrown new light. A chapter on the medieval cosmos summarises studies of Grosseteste, the terrestrial region with a brief sketch of cartography and of Jean Buridan and Nicole Oresme on the Earth's possible rotation, astronomy and its instrumentation, and astrology. This is all useful and the illustrations are excellent, but one misses any discussion of Richard of Wallingford or Chaucer and the profound and precise


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studies of them by John North. Also missing in a book making the claims of its subtitle is any reference to Dante. Coming to the physics of the sublunar region, after a few pages on matter and alchemy, Lindberg reaches the fundamental studies of his mentor, and his mentor's mentor, on the fundamental science of motion. This is well described in a few pages on the conception of motion in the thirteenth and fourteenth centuries, its mathematical representation, and dynamics and its quantification. Next comes the science of optics on which Lindberg himself has published good work, especially on the pinhole camera. The essential sources were Aristotle, Euclid, Ptolemy and Alhazen, with for the eye also Galen, and the essential medieval authors were Roger Bacon and Witelo. The study of the history of optics were pioneered by Vasco Ronchi, and that of medieval optics by myself, followed by A.I. Sabra, Lindberg, Stephen Straker with his fundamental Kepler's Optics (1971; Ann Arbor, Mich., 1980) and 'Kepler, Tycho, and the "Optical part of astronomy": The Genesis of Kepler's Theory of Pinhole Images' in Archive for History of Exact Sciences, xxiv (1981) 267-93, and later by others. Ronchi made his mistakes, as who does not, but he established the field in which we have all worked and put us all in his debt, just as Pierre Duhem did for medieval science in general. I note that Lindberg does not cite me in his section on medieval optics. This is a mistake, because my original monograph (1967) on the subject which he used is well known and is now readily available in my collection Science, Optics and Music in Medieval and Early Modern Science (London, 1990), and my more recent study, 'Expectation, Modelling and Assent in the History of Optics: i, Alhazen and the Medieval Tradition; ii, Kepler and Descartes', has a direct bearing on some of Lindberg's controversial opinions, especially on Kepler's relation to the medieval tradition. This long article was published in Studies in History and Philosophy of Science, xxi (1990) 605-32, xxii (1991) 89-115 and is reprinted above, ch. 16. The last chapter of any substance is an account of medieval medicine and natural history written under the guidance mainly of Nancy Siraisi and Michael McVaugh. On the latter subject a strange omission is the classic work of Agnes Arber on herbals, and more recently there are the original and indispensable studies of the manuscript tradition by Evelyn Hutchinson, Wilma George and, as further evidence of activity in the field, by the contributors to Die Kunst und das Studium der Natur vom 14. zum 16. Jahrhundert, herausgegeben von W. Prinz und A. Beyer (Weinheim, 1987). Lindberg has missed the opportunity offered by this book to develop a systematic historical study of important themes showing the character of scientific thinking in particular contexts and its changes. For example, his references to experiment are minimal, even though this is a subject of lively and serious discussion by medievalists such as myself, Jole Agrimi and Chiara Crisciani, and others. There is no reference at all to Pierre de Maricourt and his systematic experimental investigation of magnetism, to be respectfully acknowledged by William Gilbert. The well designed systematic experimental investigation of the rainbow by Theodoric of Freiberg, with a telling use of

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models, is mentioned in three lines without any indication of the experimentation but only as offering 'an explanation very close to the modern one' (p. 253; no reference in the attendant footnote to my basic analysis in my Robert Grosseteste and articles in Science, Optics and Music). This questionable judgement entirely misses the opportunity to point out the change of scientific style between Theodoric and Descartes. The change involved the fundamental structure of scientific thinking and in the object of scientific inquiry. Theodoric looked by an Aristotelian taxonomic analysis for the necessary and sufficient causal conditions defining a particular phenomenon. Descartes looked for a general quantitative law from which this and other such phenomena could be quantitatively deduced. Another example is the general question of quantification in medieval physics. Theodoric gave a false figure for the maximum elevation of the rainbow, which Roger Bacon had reported correctly from measurements with an astrolabe. There is no reason to doubt that Bacon's contemporary Witelo (only a passing reference by Lindberg) carried out original experiments which he described showing the production of colours by refraction through hexagonal crystals and spherical glass vessels filled with water, but there is every reason to doubt whether he made his alleged experimental measurements, like those of Ptolemy, correlating angles of incidence and refraction (as I pointed out in my Robert Grosseteste, pp. 223-5, and in my article of 1961 on quantification reprinted in Science, Optics and Music, p. 79). Why was there such manifest indifference to actual measurement? As I showed in this article, we must look at the context. Physics as developed from Aristotle in the universities, even the powerful procedures for representing qualitative change quantitatively leading to new sciences of kinematics and dynamics, required no reference to experiment or measurement in its internal logic, nor was this imposed by external professional or practical pressure. Experiments in the academic context were made in the mathematical scientiae mediae, notably optics, or in the realm of natural magic like magnetism. Accurate measurements were made when they were required by practical need as in astronomy. In my article I showed by comparing the treatment of three quantities, time, space and weight, in the academic context and in that of the practical arts, that it was practical demand that produced consistent measurement. The penetration of causal physics by the concepts of the mathematical scientiae mediae profoundly affected the whole structure and style of scientific thinking. This is evident in the influence of the Timaeus in the twelvth century; in the distinction by Grosseteste between the primary mathematical properties of matter and the secondary sensory qualities they produced in us; and in the conceptual shift in the fourteenth century that moved the object of inquiry away from the definition of natures to the discovery of relations between quantities expressible by what became algebraic functions. Corresponding to this was the use of the term laws of nature (leges naturae) by Roger Bacon in a scientific sense for the laws of reflection and refraction, with the notion of a universal nature constituted by such laws (Science, Optics and Music, pp. 68-9,


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77-8,148-50). In the end from Galileo onwards it was within the mathematical middle sciences that physical problems were formulated, so that the certification of their conclusions by measurement came to yield there, and not in the traditional conception of causes, the only true science of nature that could be discovered. It is a serious omission, both for understanding the scientific thinking and for relating it to its cultural context, to exclude from a book like this a discussion of the practical rational arts. The ingenious mechanism sketched in the thirteenth century by the architect Villard d'Honnecourt, the mechanical clock itself, the planetaria of Richard of Wallingford and Giovanni de' Dondi in the fourteenth century, and many other devices, were all rationally designed to facilitate the control of movements and the representation of quantities, the last two by academic men. Scientific instruments, notably in astronomy, were a product of the intercourse between theory and practice. Mechanisms also provided analogies for scientific theory, as they did for Jean Buridan and Nicole Oresme in likening the created world to a clock set going by God. At the end of the fourteenth century the universities went into decline and the leaders in original thought and action became a different group, largely outside them, of what Leonardo Olschki called artist-engineers. Their expertise lay in the rational control of materials, processes and practices of all kinds, from painting to music, from architecture to machinery, from cartography and navigation to accountancy. They brought about a general transformation of European intellectual life. An obvious example is the control of visual representation by means of the linear perspective invented by Filippo Brunelleschi at the beginning of the fifteenth century and explained by Leon Battista Alberti in his Depictura (1435). The analogy of artificial devices used to explain and apply perspective in painting came later to transform the science of vision. As I have shown in my article on Alhazen and Kepler (1990-91) mentioned above, using Straker's excellent account of the camera obscura, Alhazen in his brilliant geometrical model of ocular physiology did not make the reception of the forms of visible objects in the eye a purely geometrical inanimate process, as it was in inanimate transparent bodies, but a process modified geometrically by the sensive power in the receptor. Kepler, by taking the inanimate camera obscura as a true model of the eye, made ocular geometry a purely physical process and, by separating this from the questions of sensation and perception that had confused the issue since antiquity, demonstrated the formation of the image on the retina. Certainly, as Lindberg likes to insist, Kepler used his knowledge of existing optical theory in making his analysis: what else? His solution required a radical conceptual change, facilitated by the innovations and the innovative mentality of the rational arts. Aspects of this subject are well presented in three recent books: Science and the Arts in the Renaissance, edited by John Shirley and David Hoeniger (Washington, D.C., 1985), The Science of Art by Martin Kemp (Yale University Press, 1990), and The Heritage of Giotto's Geometry: Art and Science of the Eve of the Scientific Revolution by Samuel Y. Edgerton, Jr.

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(Cornell University Press, 1991). To conclude this litany of omissions, a book like this should address a further important aspect of the mentalities involved, the perception or otherwise of original progress by the natural philosophers building on the recovery of ancient learning: see my article 'Some Attitudes to Scientific Progress: Ancient, Medieval and Early Modern' (1975) reprinted in Science, Optics and Music. In my article 'Historical Commitments of European Science' (1982), also reprinted in Science, Optics and Music, I wrote: We may see the origins of modern science in the recovery, exegesis and elaboration of the Greek conceptions of rational decision and proof and of a rational system by medieval and early modern Europe. The recovery was made in a series of responses to ancient thought by a new society with some different mental and moral commitments and expectations, with a different view of nature and of man and his place in nature and his destiny, a different theology, a different economy and a different view of technology, but also with a vision of continuity. Much light can be thrown upon the intellectual orientations of European society, in making these responses, by attention to its apprehensions of continuity or discontinuity with the past and programmes projected therefrom. When philosophers pictured themselves in the twelfth century as dwarfs standing on the shoulders of giants, or looked in the fifteenth century for guidance from a Hermetic wisdom of supposedly Mosaic antiquity, or insisted in the seventeenth century that they were doing something entirely new, they were all making evaluations of the past which entailed programmes for future action. The same applied to the evaluative use of the historical terms middle ages, renaissance, reformation, scientific revolution, enlightenment and so on. These may tell us more about the periods in which they were invented than about those to which they refer. To characterise the process by which the science of nature developed its identity within the intellectual culture of medieval and early modern Europe is not easy. We may distinguish three broad stages of intellectual response and orientation brought about by the recovery and exploitation and then transcendence of ancient models. Each acquired a characteristic style of formulating and solving its problems. With the first intellectual impetus given by the recovery of ancient philosophical, scientific and mathematical texts in the twelfth and early thirteenth centuries came a primary intellectual achievement. This was the grasp and critical elaboration by the philosophical community of the medieval schools and universities of the construction of a demonstrative explanatory system on the models of Euclid's geometry and Aristotle's physics and metaphysics. Together with this came a critical elaboration of logical precision, from methods formalised by Aristotle, for the control of argument and evidence to decide a variety of questions, including decision by calculation and observation and experiment. I continued: The movement of intellectual orientation generated in Western Europe first then an organised capacity to act with rational intent in the control at once of argument and calculation. It generated at the same time an organised capacity to control a variety of materials and practices. We may distinguish this matching of logical control of argument by a likewise theoretically designed and measured control of matter as the second stage of European response to ancient


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models. . . . The painters, sculptors, architects, engineers, metalsmiths, assayers, surveyors, navigators, musicians, accountants and so forth comprising this group generated an effective context for seeing and solving the exemplary technical problems shared by the mathematical sciences with the visual, plastic, mechanical, musical, navigational and commercial arts. Training in the arts provided for both theory and practical skill. Their practitioners responding to a diversity of particular demands brought about a general transformation of European intellectual life by their search for precise understanding and control of materials in a variety of circumstances. . . . At the same time, for the philosophical and scientific community at large, the nature and range of the effects that might be anticipated still remained at the beginning of the seventeenth century in varying degrees open questions. There was by no means general agreement on the kind of world men thought themselves to inhabit, how they should investigate it and what kind of explanation should be accepted as satisfactory, how best to control it and to what ends control was most desirable. In this context the confident establishment during the seventeenth century of the rational experimenter and observer as the rational artist of scientific inquiry, designed first in the mind and proceeding by antecedent theoretical analysis before execution with the hands, marked the culmination of European orientation in response to ancient scientific sources in its third stage. The experimental philosopher as the rational artist might make his analysis by means of theory alone, quantified as the subject-matter allowed, or my modelling a theory with an artifact analytically imitating and extending the natural original. Both artist and philosopher could obtain the effect sought only as Galileo put it 'according to the necessary constitution of nature. . . . For if it were otherwise, it would be not only absurd but impossible. . .' (Le Opera, ed. naz., ii, 155,189). Art then could not cheat nature, but by discovering, obeying and manipulating natural laws, with increasing quantification and measurement, art was seen to deprive nature of its mysteries and to achieve a mastery exemplified by rational prediction, whether in the representation of a scene or the prognosis of a disease or the navigation of a ship. Galileo himself marks the connection and transition between two great European intellectual movements: from the world of the rational constructive artist to that of the rational experimental scientist. It was above all as the designer of an explicit scientific style, providing a philosophical strategy for the sciences of nature, that he illuminates the specific identity of natural science within the contemporary intellectual scene (pp. 9-17). This article is based on the historiographical introduction to my Styles of Scientific Thinking in the European Tradition: The History of Argument and Explanation Especially in the Mathematical and Biomedical Sciences and Arts, 3 vols. (London, 1994). The work offers an analysis of these questions, some of them discussed above, from antiquity to the nineteenth century. In my Augustine to Galileo, under the heading The continuity of medieval and seventeenth-century science', I summarised 'the original contributions made during the middle ages to the development of natural science in Europe' (1959, 1979, same pagination ii, 117-30). These I list as being in the logic of experimental argument, the application of mathematics to physics, theories of space and motion, the technical arts, descriptive medicine and natural history aided by naturalistic art, and conceptions of the purpose of natural science and of its knowability. I continued:

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But when all is considered, the science of Galileo, Harvey and Newton was not the same as that of Grosseteste, Albertus Magnus and Buridan. Not only were their aims sometimes subtly and sometimes obviously different and the achievements of the later science infinitely the greater; they were not in fact connected by an unbroken continuity of historical development. . . . Apart from anything else, the enormously greater achievements and confidence of the seventeenth-century scientists make it obvious that they were not simply carrying on the earlier methods though using them better. But if there is no need to insist on the historical fact of a Scientific Revolution in the seventeenth century, neither can there be any doubt about the existence of an original scientific movement in the thirteenth and fourteenth centuries. The problem concerns the relations between them.

One of the indispensable contributions made by medieval Western Europe was to provide in the universities a secure institutional context for learning and teaching over a wide range of subjects: the seven liberal arts, the three philosophies (natural, metaphysical and ethical), and medicine, law and theology. No such context was established in the ancient or Islamic worlds, and this certainly left the natural sciences in a much weaker position in those societies than was achieved in the West. One important cause of the discontinuity between fourteenth and sixteenth century science was the decline of the universities. I went on to consider briefly 'what the scientists of the sixteenth and seventeenth centuries in fact knew of the medieval work, and how the similarities and differences of their aims may be characterised'. The answer is that they knew quite a lot, as we might expect. The universities revived in the sixteenth century, especially in Italy, and scientific activity revived with them; learning in general also found new institutions in the new philosophical, literary, artistic and finally scientific academies. As for the differences of aims, I characterised this by saying that the 'main interest of scientists since Galileo has been in the ever-increasing range of concrete problems that science can solve', whereas the medieval natural philosophers were 'primarily philosophers' interested rather in clarifying the kinds of problems addressed by natural science than in solving them in particular. I added: 'It was a direction of interest that could have been fatal to Western science'. But the direction changed. This is all old stuff, so what is the point of Lindberg's somewhat bizarre presentation of what he calls 'the continuity debate', starting with Duhem, quoting from the unrevised edition of my Augustine to Galileo (1952) and out of context from my Robert Grosseteste (1953), citing my old friend Alexandre Koyre's criticism in a nevertheless flattering review, and so on? I find myself credited with a 'defense of the continuity thesis' (p. 361). I confess that I find this 'debate' as it has 'erupted' (p. 357) especially in the United States something less than rivetting. The question of what continued and what changed from one period to another, and what at any time was thought to have continued or changed, is a subtle one, not only from medieval to early modern and not only for scientific thought. It needs and deserves subtle and sophisticated treatment, and scholarly respect for the real thought that has


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been given to it, not a rhetorical travesty. Since I seem to figure prominently in this comedy, I have quoted some of my own continuing thoughts on the subject above. Koyre greatly illuminated our understanding of Galileo, and much else, by his brilliant demolition of the older image of Galileo as primarily rather a dedicated experimenter than a theoretician, but he was not himself much interested in experimental science and he misinterpreted Galileo's attitude to experiment. I have discussed this in my articles 'Galileo Galilei: A Philosophical Symbol' (1956) and 'Alexandre Koyre and Great Britain' (1987), reprinted above, chs. 12,13. The history of the historiography of any subject can be of profound and valuable interest for historians, and one of the most interesting perceptions of it can come from the intellectual and social contexts of knowledge and beliefs and prejudices within which the historical vision of scholars like Duhem and Koyre developed. But that is beyond the range here. Lindberg terminates his book with a list of medieval scientific achievements somewhat different from the one I published in Augustine to Galileo (1959), but coming to the same rather obvious conclusion: something continued, something changed. The truly dramatic cultural change brought about with the emergence of the new mentality of the Renaissance man of virtu, the rational artist designing the control of all his thoughts and actions, between the scholastic natural philosophers and the seventeenth century rational experimental and mathematical scientists, is not noticed. Is this a 'landmark book' as the publisher claims on the back cover? I hardly think so. It misses the lively innovative thought and research into the subject that has continued since Federigo Enriques, Marshall Clagett and I and others published our early books, and indeed to which some of us continue to contribute. But it is written by a distinguished scholar who is also an experienced teacher, and it will offer a valuable introduction to many interesting aspects of the beginnings of Western science. Postscript

H.F. Cohen, in his eccentric The Scientific Revolution (Chicago, 1994) 105-10, 153, manages to characterize me in a way similar to the above (p. 476), citing Koyre on me but not me on Koyre (as above chs. 12, 13, cf. also ch. 1), and referring to nothing published by me after 1963. This has some bizarre consequences. He writes that "in the early eighties, William Wallace (roughly simultaneously with Adriano Carugo and Alistaire Crombie) established a direct link between Galileo and previous thought on nature through the Jesuit Collegio Romano" (pp. 109-10; cf. 281-2, 573 n. 99). Everyone familiar with this subject knows that Carugo discovered this link first during 1969-71 through Pereira and Toletus, then in 1975 through Carbone, that I discovered in 1971 the link through Clavius, and that we gave this information to Wallace in 1972: see above ch. 9 and ch. 10, n. 11 with Appendix (a), and my Styles of Scientific Thinking . . . (1994) 549-51, 766 nn. 165-6, with for historiography Part I, pp. 3-89 of this work.

Oh, what a tangled web we weave, When first we practice to deceive! (Walter Scott, Marmion v.17)

Appendix to Chapter 10 (a)

Sources and Dates of Galileos Writings [with Adriano Carugo] The essential facts of the discovery by Adriano Carugo and myself that Galileo used, for his three sets of scholastic essays, sources connected with the Jesuit Collegio Romano, are outlined above in Chapter 10 on pp. 167-74 and in n. 11; see also ch. 9. Further details are set out in my review of W.A. Wallace's Galileo and his Sources (Princeton, 1984) in the Times Literary Supplement (22 November 1985, pp. 1319-20) and in subsequent correspondence (3 January 1986, pp. 13, 23,14 February p. 165, 25 July p. 815, and 29 August p. 939). In that review and correspondence I addressed two questions: Wallace's treatment of the authorship of our discoveries on which his book is based, and his treatment of those discoveries. I shall comment here only on his conception of evidence concerning Galileos logical Disputationes (MS Galileiano 27). The evidence is quite specific: the correspondence between Carbone's Additamenta published in 1597 and Galileo's MS 27. There is also the accusation published long afterwards by the Jesuit Paolo Delia Valle (Latinized as Paulus Vallius) in his Logica (1622) that someone identified with Carbone (naming the Additamenta) had plagiarized his lectures given at the Collegio Romano in 1587-88. No such lectures have been found, nor is there any mention of them in Jesuit records at present known. Moreover, supposing the Carbone had plagiarized Delia Valle's lectures, there is no evidence whatsoever, either from the contents of the Logica or from other sources, to connect them with Galileo. Undaunted by this Wallace imagined a connection: namely that Galileo had used for MS 27 a set of Delia Valle's alleged lecture notes, that these were obtained for him by Christoph Clavius on his request, that Carbone had plagiarized the same notes which Delia Valle allegedly distributed to his students, thus accounting for the correspondence between his and Galileo's texts, and that MS 27 must have been written by Galileo 'around 1590' when he was mathematical lecturer at Pisa (Galileo and his Sources, pp. 9, 89-94). For each and every one of these speculative assertions there is no evidence whatsoever: about Galileo's alleged request, about Delia Valle's ghostly lectures and their alleged distribution, about Carbone's alleged plagiarism, and for the date. Early in 1588 Galileo, after visiting Clavius in

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Rome at the end of the previous year, exchanged some letters with him about the demonstrations he had given in his theorems on centres of gravity (Opere, x, 22-30; cf. above n. 17). Clavius suspected in these quotpetitur principium, and perhaps also in Archimedes. Galileo explained more precisely. Clavius remained unconvinced. The correspondence was entirely mathematical, with no reference to logic or to Delia Valle or any other Jesuit, as was that contemporaneously on the same subject with Guidobaldo del Monte (x, 2536). There is no evidence for any discussion of logic. The petitio principii is evidently catching. Since our paper was published Carugo has made a thorough examination of the two massive volumes of Delia Valle's Logica and compared it with Carbone and Galileo. He has written to me with his new conclusions as follows: I found no evidence that either was in any way dependent on Delia Valle. Although similar questions were discussed by all three, as well as by many other contemporary authors both in print and in manuscript (contrary to what we believed in 1983; above p. 169), using the same stereotyped terminology, there is no textual correspondence between either Carbone or Galileo and Delia Valle. Beyond that there is positive evidence that Delia Valle could not have been the source for Galileo. Focusing on questions treated by both, in particular the praecognitiones, the species demonstrationis and the regressus, I found that Delia Valle drew extensively from, and actually plagiarized, Zabarella's logical tracts on these topics, frequently reprinted from 1586. For example: Zabarella, Opera omnia, (Venetiis 1600): 'Liber de speciebus demonstrationis',

Vallius, Logica, ii, (Lugduni 1622): Disput. 2, Pars 3: 'De speciebus demonstrationis',

Caput iii: 'De demonstratione a causa remota' (p. 302).

Quaest. 2, Caput iv: 'Qualis debeat esse demonstratio a causa remota etc.' (p. 305a).

Demonstrationem a causa remota docet Aristoteles negativam semper construi et in secunda figura in Camestres. Cuius ratio est, quoniam causa remota ut plurimum est amplior effectu: quare ea posita, non ponitur necessario effectus; proinde non potest effectus affirmative colligi ex ilia causa; ea vero ablata, effectus ex necessitate aufertur . . .

Quando vero est demonstratio a causa remota, docet Aristoteles necessario de bere esse in secunda

In omni demostratione tres terminos esse oportet . . . Termini igitur erunt causa, effectus et subiectum

In omni enim demonstratione tres terminos reperiri necesse est; quare in hac demonstratione tres erunt

figura et in Camestres, ac prohinde

conclusionem illius semper debere esse negativam . . . Cuius ratio est, quia causa remota ut plurimum solet esse universalior effectu: quare ea posita, non ponitur necessario effectus; ergo non potest ex huiusmodi causa colligi effectus affirmative; tamen ilia ablata, aufertur necessario effectus . . .

Appendix to Chapter 10 tertium, cui ambo insunt, sive a quo ambo negantur; et causa ipsa remota erit terminus medius, effectus maior extremitas, subiectum vero minor extremitas . . .

termini: nimirum causa, effectus et subietum, cui utrumqe inest, vel de quo utrumque negatur; et causa remota erit medius terminus, effectus maior extremitas, subiectum minor extremitas . . .

In propositione quidem maiore manifestum est poni medium terminum cum maiore extremitate, pro inde causam et effectum. Quare maiorem necesse est esse affirmativam, quoniam ex effectu et causa non potest nisi affirmativa enunciacio fieri: non enim hoc illius causa esset, si alterum de altero negaretur.

In maiore autem propositione ponitur maiore autem extremitas cum medio termino, consequenter causa cum effectu. Quare maior debet esse affirmativa, quia de causa affirmari debet effectus vel de effectu causa, non autem negari, si propositio vera est fututa.

At vero si ea maior debeat esse universalis, oportet causam de effectu predicari, non effectum de causa: quam effectus, non potest effectus de causa universaliter praedicari.

Maior autem debet esse universalis . . . ergo debet necessario praedicari causa de effectu, non autem effectus de causa, quia cum causa sit universalior effectu, non potest de illo universaliter praedicari.

"Liber de speciebus demonstrationis", Cap. xix: "In quo ostenditur etiam respectu nostri nullam demonstrationem notificare propter quid est, quin notificet etiam quod est." (p.333).

Disp. 2, Pars 3: "De specie bus demons rationis", Quaest.3, Caput ix: "Ostenditur non posse per demonstrationem cognosci propter quid, quin simul cognoscatur an sit" (p.321 a).

Ostendere possumus quod non modo naturam demonstrationis spectando, verum etiam nos ipsos demonstrantes respiciendo, omnis demonstratio notificans propter quid est notificat etiam quod est, et nobis tradit novam utriusque cognitionem quam ante demonstratio nem non habebamus.

Non solum naturam demonstrationis considerando, sed etiam si nostri et intellectus demonstrantis ratio habeatur, omnem demonstrationem perfectam ostendere propter quid et an sit rei, ita ut semper nobis per huiusmodi demonstrationem nova cognitio adveniat et ipsius propter quid et an sit ... etiam si antea habita sit cognitio aliqua ipsius an sit.

Aristoteles in 39. particula secundi libri Posteriorum, reddens rationem cur ille, qui rem esse cognoscit sine cognitione causae, non cognoscat quid ea sit, hanc rationem adducit: quia ille neque quod res ilia sit cognoscit, nisi leviter et ex accidenti:

Quod possumus colligere ex lib.2. Post. Text. 8 vel 9, qui reddens rationem cur ille, qui cognoscit rem esse sine cognitione causae, non cognoscat quid ilia res sit, ait hoc ideo contingere, quia ille neque quod res sit cognoscit, nisi leviter et

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quum enim res ita cognosci debeat uti est, ut autem sit habeat a sua causa, sequitur tune vere cognosci quod ea sit quando per causam per quam est cognoscitur.

ex accidenti; quia cum res eo modo, quo est, cognosci debeat, et esse habeat a sua causa, ideo tune vere et perfecte cognoscitur esse, quando cognoscitur causa prop ter quam est.

Zabarella's detailed and subtly argued analysis of the mental process called negotiatio intellectus or mentalis consideratio, by which the cause discovered through the first phase of the regressus (demonstratio quia) becomes known perfectly and precisely and can thus constitute the starting point of the second phase (demonstratiopropter quid), was closely followed and often copied almost word for word by Delia Valle: Zabarella 'Liber de regressu', Caput iv: 'In quo declaratur qualis sit in regressu primus processus etc.' (pp. 350351).

Vallius Quaest. 2: 'Quid sit regressus demonstrativus et quomodo fiat', Caput iii: 'Ostenditur qualis sit processus in demonstratione quia, quae est prima in regressu.' (pp. 344345).

Cognitio nostra duplex est, alteram confusam vocant, alteram vero distinctam; et utraque turn in causa, turn in effectu locum habet.

Cum duplex possit esse rerum cognitio, altera confusa, altera distincta; et utraque possit esse vel in causa vel in effectu.

Effectum confuse cogniscimus quando absque causae cognitione novimus ipsum esse, distincte vero quando per cognitionem causae; ilia quidem dicitur cognitio quod est, haec vero propter quid et simul etiam quid est.

Effectum quidem tune distincte cognoscere dicamus quando cognosciumus ilium per cognitionem causae, quando vero cognoscimus sine hoc, confuse; et haec cognitio confusa vocatur quod est, alia vero propter quid, in qua simul etiam cognoscimus quid est.

Causa vero quatenus causa est per causam sciri non potest, quia causam aliam non habet; si namque causam habet priorem, earn habet quatenus est effectus, non quatenus est causa.

Causa temen quatenus causa non potest cognosci per causam, quia non habet aliam causam; et si habet, sub hac ratione non est causa, sed effectus.

Datur tamen causae qui que cognitio turn confusa, turn distincta: confusa quidem, quando ipsum esse cognoscimus, sed quidnam sit ignoramus; distincta vero, quando cognoscimus etiam quid sit et ipsius naturam penetramus.

Datur tamen illius cognitio confusa et distincta eodem modo quo datur congnitio effectus; ita ut tune confuse causa cognoscatur, quando illius esse seu existentia cognoscitur; tune vero distincte, quando illiusnatura penetratur.

Appendix to Chapter 10 Exemplum aliquod nobis proponamus, in quo ipsam regressus naturam melius inspiciamus . . . Sumamus demonstrationem Arist. in lib. I Physicorum, qua ex generatione, quae substantiarum est, ostendit materiam primam dari ex effectu noto causam ignotam: generatio enim sensu nobis cognita est, subiecta vero materia maxime incognita.

Qualis sit regies us facile intelligemus: id quod otime explicat Zabarella exemplo desumpto ex Arist. in lib. I. Phys. ubi ex generatione, quae convenit substantiis, ostendit materiam primam dari. Ex effectu omnibus noto, qui est generatio, investigat existentiam materiae nobnis ignotissimae, quae est illius generationis causa.

Caput v: "Quod facto primo processu non statim regredi ad effectum possumus, sed mediam quandam considerationem interponi necesse sit" (p.351-354)

Caput iv: "Ostenditur post primam demonstrationem non sequi immediate deonstrationem propter quid, sed debere intercedere aliquid medium" (p.345-346)

Causa inventa, videtur statim ab ea regrediendum esse ad effectum demonstrandum propter quid: attamen hoc nondum facere possumus . . . Per regressum quaeramus cognitionem effecttus distinctam; hanc nobis causa confuse tantum cognita tradere non potest, sed earn prius distincte cognitam fieri oportet quam ab ea ad effectum regrediamur. Facto itaque primo processu, qui est ab effectu ad causam, antequam ab ea ad effectum retrocedamus, tertium quemdam medium laborem intercedere necesse est, quo ducamur in cognitinem distinctam illius causae . . .

Cum ergo in hoc primo discursu non habeamus cognitionem causae et effectus distinctam, neque cognoscamus causam et effectum formaliter . . . sed solum materialiter, et in premissis demonstrationis propter quid cognosci debeant causa et effectus formaliter . . ., non potest immediate post demonstrationem quia sequi demonstratio propter quid, sed debet intercedere aliquid morae . . . et illo tempore intermedio debeant aliqua considerari. . . quibus possimus cognoscere causam et effectum formaliter.

Hune aliqui vocarunt negotiationem intellectus, nos mentale ipsius causae examen appellare possumus seu mentalem considerationem . . .

Hanc intermediam intellectus considerationem aliqui vocant negotiationem intellectus, alii mentalem examen. . .

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Zabarella goes on to explain what this mentalis consideratio is and how it takes place by examining in detail two examples of regressus taken from Aristotle. He claims that nobody else has ever explained it in the same way. Delia Valle also refers more briefly to the two Aristotelian examples of regressus examined by Zabarella and adds this remark: 'Quae duo exempla ex Aristotele desumpta explicat Zabarella Cap. 4, 5 et 6 de regressu, ubi audit se primum advertisse et explicasse artificum Aristotelis in his duobus locis et regressibus, ab aliis antea non animadversum' (p. 345). In Galileo's autograph the question 'An detur regressus demonstrativus' is discussed without mentioning either Zabarella or his explanation of the mentalis consideratio. Something corresponding to the latter is

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only briefly hinted as one of several requirements or 'conditiones regressus': 'ut facto primo progressu non statim incipiamus secundum, sed expectemus donee causam, quam cognoscimus materialiter, formaliter cognoscamus' (MS. Gal. 27, f. 31 v). Even if there was a purely theoretical possibility of a common source for Carbone and Galileo, this could not have been lectures given by Delia Valle. Since Carbone's text was published from 1597 in successive editions of Toletus's Commentaria, of which Galileo owned a copy (above p. 172, n. 10), it is reasonable to conclude that Galileo drew the excerpts with which he compiled his logical Disputationes either directly from Carbone as well as from other so far unidentified sources, or from some also unidentified existing compilation including these excerpts from Carbone. In either case Galileo's autograph of the Disputationes could not have been written on present evidence before 1597'.

Carugo's new work disposes of speculation that Delia Valle could have been a source of Galileo's MS 27. In 1988 Wallace published with the Universita di Padova a volume entitled ' Tractatio de praecognitionibus et praecognitis and Tractatio de demonstration, transcribed from the Latin autograph by William F. Edwards, with an introduction, notes and commentary by William A. Wallace' (Padua 1988). From his preface we learn that Edwards had made an incomplete transcription some years before which he had made available (see also Wallace in the Times Literary Supplement, 3 January 1986, p. 13). Before that Wallace had already used Carugo's transcription of MS 27 for his Galileo and his Sources. He had now in his possession one complete and one seemingly partial transcription. The relation between them will not be discussed here. It is regrettable that Wallace's wild conjectures, repeated here, should be mistaken for established facts by some, even if happily only very few, scholars unfamiliar with the documentary evidence, including that in the Edizio Nazionale, and with critical scholarship. Thus Anthony Grafton in his recent review in Isis (Ixxx iii, 1992, p. 656) of the 1988 volume writes uncritically that Wallace 'has redated' the logical essays in MS 27 'to the years 1589-1591', and 'identifies their ultimate source, convincingly, as a transcript or reportatio of one of the courses in logic held at the Collegio Romano', then 'pinpointing the course that Galileo probably used: that of Paulus Vallius'. Wallace's principal objective, since we informed him of Galileo's use of Jesuit textbooks for his scholastic essays on logic, cosmology and natural philosophy, seems to have been to show that Galileo's Jesuit sources were different from those which we have identified. Thus in his Prelude to Galileo he wrote (omitting any reference to our information) that, following his article 'Galileo and the Thomists', his own 'subsequent research . . . has revealed that the physical questions' (i.e. the Tractatus de alteratione et de elementis) 'are based . . . on reportationes of lectures given by Jesuit professors at the Collegio Romano around the year 1590' (p. 181). What Wallace has in fact shown is nothing of the kind about either the content or the date of Galileo's essays, but simply, in laborious detail, that these successions of lecture notes from the end of the 16th century have general similarities in content and organization among themselves and with Galileo's scholastic writings. This we might expect if they were all based on the same Jesuit textbooks. But there are no specific

Appendix to Chapter 10

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correspondences of Galileo's manuscripts with those of the reportationes such as we found with the printed textbooks, including corresponding lists of references to ancient and medieval authors. All of these are fully documented in the sections of our book which were sent to Wallace in 1973 (acknowledged in the preface of his Galileo's Early Notebooks, 1977). In Galileo and his Sources Wallace vacillated between claiming that there is a closer correspondence of Galileo's essays with the manuscript reports and lectures than with the printed books (with the possible exception of Clavius's) and admitting the contrary. Thus, after comparing parallel texts of the Jesuit Mutius Vitellesch's manuscript lectures with Pereira's printed book, he wrote that Galileo's composition is much closer to Pererius's than to Vitelleschi's (p. 87). The obvious conclusion would be that Galileo used Pereira's textbook, easily available in several editions, rather than taking notes from any unique and obscure manuscript containing Vitelleschi's lectures or any others. Nothing in Wallace's book, or in his Prelude to Galileo (pp. 200-17), or in Galileo's Early Notebooks, supports his later claim in the TLS (3 January 1986, p. 23) that this 'was presented by way of exception' to the many closer parallels alleged with Vitelleschi. But Wallace found 'more likely' an even more bizarre conclusion: that Galileo's source was Delia Valle's lectures on the same subject, 'that Valla had himself used Pererius when writing a revised version of his notes, and that Galileo appropriated these for his own use, thus basing himself on Pererius at second remove' (Galileo and his Sources, p. 87). This is absurd.1 Galileo is notorious for seizing the opportunities of the moment. When we attempt to evaluate what was written by so complex and contentious a person, and what was written about him, or may seem to have been connected with him, as evidence for his thoughts, intentions, discoveries or sources, we need to be critically wide awake, or just normally awake. We must be strictly guided by the critical criteria established in his own time, equally in classical textual scholarship and in experimental science, for deciding the boundaries between what, on the evidence, we know and what we do not know. Galileo habitually made claims unsupported by any known evidence and frequently refuted by it. When he heard of a discovery or contribution to science he would claim that he had made it himself, even many years before, as with Santorio's thermometer (Opere, xi, 350, 506), and Bonaventura Cavalieri's demonstration of the parabolic trajectory of a projectile (xiv, 386). Sometimes he would appropriate the work without acknowledgement, as perhaps with Francois Viete's treatise on mechanics (above p. 225) and with Mersenne's formulation of the law relating the frequency of a pendulum to its length (see below ch. 13). He would use every rhetorical device to misrepresent the scientific competence and arguments of opponents, as he did with the Jesuit mathematician and 1

Cf. Michael Sharratt, Galileo: Decisive innovator (Oxford: Blackwell, 1994) 47-60, 226-8, for a scholarly account of these questions, refreshingly contrasting with the neoscholastic axe-grinding, ideological posturing, and omissions currently plaguing too much of the Galileo industry.

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astronomer Orazio Grass! in their dispute over comets, while obstinately rushing himself into some wrong headed and untenable conclusion (see Pietro Redondi, Galileo eretico, Torino, 1983; below appendix b). He was capable of ignoring almost completely fundamental contemporary theoretical and experimental discoveries, as he did with Kepler's astronomy and optics. He would opportunistically present an opinion, or even change his own opinion, in order to cultivate some possible supporter or patron, as in his apparent conversion to Neoplatonic cosmology in his exegetical letter of 23 March 1615 to Piero Dini, meant for the eyes of Cardinal Bellarmino (Opere, v, 297-305, xii, 151-2). He could take up a succession of contrary positions in the same assertive style without any reference to any change, as in his treatment of Copernican cosmology. Should we accept literally his outline of work in progress, and claim to years of studying philosophy, in his letter to Vinta in 1610? (above p. 179). Self-promotion was usual with those wanting to impress a patron and gain a position, but Galileo's gladiatorial competitiveness and slipperiness seem to have been excessive even in his context (cf. Mario Biagiolo, Galileo Courtier, Chicago, 1993; below appendix c). Evidence of Galileo's engagement in astronomy and in philosophy has a direct bearing on the problem of dating his three sets of scholastic essays in MSS 46 and 27. According to the records of the University of Pisa he lectured during 1589-91 on Euclid and in 1591 on the 'caelestium motuum hipotheses', which was probably Sacroboscos Sphaera (C.B. Schmitt, The Faculty of Acts at Pisa at the time of Galileo', Physis, xiv, 1972, p. 262). He wrote to his father on 15 November 1590 to thank him for the Galen in '7 tomi' as well as 'la Sfera' which his father was sending and added that he was 'studying and having lessons with Signor Mazzoni, who sends you greetings' (Opere, x, 44-5). It was Galen the natural philosopher whom he cited in the Tractatus de elementis (cf. above ch. 9, pp. 156-8). When Galileo wrote from Padua in 1597 to congratulate Mazzoni on his book In Universam Platonis et Aristotelis (1597) and to refute his argument there against Copernicus (above pp. 176,196-8), he added warmly his 'satisfaction and consolation' at finding that his old mentor, 'in some of the questions which in the first years of our friendship we used to dispute together with such delight, inclined to the side that had seemed true to me and the opposite to you'. It would be hard to believe that these disputed questions did not include those to which Mazzoni had devoted his book: general questions such as the necessity of mathematics for physical demonstrations, and more particular questions of natural philosophy concerning relative gravity, the elements, Archimedes, Plato versus Aristotle, etc. Accepting that Galileo could have developed a serious interest in natural philosophy as well as in mathematics after his return to Pisa in 1589, nothing yet follows for the dating of his scholastic essays or of De motu gravium. A common feature in all these undated writings is his use of Jesuit publications. He continued over a long period to draw from Jesuit textbooks simplified accounts of traditional theories which he discussed in his original works. Thus he used Pereira's De communibus . . . for the Tractatio prima de mundo and


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Tractatus de elementis and also for falling bodies in De motu gravium (above pp. 220-3; and see Carugo, 'Les Jesuites et la philosophic naturelle de Galilee: Benedictus Pererius et le De motu gravium de Galilee', History and Technology, iv, 1987, pp. 321-33). He used Clavius's Sphaera for the Tractatio de caelo and again for his account of the 'horizontal plane' of the Earth in De motu gravium, a question recurring in the Dialogo (Opere, vii, 174 sqq.; above pp. 221-2, cf. 177-8,226-7). He used Clavius yet again and another work by Pereira for his dated Lettere a Madama Cristina (1615), and, as Carugo has informed me, he drew from Giovanni Giorgio Locher, Disquisitiones mathematicae de controversiis et novitatibus astronomicis (Ingolstadt, 1614), the formulation of traditional arguments against the motion of the Earth discussed in the Dialogo (1632). Galileo's changes back and forth between Copernican and traditional cosmology are an object lesson in the dangers of trying to link his undated with his dated writings. In 1597 he defended Copernicus against Mazzoni and claimed to Kepler, characteristically congratulating him for having avoided 'a perverted method of philosophizing', that he himself had come to accept Copernicus 'many years ago' but had not dared 'until now' to bring his arguments into the open. A few years later in 1604 he assumed the traditional cosmological arrangement to assert an explanation of the new star scarcely compatible with his mathematical refutation of Mazzoni. Again in his Trattato delta sfera, despite his reference to Copernicans, he assumed the old cosmology. In the undated Tractatio de caelo he explicitly refuted Copernicus, while in De motu gravium he cited him once on another subject but assumed the geocentric cosmology throughout and made it explicit in the final draft of the introduction (above pp. 176-8, 222-3). We cannot then draw any conclusions about dating from this series of contradictory opinions presented in the same assertive style, not even that Galileo could not have written De motu gravium during his public campaign for Copernicus which opened in 1610. It seems clear that he composed the parts forming this work over a long period, but for how long remains a problem. In several parts of De motu gravium (Opere, i, 254-7, 269-72, 350-2) he applies to the motion of falling bodies some theorems on floating bodies that he had first conceived early in 1612, when he reworked an account, drafted late in 1611, of an experimental and philosophical dispute on floating bodies into the mathematical, experimental and philosophical treatise published in the summer of 1612 as the Discorso (iv, 69). Again, as noted by Carugo, one of the writings De motu gravium (i, 297-8) contains a mathematical demonstration of the motion of bodies on inclined planes which was based on a theorem ascribed to Viete sent by Giovanni Battista Baliani to Galileo in 1615 (xii, 186-8; above pp. 224-5). Yet again, in these writings (ii, 261-6) there is a draft of the correct analysis and definition of the accelerated motion of falling bodies, which Galileo first published in the Discorsi (1638; viii, 197-8; cf. above pp. 226-7). Since there is no mention of this in the Dialogo (1632), where Galileo makes a point of informing the reader of his most interesting results concerning motion, should

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we date this draft after 1632? As already shown above (pp. 225-6), the Dialogo, planned in 1624-25, was linked with De motu gravium and the scholastic essays on cosmology and natural philosophy both through the fragmentary notes in MS 46 and through their common use of Jesuit sources. If we must accept that MS 27 was written after 1597, is it absolutely impossible that the essays in MS 46, with their links with Galileo's earlier interests at Pisa, were written before that date? What about the passages in MSS 27 and 46 for which no sources have come to light anywhere? Perhaps they all come from some undiscovered Jesuit compendium hidden in some library? 'Far from it being true that he spoke with scorn and little respect of the ancient philosophers, and particularly of Aristotle, as some of those who profess to be his followers foolishly and wrongly assert', wrote Niccolo Gherdardini, who had known him, 'he said only that this great man's way of philosophizing did not satisfy him, and that there were in it fallacies and errors' (Opere, xix, 645; see above ch. 9, p. 149). He defined his position in two letters to Fortunio Liceti shortly before his death. 'I believe . . .' he wrote on 15 September 1940 'that to be truly a Peripatetic, that is an Aristotelian philosopher, consists principally in philosophizing in conformity with Aristotelian teaching, proceeding with those methods and with those true suppositions and principles on which scientific reasoning (discorso) is based, supposing those general notions from which deviation would be the greatest flaw. Among these suppositions is everything that Aristotle taught in his Dialectics (i.e. Posterior Analytics), taking care to avoid fallacies of reasoning, directing and disciplining it to syllogize well and to deduce from the admitted premises the necessary conclusion; and such doctrine concerns the form of arguing directly. With regard to this part, I believe that I have learnt from innumerable advances in pure mathematics, never fallacious, such certainty in demonstration that, if not never, at least extremely rarely, have I in my arguments fallen into equivocation. Here then I am a Peripatetic' (xviii, 248). Galileo was confirming here his lifelong adherence to the conception of truly scientific demonstration set out by Aristotle in the Posterior Analytics and most perfectly examplified in mathematics (cf. above ch. 9, below ch. 13). He went on in a letter of January 1641 to insist that, concerning the content as distinct from the the form of natural philosophy, he was far from being a Peripatetic. Natural philosophy, as he had said so often before, was not 'what is contained in Aristotle's books', but rather 'I truly hold the book of philosophy to be that which stands perpetually open before our eyes; but because it is written in characters different from those of our alphabet, it cannot be read by everyone: and the characters of such a book are triangles, squares, circles, spheres, cones, pyramids and other mathematical figures, fittest for this sort of reading' (xviii, 295). As his old friend Mazzoni had declared and he had illustrated in all his mature investigations: 'Aristotle, from failure to apply mathematical demonstrations in the proper places, has widely departed from the true method of philosophizing' (above p. 197). Galileo himself failed to understand that the criterion of range of confirmation as the test of a theory, which he so brilliantly used, put an end to the possibility of reaching in natural philosophy Aristotle's epistemological goal of necessary apodeictic demonstration (cf. above ch. 9, p. 161).

(b)

Pietro Redondi, Galileo eretico (Torino, 1983) [with Adriano Canugo]

This fascinating and important book is a brilliantly perceptive and learned study of the cultural context of Galileo's Copernican disputes. Unfortunately it is flawed by an untenable specific thesis based on a document of dubious authorship. The following are comments by Adriano Carugo and myself published in the Times Literary Supplement on 28 October - 3 November 1988, p.1203: Sir, - Your reviewer of Pietro Redondi's Galileo: Heretic (September 23-29) correctly casts some doubts on the authorship of the document on which alone the entire argument of the book is based, but he seems none the less to agree with the argument itself: namely, that the first and main motive that started the sequence of events which led to Galileo's trial and recantation was his atomistic explanation in // Saggiatore of the sensory qualities and its heretical implications for the dogma of the Eucharistic transubstantiation; and that this motive was deliberately kept secret and never surfaced in the documents relating to the trial because Pope Urban VIII, an old friend of Galileo and the dedicatee of // Saggiatore, wanted to avoid the scandal of condemning him for heresy. Anyone familiar with the National Edition of Galileo's works and writings, which contains every document hitherto known concerning his life, is aware that the new document brought to light by Redondi has nothing to do with the trial, but is connected with a much less dramatic event already well known through the National Edition. The Jesuit Orazio Grassi, who had been violently attacked by Galileo in // Saggiatore, replied with a lengthy and detailed rebuttal in which he exploited every chance of paying back Galileo in the same coin of mockery and insinuation. When he came to discuss Galileo's digression on the cause of heat, Grassi, among many other things, expressed en passant 'some scruple' about the difficulty of reconciling Galileo's explanation of the sensory qualities as pure names with the miracle taking place in the Sacrament of the Eucharist, where the properties of bread and wine are preserved while the substance is transformed. At first Galileo dismissed such a scruple as nonsense. In his own copy of Grassi's work he annotated: 'I leave this scruple for you, since // Saggiatore was printed in Rome, with the permission of the superiors, and

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dedicated to the supreme head of the Church; it was revised by those who are responsible for the protection of true faith and who, by approving it, must also have thought of the way to remove such a scruple' (National Edition, Volume VI, page 486). On the other hand, Galileo was quick to point out, Grassi had encountered the opposition of the Jesuits themselves over having his own book printed in Rome and had to publish it abroad, in Paris, as Galileo wrote 'without his superiors' permission' ('senza licenza dei superiori'). Later on Galileo must have had some scruple himself, for in January 1628 he wrote to his Benedictine friend Benedetto Castelli in Rome to ask him to inquire of Padre Riccardi, Maestro del Sacro Palazzo, whether he was taking Grassi's objections seriously. Castelli assured Galileo that Padre Riccardi was on his side: 'He said that your opinions are not against the Faith, since they are merely philosophical . . . and he intends to help you if any trouble should be caused to you in the Tribunal of the Holy Office' (XIII, 393). The question was never raised again in Galileo's correspondence, nor is it mentioned in any other document in the National Edition. The new document found by Redondi, which is an anonymous assessment of Galileo's atomism in relation to the dogma of transubstantiation, and is addressed to an unnamed Padre (possibly Padre Riccardi himself), throws further light on this episode in Galileo's life. As such it constitutes an interesting and important addition to the National Edition, but that is all. As for 'Why the Church really quarrelled with Galileo', as announced on the front page of the TLS, the unique issue of Copernicanism is unequivocally documented in the records of the trial. There is no other doctrinal issue there, but there was a disciplinary issue concerning Galileo's behaviour in breaking his promise formally made in 1616 to Cardinal Bellarmine 'not to maintain, teach, or defend in any way, in words of writing', the Copernican opinion. Urban did not know of this promise, neither had Galileo informed him, when in 1630 he gave Galileo permission to publish a dialogue discussing nonconclusively the philosophical and physical arguments for and against both the Copernican and the Ptolemaic systems. This permission was given on condition that the book was published in Rome with the imprimatur of the Maestro del Sacro Palazzo. Because of the plague Galileo decided to have it printed in Florence, and in order to start this he asked Riccardi to send him a formal imprimatur on condition that he sent Riccardi the proofs sheet by sheet for final approval. Galileo did not send the proofs except for those of the preface and conclusion. The Dialogo sopra i due massimi sistemi del mondo was published in 1632 in Florence with Riccardi's imprimatur, which applied only in Rome, together with a second imprimatur from the Florentine Inquisitor. When the Pope received his copy he was furious. The documents do not state explicitly why. The first Commission which he appointed to examine the case discovered among the earlier records that of Galileo's promise to Bellarmine. The trial proceeded from there. It seems to us that, like many complex and influential historical events, the trigger was probably something accidental and even trivial, namely Urban's


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irritation at the apparently deceptive way in which Galileo had manipulated his permission to publish his book. Rivers of inky imagination have dramatized this event in ways that distort the real intellectual importance of its consequences. Recent writing on seventeenth-century history has been plagued, notoriously by the neo-puritan, neo-Marxist persuasion, with supposititious 'reasons of state' and other hidden motives behind the plain evidence of the documents. It would be a pity if Galileo studies were to go the same way.

(c)

Mario Biagioli, Galileo, Courtier: The Practice of Science in the Culture of Absolutism (Chicago, 1993); review published in the Washington Post; Book World, 12 December 1993, p. 9.

'It is in the royal interest to keep everybody suspended between fear and hope' (p.20). The author of the contemporary handbook on court manners under absolute princes quoted here went on to describe 'how the natural instability of favour is in the interest of the powerful' (p.325), how the successful competitor for 'the fruits of servitude' under princely patronage was permanently exposed to danger from mutations of princely interest of which he had neither intimate understanding nor control, and how on falling 'from the summit of favour one does not descend through the same steps which lead to the top. Often nothing stands between one's highest and lowest status' (p.327). The fallen favourite could not comprehend what he had done wrong; he found himself shunned by former friends at court; he did not just lose his privileges but had to be humiliated. The mythology of the system required that the princely patron possessed everything that he could possibly want. He received gifts, as he provided favours, by pure grace. Yet in fact both sides needed the other, the one for the benefits acquired, the other in order to manifest the honour and power on which his position rested. The problem for the ambitious client lay in the asymmetry of a relationship in which the prince alone had the power and could demand unlimited service and honour without any obligations. It is within a fascinating account of this courtly system that Mario Biagioli places the second and most celebrated half of Galileo's long scientific career. Galileo seems to have embarked in 1601 at the age of thirty-seven on the strategy that would enable him to escape from his position as a mathematical professor at Padua into an enhanced status at court. Along this social trajectory he constructed what Professor Biagioli calls 'a new socioprofessional identity for himself (p.5) as a philosopher creating at once a new natural philosophy and an audience for it. After some false starts with his military compass presented to the Gonzaga at Mantua, and an adroitly flattering emblematic play on the words cosmos and Cosimo II equating the attractive power of the ruling Grand Duke of Tuscany with that of William Gilbert's


493

great cosmic magnet, he hit upon the right formula with his discovery of Jupiter's four satellites early in 1610. By getting permission to call these the Medicean stars and to dedicate the Sidereus Nuncius describing them to the Grand Duke, he obliged this prince to endorse his discoveries. Since, he wrote in his preface, 'under Your auspices, Most Serene Cosimo, I discovered these stars unknown to all previous astronomers' (p. 132), they should rightly have his family name. His reward was his invitation back to Florence as the Grand Duke's chief mathematician and philosopher, a privileged entry into the world of the court. Galileo particularly requested that his title should include philosopher as well as mathematician, and this raises the interesting question of when and how he acquired his quite considerable knowledge of Aristotle. Certainly it was not as a student at Pisa, but some light may be thrown by the discovery some years ago by Adriano Carugo and myself that three unpublished essays in his hand on Aristotelian logic, physics and cosmology were based on well known textbooks written by, or associated with, Jesuit professors at the Collegio Romano. These (despite some unhappy American publications on the matter) cannot be dated by any known evidence, except that, as we have shown, the logical essay cannot have been written before 1597. Since Galileo's earlier interests were essentially in mathematics and its applications, it could be that his philosophical studies were part of his strategy of 'self-fashioning as a court philosopher' (p. 11). Besides this crucial move to the Florentine court, Biagioli gives detailed treatment on the same sociological lines of some further important episodes in Galileo's life: the dispute in 1611-13 over floating bodies which involved the fundamental difference between Aristotelian and mathematical (here Archimedean) physics; the transfer of his patronage focus to Rome; the dispute in 1619-28 with the distinguished Jesuit Orazio Grassi over comets to which Galileo contributed his brilliantly dialectical // Saggiatore (1623); and the publication of the Dialogo (1632) on cosmological systems, followed by his trial. The whole book makes interesting reading, despite its frequent repetitiveness, and it was a good and original idea to locate Galileo within the world of the courts, of which Biagioli gives so learned an account. Thus 'Galileo is presented not only as a rational manipulator of the patronage machinery, but also as somebody whose discourse, motivations, and intellectual choices were informed by the patronage culture in which he operated throughout his life' (p.4). He insists that Galileo's science was not 'determined by these concerns . . . Power does not censor or legitimate some body of knowledge that exists independently of it' (p.5). For all that he asserts repeatedly that Galileo's position and title as court philosopher was 'a crucial resource for the legitimation of Copernicanism and mathematical physics' (p.49); that this connection 'gave Galileo credibility' (p.58); that 'Galileo's strategy was aimed at legitimizing scientific theories by including them in the representation of his patron's power' (p. 125); that his recognition by the Medici 'allowed him to become even more credible and draw further assent to his discoveries from

494


others' (p. 133). Galileo certainly knew what he was doing in getting court patronage, both in Florence and in Rome, to support his scientific work and his personal career, but while he was a master of all the arts of rhetoric, persuasion and political manoeuvre, he certainly did not confuse the presentation and acceptance of his discoveries according to the manners of courtly culture with their credibility to his scientific peers. Court culture was irrelevant to scientific knowledge. Confirmation of the reliability of the telescope and of Galileo's discoveries made with it were requested by Cardinal Bellarmine from the competent Jesuit mathematicians at the Collegio Romano, and by the Emperor Rudolph II and the Medici ambassador from Kepler. They knew what they were doing. You cannot cheat nature was a favourite of Galileo's aphorisms, however much you may cheat your fellow men; and in the margin of the Dialogo: 'In the natural sciences the art of rhetoric is ineffective' (Opere, vii, 78; cf. below ch. 11). I had a sense in reading Professor Biagioli's reconstructions that Galileo and his contemporaries and disputes were being translated from 17th-century Italy into the world of 20th-century transatlantic sociology. Anthropological comparisons across cultures far apart in time and place may indicate certain constants of human behaviour, but may abstract these from recognizable distinctions of different cultures and from the individuality of real people. For all that the exercise can be illuminating, as in Biagioli's plausible, though not necessarily credible, interpretation of Galileo's fall from Papal favour. 'I do not hope for any relief, because I have not commited any crime', Galileo wrote on 21 January 1635 to Nicolas Fabri de Peiresc, who had been trying through the Pope's nephew Cardinal Francesco Barberini to get some relaxation of Galileo's house arrest at Arcetri. 'I could hope for and obtain mercy and pardon if I had erred, for faults are matters upon which a prince can exert mercies and dispensations, whereas upon someone who has been innocently condemned it is convenient to be rigorous, so that it seems that it has been done according to the law' (Opere, xvi, 215). Galileo certainly knew the score, even as a fallen favourite.

Corrections to Science, Optics and Music in Medieval and Early Modern Thought (1990)

p. vii, ch. 12: for Theory and Change read Theory Change. p. xvii: Science, Art and Nature 1995, Styles of Scientific Thinking 1994. p. 24, para. 3, line 9: "overweening". p. 29, para 3, line 3: "assertion". p. 55, Fig. 1 caption line 7: for "respectively; the rays" read "respectively, the rays". p. 117, line 2 from bottom: for "local" read "logical". p. 195, Fig. 17 caption line 4: after "ends" add "(labelled in reverse in MS)", and line 7: after "with" add "the". p. 228, Fig. 33 is printed upside down: see Fig. 49. p. 258, line 3 from bottom: for "(1986)" read "(1983)". p. 417: Further references were inadvertently omitted and will be found in the present volume at the ends of chapters 13 and 14.

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Index

(Sub-headings are in alphabetical order, except where chronological order is more helpful) Abano, Pietro d' 292 Abd al-Rahman ibn 'Umar al-Sufi (Asophus) 62 Abu Ma'shar 60 academies: —, Academia Fiorentina del Disegno 173 —, Academie Royale des Sciences 299, 347, 409, 411, 460, 461 —, see also colleges and universities acoustics see hearing; music; sound Adam 275, 276, 279 Adelard of Bath 16, 31, 32, 56, 59 Adrastus 293 Agricola 320 Agrimi, Jole 471 Aguilon, Francois 347 AIDS 449 Ailly, Cardinal Pierre d' 59, 62 Aix-en-Provence 271, 287 al-Battani 47, 62 al-Bitruji 58 al-Farabi, Abu Nasr 59, 79, 96 al-Farghani 59, 60 al-Kindi see Alkindi Albert of Saxony 80, 277 Alberti, Leon Battista 89, 98-9, 132, 453 —, and history of optics 319, 473 —, and origins of language 277 Albertus Magnus 47, 52, 126, 454 albinism 418, 421,424 alchemy 52, 54, 57, 63, 155 Aldobrandini, Ippolito see Clement VIII, Pope Alembert, Jean le Rond d' 392, 409, 462 Alexander of Aphrodisias 221 Alexander of Hales 52

Alexandria (city) 70 Alfarabi, Abu Nasr 59, 79, 96 Alhazen (Ibn al-Haytham) 55, 56, 132, 292, 336 —, critics 331, 333, 334 —, and history of optics 76, 305-17, 323, 326-7, 471, 473 —, —, model of eye 38 —, —, Optica 316, 319 —, visual theories 304, 325, 327-8, 329, 354-5 Alkindi (Al-Kindi) 55, 305 Alphonsine tables 62 Ambrosian Library of Milan 175, 187, 288 America see United Sates anatomical research 278, 320, 334 'Ancients and Moderns' 36, 453, 454, 460-1 Anglicus, Robertus 60 animals: —, and albinism 421 —, antelope 288 —, ass 418, 420 —, chickens 412, 421 —, dogs 418 —, monkeys 418 —, and origins of language 278, 280, 282 —, pigeons 418 —, salamander 411 —, scorpion 412 antelope 288 antibiotics 448 Apollonius 341-2 Apuleius, Lucius 357 Aquinas, St Thomas 77, 81, 126, 183-4, 228

498


—, and assent 370 —, and Galileo 189, 190, 193 Arabic texts 32-3 Aranzi, Giulio Cesare 324 Arber, Agnes 471 Arcetri (Italy) 24, 494 Archimedes 95, 102, 126, 129, 131 —, and the balance 208, 224, 469 —, and Galileo's undated writing 222, 223, 224, 225 —, and gravity 175 —, and mathematics 59, 151, 197 —, and scientific revolution 456 —, and theology 470 —, alluded to 149, 204, 486 architects/architecture 101, 103, 132, 212, 320 Archytus of Tarentum 9, 129, 219 argument, history of 12, 180-1, 357-400, 443-9, 467 Argyll, Duke of 398 Aristides Quintilianus 293 Aristotle 60, 190, 191, 192, 261 —, and acoustics 297-8 —, on art & nature 93-5 —, and causality 440-1 —, and Christian theology 22, 151, 470 —, on comets 177 —, and ethics 16 —, and expectation and choice 358, 3624, 367, 387, 390, 391 —, and false premise 182 —, and gravity 259, 260 —, as historian of science 37 —, and history of optics 325, 471 —, and influence on Galileo 149-61 —, and logic 51, 369, 440-1, 467 —, and mathematics 197, 198, 200 —, on mechanics 129 —, on morals 94 —, and music 292 —, and origins of language 275, 278 —, and philosophy 20, 21, 127 —, and physics 16 —, on politics 95 —, and primary & real properties 218, 219 —, and rhetoric 232, 236-40, 243, 247-8, 250-2, 362-3 —, and scientific revolution 456 —, and scientific style 159, 467, 468 —, and undated writing of Galileo 222, 226

—, alluded to 17-18, 40, 42, 43, 68, 71, 82-3, 87, 102, 121, 128, 132, 180, 183, 189, 206, 211, 357, 358, 414, 469, 470, 483,486, 488 Aristotelian/Thomist revival 166 Aristoxenus 131, 219, 292, 293, 295 arithmetic 59, 115, 178 —, commercial 377 —, political 385 Arnauld, Antoine 379, 382-4 artists, rational 89-114 art(s) 19 —, and geometry 99 —, and nature —, —, Aristotle on 93-5 —, —, Ficino on 100, 136 —, rational 473 Arundel, Lord (Thomas Howard) 288 Aselli, Gasparo 111 Ashmolean Museum 288 Asophus (Abd al-Rahman ibn 'Umar alSufi) 62 assent/judgement 367, 369-74, 380, 381 asses 418, 420 astrology 61, 115, 132, 136, 470 —, R. Bacon on 52, 54, 58, 60-1 —, Bonaventura on 52 —, Grosseteste on 47 —, and Possevino 132 —, Vieri on 136 astronomy 42, 181, 209, 257, 470, 471 —, Babylonian 86 —, and R. Bacon 54, 58, 61 —, and calendar reform 61 —, and camera obscura 320-3 —, and Clavius 155, 177, 178 —, clocks 82 —, and Copernicus 155, 209 —, education in 115, 117 —, and Galileo 178, 185, 209, 258, 486 —, Greek 86, 413, 441 —, Grosseteste on 40, 42, 46, 47 —, Hebrew tables 62 —, Leonardo da Vinci on 100-1 —, mathematical, & celestial motion 99, 155, 183 —, new star of 1604 177, 178 Atestinus, Cardinal 129 Athenaeus132 Athens, plague of 13 atomism 58, 71, 72, 157, 158, 490 atomists 68, 204 auditory perception 107-10, 291-9

Index Augustine, St (Augustine of Hippo) 69, 72, 127, 469, 470 —, and expectation and choice 368 —, and hearing 292 —, on laws of nature 69, 72-5, 77 —, and origins of language 276 —, and Platonism 139 —, and providential creation 27, 33 Augustine to Galileo (Crombie) 475-6 Avempace 153 Averroes 79, 126, 153, 189, 191 epicycles & eccentrics 181-2, 183 Avicenna (Ibn Sina) 56, 76, 79, 190 Avignon 125 Babel 109, 276, 279 Babylonian astronomy 86 Bach, J. S. 427 Bacon, Francis 211, 258, 387, 454 —, and expectation and choice 379-80, 383 —, and history of optics 343 —, and intellectual reform 17 —, and new science 35, 36, 279, 459 —, and scientific revolution 456, 457-60, 463 —, and universal language 278 Bacon, Roger 276, 278, 471 —, biography —, —, birth, date of 51 —, —, family background 51 —, —, education 51, 54 —, —, and Franciscan order 52, 53 —, —, imprisonment 53, 61 —, —, last written work 53 —, on alchemy 57, 63 —, analytical skills of 58 —, on astrology 52, 54, 58, 60-1 —, and astronomy 54, 58, 61 —, and benevolent destiny 27 —, and calendar reform 58, 61, 62, 63 —, and causality 441 —, on church reform 53 —, on experience 53-4 —, and geography 59 —, on geometry 58 —, and Grosseteste 39, 47, 52, 55, 56, 61 —, and language 51, 52, 56, 276 —, on mathematics 52, 54, 56, 60, 97 —, —, and logic 59 —, —, usefulness of 58 —, nature, and laws of 75-7, 472 —, optics 52, 54, 55, 56, 63, 292

499

—, —, history of 316, 317-19, 326 —, at Oxford 51, 52 —, at Paris 51, 52,58 —, on radius of earth 60 —, and rainbows 472 —, and reform 16-17, 33 —, and scientific revolution 454 —, scientific thought 53-63 —, on truth 53 —, written work 51, 52, 53, 57-8, 62-3 Bailly, J.S. 463 balance, theories of 208, 224, 469 Balduino, Girolamo 155 Bale, Bishop John 455 Baliani, Giovanni Battista 161, 208, 2245,487 Barbaro, Daniele 101, 132, 212 —, and history of optics 324, 327, 343 Barberini, Cardinal Francesco 272, 287, 494 Bardi, Count Giovanni 294, 295 Baronio, Cardinal Cesare 126 Barozzi, Francesco 117, 122, 131, 175, 194 —, and mathematics 195 Basel 324 Basil, St (of Cappadocia) 56, 127, 470 al-Battam 47, 62 Bayes, Thomas 387, 448 Bayle, Pierre 36, 456 'Beagle' voyages of Darwin 429, 431, 433 Beaulieu, Armand 287 Beeckman, Isaac 108, 296 The Beginnings of Western Science (Lindberg) 465, 468-74, 476-7 belief and doubt 166, 490 —, 'Bibliotheca selecta' (Possevino) 126 —, Christian 54, 61,68 —, Hebrew thought 68, 69 —, Islam 54, 61 —, Judaism 54 —, see also Catholicism; Creator; God; theology Bellarmine, Cardinal Robert 126, 184 186, 257, 258 —, Galileo's promise to 490 —, alluded to 185, 486, 494 Bellini, Lorenzo 118 Benedetti, Giovanni Battista 108, 132n, 219, 294, 296 —, and optics 327-8, 329 benevolent destiny, concept of 27 Berkeley, George 354

500


Berlin Academy of Frederick the Great 407, 410 —, see also colleges and universities Bernard of Chartres 31, 454 Bernardino of Siena 375 Bernoulli, Daniel 448 Bernoulli, Jakob 384-5, 387, 388, 392, 427 —, and expectation and choice 379, 384 —, and mathematics 447 Besson, Jacques 320 Biagioli, Mario 492-4 Bianchi, Luca 470 Biblioteca Nazionale Centrale di Firenze 167 Bibliotheca selecta (Possevino) 126-32 biology 21-2, 27, 106, 118, 435 Biondo, Flavio 453 al-Bitruji (Alpetragius) 58 Bodin, Jean 35, 383 Boethius, Anicius Manlius 18, 59, 219, 469 —, and music 42, 292, 293 Bologna 115, 117, 118, 139 Bonamico, Francesco 126, 158 Bonaventura, St 52 Bonnet, Charles Etienne 427 Borelli, Giovanni Alfonso 118 Borri, Girolamo 135, 139 Bossuet, Jaques Benigne 462 Bouchard, Jean-Jacques 272 Bourdelot, Pierre Michon 272 Boyle, The Hon. Robert 67, 84-5 Bradwardine, Thomas 59, 80, 454 Brahe, Tycho 177, 329-30, 331, 334, 471 Brengger, Johann 301, 342 Breslau (town) 387 Bresson, Agnes 287 Briggs, William 345 Britain 264, 399 —, see also England Broad, C.D. 263 Broussais, Francois 447 Brunelleschi, Filippo 319, 320, 473 Brunei, Pierre 407 Bruni, Leonardo 453 Bruno, Giordano, 166, 249 Brunschvicg, Leon 263 Brussels 264 Buff on, George-Louis Leclerc, Comte de 387, 388, 417, 418, 432 —, and classification of species 418, 427 —, on geology 418 —, and history of science 462

—, and statistical analysis 448 Bulver, Ezekial (fict) 28 bulverism 28 Buridan, Jean 80, 82, 470, 473 Burnet, Thomas 385 Burtt, Edwin 264 Butler, Bishop Joseph 416 Byzantinum 470 Caietanus, Thomas de Vio see Cajetan Cajetan (Thomas de Vio) 126, 155 Calcidius 69, 469 calendar reform 19, 47, 61, 62 —, and al-Battani 47, 62 —, R. Bacon on 58, 61, 62, 63 —, Gregorian 62, 125-6, 156 —, Grosseteste on 40, 47, 62 Cambridge 263, 433 camera obscura 340, 345-7, 350 —, in astronomy 320-3 —, experiments with 305, 310-11 —, as model of the eye 38, 105, 327, 329, 336-8 —, and ocular physiology 301 —, and painting 343 —, and screen image 326, 332 —, and solar eclipses 329-30, 332 —, Straker's account of 473 —, and visual theory 326 Campanella, Tommaso 80, 456, 457 Campanus of Novara 59 Carbone, Ludovico 169, 222, 270, 480 —, and correspondences with Galileo's texts 169-72, 479 —, and undated writing of Galileo 222 Carcavy, Pierre 208 Cardano, Girolamo 115, 126, 131, 132n —, and expectation and choice 377 —, and origins of language 284 —, and rhetoric 249 Carneades of Cyrene 364-6 Carrara, Bellino 165 cartography 19, 99, 106 Carugo, Adriano 155, 156, 158, 484, 489 —, and Galileo's Jesuit sources 269-70, 479-80, 486, 493 —, and Pinelli collection 175, 187 —, and sources of Galileo's scholastic essays 151, 153, 156, 167-9, 487 Casaubon, Isaac 289 Casserio, Giulio 298, 320 Cassirer, Ernst 194 Castelli, Benedetto 118, 209, 211, 272, 490

Index Catena, Pietro 117 Catholicism 135, 166 —, see also belief and doubt; Creator; God; theology causality 68, 71, 455, 459, 466-7 —, language of 440-1 cause and effect 86, 446 Cavalieri, Bonaventura 118, 226, 485 Ceredi, Guiseppe 102, 132, 212, 301, 302 Cesi, Frederico 223, 226 chance, games of 381, 382, 384 Charles, E. 51 Charles V, King, of France 82 Charron, Pierre 167 Chatelet-Lomont, Gabrielle Emilie, Marquise du 462 Chaucer, Geoffrey 81, 469, 470 Chiaramonti, Scipione 244, 245 chickens 412, 421 Children's Crusade 54 Chillingworth, William 380 Chinese medical practice 446 Chinese and origins of languages 278, 283 Christian moral theory 99 Christian theology 5, 72, 79, 99, 469 —, and Aristotle 22, 151, 470 Christianity and cosmology 27 church reform 36, 53, 456 —, see also belief and doubt Cicero, Marcus Tullius 51, 127, 455, 469 —, and expectation and choice 366-7 Cimabue, Giovanni 34, 453 Cimento, Academia del 118 —, see also colleges and universities Clagett, Marshall 477 Clarke, Samuel 408 classical languages 118 classification of species 413 Claudius Galius 129 Clavelin, Maurice 270 Clavius, Christopher 119, 122, 132n, 182 —, on astronomy 155, 177, 178 —, and calendar reform 62 —, Galileo visits 156, 175, 479 —, and influence on Galileo 176, 181, 194, 269-70 —, and influence on Possevino 128, 131 —, and mathematics 119-21, 122, 196, 198, 216 —, and MS Galileiana 27, 479, 480 —, and optics 326-7 —, and science 181-3, 184, 185, 187 —, and telescope 217

501

—, and undated writings of Galileo 2212, 224, 226, 227, 486-7 Clement of Alexandria, St 127 Clement IV, Pope 52, 53, 60 Clement VIII, Pope (formerly Ippolito Aldobrandini) 116n, 126, 139, 140 clepsydra 56 climate 43, 387 clinical trials 447 clock, mechanical 19, 473 clocks 60, 82 Goiter, Volcher 298 colleges and universities 115-40, 455 —, Academic Roy ale des Sciences 299, 347, 409, 411, 460, 461 —, 'Accademia della dottrina Platonica' 133 —, Basel 324 —, Berlin Academy of Frederick the Great 407, 410 —, Bologna 115, 117, 118, 139 —, Cambridge 433 —, Cimento, Academia del 118 —, Collegio Romano 132n, 153, 154, 165, 167, 168 —, —, and Carbone 172 —, —, and Clavius 217 —, —, founded 119 —, —, and Pereira 133, 270 —, —, and Rocco 186 —, —, and Scheiner 345 —, —, and Vallius 169 —, decline of 476 —, Ferrara 139, 140 —, Fiorentina del Disegno, Academia 103, 173 —, Florentine Academy 134 —, Gymnasium Patavium Societatis Jesu 126 —, Louvain 345 —, Messina 118 —, Padua 140, 172, 175, 177, 198, 484 —, —, and Galileo 178, 225, 227, 492 —, —, and mathematics 117, 118, 134 —, —, and philosophy 125, 133 —, —, and Possevino 126 —, Pavia 140 —, Pisa 116, 117, 118, 134-5, 139-140, 150, 486 —, Prague 334 —, Rome 133, 139, 140, 153 —, —, mathematics at 115, 116, 122 —, Venice 151, 294 Collingwood, R.G. 263

502


Colombe, Cristoforo delle 245-6 Colombo, Realdo 324, 325 colour and light 45 Columbus, Christopher 59 comets 43, 177, 178, 187, 211, 269, 485 —, Galileo v Grassi dispute 493 Commandino, Frederico 131 commerce/book-keeping methods 19 communism and truth 29 compass 175, 492 computer 90 Comte, Auguste 259, 260, 262, 463 Condillac, Etienne Bonnet de 410 Condorcet, Marie Jean Antoine Nicolas de Caritat, Marquis de 461, 463 Constantine I 453 Cooper, Lane 259 Copernicus 61, 131, 182, 187, 258 —, and astronomy 155, 209 —, and Galileo 153, 176, 177, 181, 186 —, —, and undated writings 222 —, and rhetoric 244 —, alluded to 344, 486, 487 coral reefs 433 Cosimo I, Grand Duke of Tuscany 117 Cosimo II, Grand Duke of Tuscany 179 cosmography see cosmology cosmology 22, 178, 228, 486 —, and Christianity 27 —, and Duhem 37 —, and Galileo 23, 80, 155, 167, 177, 487 —, and Grosseteste 470 —, and Kepler 433 —, and Maupertuis 420 Cotrugli, Benedetto 375 Council of Trent 136, 165, 166 Cournot, Antoine-Augustin 387 court manners 492 creation 27, 33, 67, 139 Creator 389, 396, 397, 441 —, benevolent 20, 22 —, eternal/onmnipotent 69, 72, 87, 113, 161 —, see also belief and doubt; Catholicism; God; theology Cremonini, Cesare 133 crime 372 Crisciani, Chiara 471 Crombie, Alistair C. 168, 172, 465-77, 471,472 Crowley, T. 51 Ctesibus 132 Cuvier, Georges 463

d'Abano, Pietro see Abano, Pietro d' d'Ailly, Cardinal Pierre see Ailly, Cardinal Pierre d' d'Alembert, Jean le Rond see Alembert Dalton, John 9 Dante, Alighieri 156 —, on origins of language 276, 441 —, and vernacular philosophy 469 —, and poetical revival 34 —, and Western science 471 Danti, Egnazio 132 Darwin, Charles —, and 'Beagle' voyages 429, 431, 433 —, and biology 21-2, 435 —, criticism of predecessors 430 —, and evolutionary theory 9, 38 —, and expectation and choice 393-8, 399 —, and letters 430, 432 —, and natural selection 425, 431, 435, 436, 437 —, rhetoric of 6 scientific method 429-37 —, and transmutation of species 434 —, see also evolution Darwin, Erasmus 429 Darwin, Francis Charles 432 de Honnecourt see Villard de Honnecourt de 1'Epee, Abbe Charles-Michel 285 De Morgan, Augustus 62 De motu gravium (Galileo) 201-5 deaf and dumb 109, 110, 276, 279, 283-4 Dee, John 48, 62, 63 Delambre, Jean Joseph 463 Delfino, Frederico 117 Delia Valle see Paulus Vallius Democritus 218 demography, population 385 Descartes, Rene 67, 83-4, 106, 408, 414 —, and expectation and choice 383, 391 —, and history of optics 345, 348-52, 353, 354 —, —, and camera obscura 350 —, and intellectual reform 17 —, on laws of nature 67, 83-4 —, and natural philosophy 228 —, and origins of language 282 —, and rainbow 38 —, and rhetoric 6 —, and scientific revolution 456, 457-8, 460 —, and scientific style 229, 270, 467, 472 —, and sound 296

Index d'Este, Cardinal Alessandro see Este, Cardinal Alessandro d' destiny, benevolent 27 determinism 22, 79 Dialogue (Galileo) 210-11 Diderot, Dennis 417, 427, 461 digestive system 111 Digges, Leonard 63 Dini, Piero 185 Diodati, Elie 271 —, and undated writing of Galileo 225 disease 372, 372-3, 443-9 —, AIDS 449 —, records 386, 386-7 —, smallpox 392 Disputationes (Galileo) 187-95 dissection 420, 433 dogs 418 Dominican order 53 Dondi, Giovanni de' 82, 473 Doni, Giovanni Battista 271, 272 Drake, Stillman 149, 161 Dryden, John 461 du Chatelet, Madam see ChateletLomont, Gabrielle Emilie, Marquise du du Laurens, Andre 298 Duhem, Pierre 37, 38, 132n, 257, 471 Duns Scotus, John 47 Diirer, Albrecht 99, 132, 320, 332 Duverney, Joseph Guichard 299 dynamics 180, 185 Earth, planet 160, 179 —, movement of 183, 184-5, 470, 487 —, orbit of 181 —, radius of 60 Eastwood, Bruce 465 eclipses 52, 329-30 ecology 7 economy 16, 22, 392 Edgerton, Samuel Y., Jr 473 education 115-40 —, arts/natural science 118 —, in astronomy 115, 117 —, classical languages 118 —, history 118 —, literature 118 —, logic 118 —, mathematics 118-40 —, metaphysics 118 —, moral science 118 —, oriental languages 118 —, physics 118

503

—, theology 118 —, see also colleges and universities Edwards, William F. 484 Elizabeth I, Queen of England 62 Empedocles 391 empiricism 262 Engels, Friedrich 394n engineering 23, 58, 96-7, 106, 320 England 35 —, and calendar reform 62 —, Peiresc travels to 286 —, see also Great Britain English philosophy 452 enlightenment 35 Enriques, Federigo 477 Epee, Charles Michel de L' 285 Epicurus 69 epicycles and eccentrics 181-2, 183, 184, 185 Erasmus 36, 455 Este, Cardinal Alessandro d' 254 ethics, Aristotelian 16 Ethiopia 288 Euclid 122, 123, 131, 132, 175, 486 —, on acoustics 96 —, and geometry 16, 17, 96, 217, 432-3, 469 —, and logic 369 —, and mathematics 96, 161, 196, 200 —, and music 18, 293, 295 —, and optics 55, 302-3, 305, 308, 471 —, —, and perspective 46, 137 —, —, treatise on 18 —, andProclus 101, 175 —, on ratios 58-9 —, and science, language of 441 —, and scientific argument 95 Eudoxus of Cnidus 68, 467 Euler, Leonhard 410 European groups and origins of languages 278 European interest in medieval history 37 ever-burning lamps 57 evolution 22, 398, 407, 412, 428, 429-37 —, see also Darwin, Charles; natural selection; transmutationof species evolution and the ass 418 expectation and choice 357-400 experience 53-4 experimental method 257 experimental philosophy 258, 262 experimental science 89-114, 467, 471 explosive powder 57 eyes 303-17, 319-28, 329, 333-42, 344-55

504


—, and camera obscura 38, 105, 327, 329, 336-8 —, see also under Alhazen; Ptolemy; see also optics Fabrici d'Acquapendente, Girolamo 126, 279 —, and language 278, 281, 282 —, and optics 320, 325, 334 falling bodies 104, 176, 208, 215-16, 268, 486, 487 Falloppio, Gabriele 126 false/true premise 182 falsification, method of 43 al-Farabi, Abu Nasr 59, 79, 96 Faraday, Michael 3, 441 al-Farghani 59, 60 Favaro 175, 205 —, and writings of Galileo 151, 156, 167, 222, 224 Ferdinand The Catholic' (Ferdinand II of Aragon) 59 Ferguson, Wallace K. 455 Ferrara 133, 139, 140 Ficino, Marsilio 19, 69, 95, 127 —, on art and nature 100, 136 —, and Catholicism 135 —, and music 293 —, and philosophy 166 —, and platonism 139 —, and rhetoric 249 —, and undated writings of Galileo 226 First Cause theory 22 First Council of Lyons (1245) 41 First Letter about the Sunspots (Galileo) 87, 150, 180, 186, 215, 216 Fisher, R.A. 448 Florence 156, 158, 159, 173, 271, 493-4 —, and Galileo's writings 224, 225, 490 —, and mathematics 118 —, Michelini returns to 272 Florence, Council of 125 Florentine Academy 134 —, see also colleges and universities Florentine Accademia del Disegno 103 Fludd, Robert 111 flying machines 33, 57 Fogliano, Lodovico 99 Fontenelle, Bernard le Bovier de 461 fossils 418, 433, 434 France 35, 125, 264, 287 —, deaf and dumb teaching 285 —, economy 399 —, and science 461

Francesca, Piero della see Piero della Francesea Francesco I, Grand Duke of Tuscany 134 Franciscan order 39, 52, 53, 59 Frederic, Jean 384 Frederick II, (the Great) King of Prussia 35, 276, 409-10, 411 Frisius, Gemma 323-4 Gaffurio, Franchino 99 Gagliardi, Achille 119, 125, 126, 133 Galapagos Islands 434 Galen (Claudius Galenus) 218, 305, 306, 456, 457, 471 —, atomist doctrine 157 —, and hearing 297 —, and micro/macrocosm 469 —, and optics 303, 307, 308, 309, 31516, 325 —, as philosopher 156 —, alluded to 102, 486 Galilei, Galileo see Galileo Galilei, Vincenzo 103, 108, 150, 156, 173, 486 —, and acoustics 174 —, and mathematics 198 —, and music 131, 151, 219 —, and sound 294-6 —, death 1591 295 Galileo 105, 260, 414 —, biography —, —, background 173 —, —, biographers 103-4, 149, 259 —, —, career —, —, —, at Padua 134, 492 —, —, —, at Pisa 117, 134, 198, 479 —, —, as court philosopher 493 —, —, critics 261 —, —, friends 24, 272 —, —, intellectual 168, 172, 173, 188 —, —, trial & house arrest 24, 489, 493, 494 —, and Aristotelian theories 149-61, 229, 259 —, and astronomy 178, 185, 209, 258 —, and causality 441 —, and Clavius 176, 181, 194, 270, 479 visits Clavius 156, 175, 479-80 —, on comets 177, 493 —, and Copernicus 153, 176, 177, 181, 186 commitment to 22, 177

Index —, and correspondences with Carbone's texts 169-72, 479 —, and cosmology 23, 80, 155, 167, 177 —, and court patronage 492-4 —, and dynamics 185 —, Earth, on motion of 184-5 —, on epicycles and eccentrics 185 —, and expectation and choice 383 —, and experimental enquiry 258, 262 —, and experimental physics 206-7 —, on gravity 104 —, on heat and light 219, 489 —, and Koyre's understanding of 26770, 477 —, letters 488 —, —, to Baliani 208 —, —, to Carcavy 208 —, —, to/from Castelli 211, 490 —, —, to Dini 185, 486 —, —, to father 198, 486 —, —, to/from Liceti 216-17, 229 —, —, to Mazzoni 198, 486 —, —, to Mazzoni/Kepler 176-7 —, —, to Vmta 179, 486 —, and light 215 —, and mathematics 118, 196, 197, 198, 212 —, —, his interest in 173, 217 —, Mazzoni, studies with 486 —, and mechanics 23, 103, 185, 212-13 —, and moon 106 —, and music 103, 219 —, and natural philosophy 23, 139-61, 167, 208, 213, 267 —, and new star of 1604 177 —, and optics 217, 343 —, meets Peiresc 286 —, on pendulum 179, 208, 279-3, 485 —, pendulum ratio, and discovery of 270-3 —, and philosophy 179, 257-62, 486 —, and properties/qualities 218 —, and Redondi's document 490 —, and rhetoric 6, 180-1, 216, 231-55, 494 —, and science 20, 35 —, science, and language of 441 —, on science and nature 165-229 —, and scientific revolution 456 —, and scientific style 270, 468 —, on sunspots 211 —, —, First Letter 87, 150, 180, 186, 215, 216 —, —, Second Letter 213

505

—, —, Third Letter 215 —, and telescope 106, 177, 185, 214 —, and theology 229 —, on tides 185-6 —, on truth 23, 24, 25 —, writings —, —, chronology/paper 155-8, 162-3 —, —, dating of 155, 165, 166n, 172-4n, 220-8, 487-8 —, —, dated 175 —, —, undated 172, 220-8, 486, 493 —, scholastic essays of 151-61, 168, 187 —, sources of 167-9, 221-2, 226-8, 26970, 486 —, —, scholastic essays 151, 155, 165, 221, 479-94 —, —, Carbone, Ludovico 169, 172, 269-70, 479, 484 —, —, Clavius, Christopher 153, 168, 269-70, 479 —, —, Paulus Vallius 479, 484 —, —, Pereira, Benito 153, 158, 168, 205, 269-70 —, —, Toledo, Francisco de 153, 158, 168, 205, 269-70 —, watermarks of paper 156, 157, 162-3 —, highest rates of citation 155, 194 The Galileo Prize 161, 167 Garin, Eugenio 158 Gassendi, Pierre 228, 229, 287, 352-3 Gaultier, Joseph 286-7 Gelenius, Sigismundus 277, 288 Geminus 131, 183 Gemistus 139 genetical disputes, Soviet 28 geography 59, 132 geology 22, 27, 418, 433 geometry 55, 58, 115, 131, 178, 441 —, analysis 45 —, and art 99 —, of Euclid 16, 17, 96, 217, 432-3, 469 —, of Greek mathematicians 4, 95-6 —, of Pascal 113 George, Wilma 471 Gerald of Wales 39, 42 Germany 37, 125, 271, 453, 464 Gesner, Conrad 278, 288, 456 Gessner see Gesner Gherardini, Niccolo 149 Ghetaldi, Marino 224 Ghiberti, Lorenzo 319, 453 Gibbon, Edward 463 Gilbert, William 35, 111, 210, 471, 492-3 Gilles of Lessines 374

506


Gilson, Etienne 263, 469 Giorgio, Francesco 131 Giotto 34-5, 453 God 33, 71, 72, 79-81,85, 182 —, omnipotent 71, 77, 79, 84, 85 —, see also belief and doubt; Catholicism; Creator; theology Goethe, Johann Wolfgang von 461 Gogava, Antonio 295 Gondisalvo, Domingo 96 Gorgias and rhetoric 234 Grafton, Anthony 484 Graham, W. 398 Grassi, Orazio 485, 489, 490, 493 Graunt, John 379, 386-7, 447-8 gravitational clocks 82 gravitational theories 117-18, 215-16, 259, 260, 434 —, and Archimedes 175 —, of Galileo 104, 480 Gray, Asa 398 Graz, solar eclipse at 330 Great Britain 264, 399 —, see also England Greek astronomy 86, 413, 441 Greek grammar 54 Greek language 68 Greek mathematics 4, 95-6, 265, 441 Greek optical theory 302-4, 315 Greek philosophy 16, 265, 456, 469 —, causal continuity 3-4 —, causality in medicine 446, 447 —, and natural science 1, 21, 440, 443 —, and probability 360-7 —, scepticism 71, 72, 167 —, and theology 70 Greek science 16, 265, 456 Greek texts 32-3 Gregorian calendar 62, 125-6, 156 Gregory III, Pope 125 Grienberger, Christopher 119, 217 Grosseteste, Robert 39-47, 472 —, background 39 —, career —, —, as bishop & statesman 40 —, —, clerk at Hereford 42 —, —, at Oxford 39 —, —, as scholar & teacher 40 —, ecclesiastical appointments 39, 41 —, Aristotle, influence of 42, 43 —, on astrology 47 —, and astronomy 40, 42, 46, 47 —, and R. Bacon 39, 52, 55, 56, 61 —, on calendar reform 40, 47, 62

—, and cosmology 470 —, and falsified conclusions 43 —, and Franciscans 39 —, and geometry 55 —, letters 39 —, on light 40, 41, 42-3, 44, 45 —, and mathematics 97 —, on methodology (4 essays on) 43-6 —, and music 42 —, and optics 316-17 —, philosophy of 40, 42-3 —, and scientific revolution 454 —, scientific writing 42 —, and sound 292 —, written work 40, 42, 43, 44, 45-6, 47-8 Grotius, Hugo 380 Guidi, Guido 298 Guiducci, Mario 215 Guy de Foulques, Cardinal see Clement IV, Pope Gymnasium Patavium Societatis Jesu of Padua 126 —, see also colleges and universities Halley Edmund 379, 387 Haly Ibn Sma 60 Harriot, Thomas 106, 349 Hartsoeker, Nicolaas 422 Harvey, William 111, 112, 414, 469 hearing 96, 107-10, 291-9 —, see also music; sound heat and light 219, 489 Hebrew. —, astronomical tables 62 —, doctrine 68, 69 —, grammar 54 —, language 275, 276, 277, 279 —, theology 27, 70, 469 Henry III, King of England 51 Herbert of Cherbury 380 Hereford 39, 42 heresy 372 Hermes Trismegistus 139 Hero of Alexandria 101, 102, 132 Herodotus 275 Hesiod 68 Hiero II, King of Synacuse, and undated writings of Galileo 223 hieroglyphics 289 Hipparchus 47, 153, 221 Hippocrates, and medical science 445 —, and rhetoric 235 —, and scientific revolution 456

Index 'Historical Commitments of European Science' (Crombie) 474-5 history —, of argument 12, 180-1, 357-400, 4439,467 —, human 458-9 —, Jesuit education 118 —, of science 451-64 Hobbes, Thomas 48, 63, 352-3, 381, 394n Hoeniger, David 473 Hohenburg, Hewart von 368 Holcot, Robert 81 Holy Scriptures 41, 53, 182, 470 Homer 68 Hook, Robert 418 Hooker, Joseph 431 Howard, Thomas, 2nd Earl of Arundel 288 Hudde, Jan 384 Hugh, Bishop of Lincoln 39 Hugh of St. Victor 33 humanists and scientific revolution 455 humankind, Western visions of 1-12 Humboldt, Alexander Baron von 59 Hume, David 258, 461, 463 Hunain (Hunayn) ibn Ishaq 56, 306 Hungary 125 Hutchinson, Evelyn 471 Huxley, Thomas Henry 398-9 Huygens, Christiaan 113, 347, 379, 3812,387 —, and expectation and choice 384 —, and mathematics 447 hydrostatic balance 224 hydrostatics 209, 211, 269 hypothesis 262, 467 Ibn al-Haytham see Alhazen Ibn Sfna (Avicenna) 56, 76, 79, 190 Ignatius see Loyola Indian medical practice 446 infinite power 67-88 inoculation 392 insurance 374, 384, 447 intellectual reform 16-17, 33 intellectual styles 2-6 Isabella of Castile 59 Islam 5, 54, 61, 470 isolated child, origins of language and 275, 276, 277, 280-1 Italian historians 453 Italian mathematicians 447

507

Italian universities, mathematics and Platonism in 115-40 Italy 35, 36, 82, 150, 452 —, Greeks flee to 456 —, Peiresc journey's to 286 —, spectacles invented in 317 Ivan IV, Czar (the Terrible) 125 Jandun, Jean de 176, 283-4 Japanese thinking 4 Javelli, Chrisostomo 126, 127 Jenner, Edward 446 Jerome, St 127 Jessen, Johannes 334, 342 The Jesuit 'Constitutions' (1556) 118, 121 Jesuits 134, 165-229 —, Aristotelian/Thomist revival 166 —, education —, —, arts/natural science 118 —, —, classical languages 118 —, —, history 118 —, —, literature 118 —, —, logic 118 —, —, mathematics 118-40 —, —, metaphysics 118 —, —, moral science 118 —, —, oriental languages 118 —, —, physics 118 —, —, theology 118 —, philosophy 132 —, as source of Galileo's writings 165, 167-9, 269-70, 493 —, and undated writing of Galileo 221, 222, 226, 227, 228 Jewish philosophy 72 Jews 127 Jews in Alexandria 70 John of Damascus 40 John of London 59 John (pupil of Roger Bacon) 53 John of Salisbury 369, 454 Johnson, Dr Samuel 416 Jordanus de Nemore 59 judgement/assent 369-74 Julian year 61, 62 Jupiter 185, 217 satellites 258, 287, 493 Justin, St (the Martyr) 139 Kant, Immanuel 260, 262 Kemp, Martin 473 Kepler, Johann 111, 176, 331, 334, 473 —, and astronomy 471, 485

508


—, and camera obscura 332, 336-8, 343 —, and cosmology 433 —, and expectation and choice 368 —, and history of optics 304-5, 329-45, 347-8, 350, 354-5, 485 —, and innovation 7 —, letters from Galileo 176, 487 —, and optical physiology 38 —, and planetary intervals 21 —, and retinal image 105 —, and solar eclipse 330 kinematics 180 Kirby, William 394n Kircher, Anthanasius 289 Kohlhans, Johann Christoph 347 Koyre, Alexandre 263-4, 267-70, 476, 477 La Galla, Giulio Cesare 215, 217 La Hire, Philippe de 347 La Mettrie, Julien Off ray de 410 Lactantius 469-70 Laertius, Diogenes 275 Lagrange, Joseph Louis de, Comte 258 Lalande, Joseph Jerome Le Francois de 410 Lamarck Jean-Baptiste Pierre Antoine de Monet de 394n language 54 —, of animals 278, 280, 282 —, Arabic 288 —, Babel 276 —, and R. Bacon 51, 52, 56, 276 —, of causality 440-1 —, Chinese groups 278 —, deaf and dumb 276, 277, 283-4 —, and electro-chemistry 441-2 —, English 91, 439 —, European groups 278, 288 —, French 439 —, German 288 —, Greek 68 —, Hebrew 275, 276, 277, 279, 288 —, history of 275-89 —, isolated child theory 275, 276, 277, 280-1 —, Italian 439 —, Latin 3, 68, 276, 439, 441, 453 —, of mathematics 442 —, of music 442 —, new terminology 3, 442 —, and the occult 276, 278, 279 —, origins of 275-85, 288-9 —, Persian 278, 288

—, philosophical 279 —, of science 3, 439-42 —, and Semitic groups 278 —, technical 442 —, universal 277, 278, 282 Laplace, Pierre-Simon, Marquis de 394, 396, 399, 448, 463 —, and analysis of numbers 392-3 —, and inverse probability 387 Larroque, Philippe Tamizey de 287 Latin language 3, 68, 276, 439, 441, 453 latitude/longitude 59, 60 laws of nature —, defined 86 —, St Augustine on 69, 72-5, 77 Le Clerc, Daniel 462 Leaning Tower of Pisa 259 least action, principal of 21, 389, 411 Lebegue, Raymond 287 Leeuwenhoek, Anton van 422 Leibniz, Gottfried Wilhelm 289, 408, 426, 462 —, and expectation and choice 379, 384, 385 —, and history of optics 301-2, 354 Leicester 39 Lenin, Vladimir Ilyich 28 Lenoble, Robert 263 lens 55, 56, 303, 304, 320, 343 Leo X, Pope 115 Leon, Pedro Ponce de 284 Leonardo da Vinci 19, 99, 100-1, 132n, 136, 252 —, and history of optics 320-3, 327, 334 1'Epee, Abbe Charles-Michel see Epee, Charles-Michel de L' Lessius (Leonard Leys) 378 letters, unidentified, of Galileo 187 Leurechon, Jean 344 Lewis, C.S. 28 Leys, Leonard (Lessius) 378 Libri, Guglielmo 463 Liceti, Fortunio 140, 216, 217, 229, 488 light 40, 42, 42-43, 44, 45, 215-6 Lincoln 39, 41 Lindberg, David C. The Beginnings of Western Science 465, 468-74, 476-7 linear scale 203 Linnaeus, Carolus (Carl von Linne) 41314, 414-15, 417, 418, 425 Linnean Society 431 Linz, Wotton 343 literature 118, 453, 455-6 Little, A.G. 51, 61, 62

Index Locher, Giovanni Giorgio 487 Locke, John 354, 461 logic 51, 118, 260, 369, 440-1, 467 London 264 —, population statistics 447 Louvain 345 Loyola, St. Ignatius 118-9, 121 Lucretius, Titus 56 —, and expectation and choice 366, 390, 391 —, nature, laws of 69-70, 388 —, and origins of language 275 Lull, Ramon 278, 384 Lavrov, P.L. 394n Lyell, Charles 6, 436 McCarthy, Senator Joseph 28 Mach, Ernst 260, 261 Machiavelli, Niccolo 35, 104, 453 macrocosm/microcosm 40 McVaugh, Michael 471 magic 57, 63, 278 Magiotti, Rafaello 272 magnetism 57, 59, 97, 111, 471, 493 magnification 55, 56, 316-17 Maieru, Alfonso 469 Malebranche, Nicolas 354 Malpighi, Marcello 118, 354 Malthus, Thomas 393, 434 Mantua 492 manual industry 97-8, 98, 100 Marciana library 288 Maricourt, Pierre de 57, 59, 97, 471 Mariotte, Edme 299, 347 Mars 185 Marseilles 288 Marsh, Adam 39, 52 Marsili, Cesare 226 Marsilius of Inghen 277 Martini, Francesco di Georgio 106, 320 Marx, Karl 394n Mastlin, Michael 330, 344 mathematics 57, 87, 97, 442 —, 16th century debate 21, 195-201 —, and Archimedes 59, 151, 197 —, and astronomy 99, 155, 183 —, and Bacon, R. 52, 54, 56, 60, 97 —, —, and logic 59 —, —, and usefulness of 58 —, at Bologna 115 —, and Clavius 119-21, 122, 196, 198, 216 —, and Euclid 96, 161, 196, 200 —, and Galileo 118, 196, 197, 198, 212, 488

509

—, —, his interest in 173, 217 —, Italian 447 —, in Jesuit education 118-40 —, and Platonism 115-40 —, and Possevino 128-31 —, at Rome 115 —, students 120-1 —, tutors 119-20 Mather, Cotton 456 Maupertuis, Pierre Louis Moreau de 407 —, biography/background 407, 410 —, —, Battle of Molwitz 410, 412, 428 —, and albinism 418, 421, 424 —, and animal studies 411-12 —, and cosmology 420 —, critics (Voltaire) 409, 410, 411, 417, 427 —, and expectation and choice 388-92, 394n, 395, 396 —, and history of science 462 —, least action, theory of 411 —, and probability 389-92 —, and salamander 411 —, and scorpion 412 Maurolico, Francesco 63, 119, 326-7, 330 Mazzoni, Jacopo 127 —, and Galileo 156, 176, 177, 198, 222, 486, 487, 488 —, —, letters from 176 —, and mathematics 196, 197, 198, 216 —, at Pisa 134, 139-40 —, and Platonism 139-40, 150 —, and Possevino 131 measurement and physical research 86-7 mechanical clock 60 mechanics —, clock 60 —, Guidobaldo del Monte and 212 —, Galileo and 23, 103, 185, 212-13 —, and scientific revolution 459 Meckel, Johann Friedrich 410 medical astrology 61 medical science 445-9 Medici, Cosimo de' 139 medicine, history of 462 medicine, university teaching of 115 Mediterranean Sea, measurement of 287 Mei, Girolamo 294 Mendel, Gregor 436 Mercurius Trismegistus 139 Mercury (planet) 185 Mersenne, Marin 132n, 186, 258, 286, 383, 384 —, and history of optics 348, 352

510


—, and Jesuits 228 —, on language 285 —, on mathematics 105-6 —, and music 107-10, 296, 297 —, and Neoplatonism 229 —, and origins of language 275-85 —, and pendulum ratio debate 270-3, 485 —, and sound 296, 297 —, and virtu 113 Mery, Jean 347 Messahala 60 Messina 118, 119 metaphysics 52, 54, 79, 118 Micanzio, Fulgenzio 271 Michelangelo 101, 101-2 Michelini, Famiano 272 microcosm/macrocosm 40 microscope 91 Milan 102 Mill, John Stuart 260, 431 Mirandola see Pico della Mirandola, Giovanni Moivre, Abraham de 387 Moleto, Gioseffe (Giuseppe) 117-18, 126, 134, 175 Molwitz 410, 412, 428 Molyneux, William 354 monkeys 418 Montaigne, Michel de 167, 184, 379 Monte, Cardinal Frances^.. Maria del 117 Monte, Guidobaldo del 102-3, 126, 132, 175-6 —, and mathematics 198 —, and mechanics 212 —, and undated writings of Galileo 225, 480 Montesquieu, Charles de Secondat, Baron de la Brede et de 461 Montpellier 286 Montucla, John Etienne 258, 463 moon 43, 47, 106, 177, 179, 186 —, mountains on 258 moral science in Jesuit education 118 morals 94, 99, 118 Morcillo, Sebastian Fox 127 More, Thomas 104, 447 mortality records 386-7 Moscow 125 Moses 139 Moslem philosophy 72 Moss, Jean Dietz 231-2 motion, inertial 38

Miiller, Adolph 165 Miiller, Johannes see Regiomontanus music 18, 96, 103, 174, 219 —, arithmetically quantified 99 —, and astronomy 42 —, fifth interval 263 —, and hearing 291-9 —, history of 291-9 —, new language of 442 —, and origins of language 282-3 —, pendulum ratio debate 270-3 —, science of 107-10 —, theories of 86 —, and vibration 219 —, see also hearing; sound musical academy of the Camerata 294 —, see also colleges and universities Muslim theology 79 mutation of species 418 National Edition of Galileo 489, 490 natural philosophy 20, 82, 149-61, 153, 228 —, and Galileo 23, 139-61, 167, 208, 213, 267 natural selection 425, 431, 435, 436, 437 —, see also Darwin, Charles; evolution; transmutation of species nature, laws of 67, 68, 69, 75-7, 470, 472 —, and St Augustine 69, 72-5, 77 —, and R. Bacon 75-7 —, Descartes on 83-4 —, designation of 86 —, and Lucretius 69-70, 388 —, medieval conceptions of 67-88 —, and Newton 67, 85, 186 —, and Philo Judaeus of Alexandria 70-2 —, and Suarez 83 —, and Bishop Etienne Tempier 80 —, and William of Ockham 77-8 nature, Western visions of 1-12 navigation/cartography 19 Neckham, Alexander 369 Neoplatonism and Catholicism 166 Nero 60 Netherlands 35, 286 Neuperg, Comte 410 new cosmology 177, 433 new philosophy see experimental philosophy New Star of 1604 177, 178, 487 Newton, Sir Isaac 408, 409, 415, 417, 430

Index —, and causality 441 —, and expectation and choice 389 —, and language of science 441 —, and laws of gravitation 434 —, on laws of nature 67, 85, 186 —, and mechanistic theory 434 —, and scientific revolution 461 —, translated by Madame du Chatelet 462 'Nicholas, Master' (teacher) 59 Nicholas (Nicolaus) of Cusa 61, 62, 99, 453 Nicole, Pierre 379, 382-4 Nicomachus 293 Nifo, Agostine 184 Noailles, Francois de 272 North, John 471 Novara, Domenico Maria 115 objectivity, scientific 13-30 Olschki, Leonardo 473 omnipotent Craftsman 247 Opus tertiwn (Bacon, R.) 52 Optica (Alhazen) 316, 319 optics 54, 55, 56, 58, 63, 99 —, and art 105 —, and colour 45 —, and Galileo 217, 343 —, history of —, —, Alhazen 38, 301-28, 471, 473 —, —, Bacon, R. 52, 292, 316, 317-19, 326 —, —, Crombie 471 —, —, Descartes 345, 348-52, 354 —, —, Euclid 55, 302-3, 305, 308, 471 —, —, Fabrici 320, 325, 334 —, —, Galen 303, 307, 308, 309, 315-16, 325 —, —, Grosseteste 316-17 —, —, Kepler 38, 304-5, 329-45, 347-8, 350, 354-5 —, —, Leibniz 301-2, 354 —, —, Lindberg 471 —, —, Mersenne 348, 352 —, and ocular physiology 301, 473 —, see also eyes Oresme, Nicole 80, 82-3, 277, 454 —, and earth's rotation 470 —, and the world clock 473 —, and scientific vernaculars 469 oriental languages 118 The Origin of the Species (Darwin) 6, 429, 431, 435, 436 Oryx beisa (antelope) 288

511

Osiander, Andreas 257 Oxford 39, 52, 151,264 Pacioli, Luca 115, 131, 376 Pacius, Jules 286 Padua 140, 172, 175, 177, 198, 484 —, and Galileo 134, 178, 225, 227, 492 —, and mathematics 117, 118, 134 —, Peiresc explores 286 —, and philosophy 125, 133 —, and Possevino 126 —, see also under colleges and universities painting 34, 96-7, 173, 320, 343 Paley, William 416, 433 Palladio 132 Pappus 102, 206, 225, 269 Paris 39, 52, 80, 82, 153, 264, 490 —, Leibniz studies in 384 Paris, Matthew 39 Pascal, Blaise 113, 379, 381-2, 384, 3989,447 Pasteur, Louis 446 Pastoreaux rebels 52, 54 Patrizi, Francesco 127, 139-40, 166 Paul of Middleburgh 61 Paul, St 135 Pavia 140 Pecham, John (also Pisanus) 316, 319, 326, 332, 344 Peiresc, Nicolas Claude Fabri de 271, 278, 286-9, 494 —, background 286 —, collections of 288 —, correspondence 287 —, Lettres a Claude Saumaise et a son entourage 287-9 —, and origin of language 288-9 Peiresc (village) 286 Pena, Jean 131, 295 pendulum 179, 208, 270-3, 485 Pequet, Jean 111, 347 perception 26 Pereira, Benito 119, 122-4, 127, 132-3 —, on astromomical hypotheses 184 —, and mathematics 194 —, as source for Galileo's writings 153, 158, 168, 205, 269-70, 485 —, and undated writings of Galileo 221, 226, 227, 486, 487 —, and Vallius 485 —, alluded to 123 periodisation (ancient, medieval, modern) 34, 36, 452, 453

512


Perrault, Claude 299, 347 Persian language 278 Persio, Antonio 134 perspective 46, 98, 105, 106, 320, 473 —, and Greek mathematicians 441 —, Vieri on 137-8 persuasion see rhetoric Petrarch, Francesco Petrarca 34, 452-3 Petty, William 379, 385 Peurbach, Georg 99 Phaedrus (Plato) 133-6 Philander 132 Philo of Byzantium (2nd C B.C.) 132 Philo Judaeus of Alexandria (1st C A.D.) 70-2, 469-70 Philoponus, John 153, 221 philosophers, mechanistic 27 philosophy 35, 37, 52-3, 54, 126 —, Christian 72 —, empiricism 262 —, English 452 —, ethics 16 —, of Galileo 179, 257-62, 488 —, Greek see Greek philosophy —, of Grosseteste 40, 42-3 —, history of 458, 459 —, humanism 455 —, Italian 166 —, Jesuit 132 —, metaphysics 52, 54, 79, 118 —, natural 149-61, 166 —, Neoplatonism 166 —, Platonic 127, 134 —, positivism 259, 260, 261 —, psychology 26 —, rationalism 89-114 —, scepticism 20, 72, 128, 167 —, Stoics/Stoicism 21, 68, 71, 72, 128 —, see also God; logic; truth physical research and measurement 86-7 physick, history of 462 physics —, experimental 206-7 —, Greek 16 —, in Jesuit education 118 Piccolomini, Alessandro 122, 124, 132, 194, 195 —, and mathematics 123 —, and mechanics 175 —, and rhetoric 236-42, 243, 245, 250 Pico della Mirandola, Giovanni 126, 139, 166 Pico, Gianfrancesco 131 Pico, Giovanni 127

Piero della Francesca 99 Pieroni, Giovanni 271 pigeons 418 pin hole image see camera obscura Pinelli, Giovanni Vincenzo 117, 126, 134, 175, 286 —, and library 288 —, manuscripts 187 —, and undated writings of Galileo 225 Pinelli library 288 Pisa 156, 173, 181, 198 —, and Galileo's writings 227, 479, 486 —, Peiresc's background 286 —, see also under colleges and universities Pisa, Leaning Tower of 259 Pisanus see Pecham, John planets 54, 61, 99, 178, 181, 185 —, Jupiter 179, 217, 287 —, planetary intervals 21 —, Venus 186 —, see also astronomy; cosmology; telescope plants and longevity 57 Plater, Felix 320, 324-5, 329, 334, 335 Plato 32, 134, 139,261,275 —, and acoustics 292 —, and architecture 91-2 —, and creation 71 —, critics of 127 —, and expectation and choice 362 —, and mathematics 123, 196, 197, 198, 200 —, and nature —, —, as a deductive system 21 —, —, laws of 68, 69 —, and origin of language 275 —, philosophy 127, 134 —, and properties/qualities 219 —, and rhetoric 92-3, 237, 362 —, and scientific style 467 —, and undated writings of Galileo 222, 226 —, alluded to 31, 95, 149, 358, 486 Platonism 115-40, 150 Platter see Plater, Felix Plempius, Vopiscus Fortunatus 345 Pliny the Elder 60, 469 Plotinus 72, 138 Plutarch 127, 129, 130 poetry 34 Poland 125, 126 political —, bulverism 28

Index —, history 453 —, role of science 21 politics 21, 28, 29, 95, 453 Ponce de Leon, Pedro 110, 284 population 385 Porphyry 293 Port-Royal 382 Porta, Giambattista della, 223, 301, 328, 329, 335 Posidonius 129 positivism 259, 260, 261 Possevino, Antonio 124-32 —, on astrology 132 —, and calendar reform 125-6 —, diplomatic missions 125 —, friendships 175 —, and influence of Clavius 128, 131 —, and Jesuit society 125, 126 —, as Papal Nuncio 125 —, written work —, —, Bibliotheca selecta 126-32, 133, 175 —, —, on Jesuit universities 125 —, —, on peace mission to Russia 125 Postel, Guillaume 288 postulation, theoretical, of Galileo 268-9 power 27, 67-88, 79-81 power, propogation of 55 Prado, Jeronimo 132n Prague 334 Priestley, John 463 primary properties/secondary qualities 157, 218-19 Princeton 264 Priscian (Priscianus Caesariensis) 31, 223 probabilities 359, 468 —, history of 360-7, 369-74 —, —, arguments from 357-400 —, —, and natural selection 388-400 —, see also expectation and choice probability theories 360-7,387, 389-92 Proclus 123, 131, 217, 269 —, analysis and synthesis 209 —, on Euclid 101, 175 —, and mathematics 195, 196, 198, 216 proof, concept of 68, 466 Protestant reformation 36 Protestantism 455 Psalms, translation of 40 Psellus, Michael 131 psychiatry, Western 446 psychology 26 Ptolemy 59, 60, 62, 131, 175 —, and astronomy 209

513

—, and R. Bacon 55, 58 —, and calendar 47 —, and Clavius 182 —, and experimental argument 467 —, and Grosseteste 45, 46 —, and music 293, 295 —, and optics 96, 303, 308, 313, 317, 471 —, —, eye, history of the 305, 306 —, and planetary tables 469 —, primary properties/secondary qualities 219 —, and refraction 86, 472 —, and rhetoric 238 —, and scientific revolution 456 —, and scientific style 467 —, and tables of refraction 332 —, and undated writings of Galileo 225 public health 448 Pythagoras 127, 131, 139, 149, 296 Querengo, Antonio 254 Quintilian, Marcus Fabius 367 Quintilianus, Aristides 293 Raimondi, Giambattista 116, 139 rainbows 38, 40, 45, 57 —, studies of 471-2 Ralegh (Raleigh), Sir Walter 36 Ramelli, Agostino 320 Ramus, Peter 36 Rashdall, H. 54 ratio 58-59, 268, 270-3, 332 rational artist 89-114 Ray, John 413, 415, 425 Reael, Laurens 270 Redi, Francesco 414 Redondi, Pietro 485, 489, 490 reefs, coral 433 reflection 56, 177 Reformation of Religion 36, 456 refraction 55, 56 Regiomontanus 61 religion and scientific revolution 455 religious reform 36, 456 renaissance 96, 452, 455 reproduction, theories of 422-3 resolution and composition (Galileo) 209 rhetoric 92-3, 231-55, 436 —, and Aristotle 232, 236-40, 243, 2478, 250-2, 362-3 —, and Cardano 249 —, and Colombe 245-6 —, and Copernicus 244

514


—, and Darwin 6 —, and Descartes 6 —, and Ficino 249 —, and Galileo 6, 180-1, 216, 231-55, 485, 494 —, and Gherardini 149, 239 —, and Gorgias 234 —, and Hippocrates 235 —, and J.D. Moss 231-2 —, and Plato 92-3, 237, 362 —, and Ptolemy 238 Riccardi, Padre, Maestno del Sacro Palazzo 490 Richard of Wallingford 82, 470, 473 Ristoro, Juliano 117 Robertson, William 463 Rocco, Antonio 161, 186 Romanticism 37 Rome 271, 272, 346, 453, 489, 490, 494 —, see also under colleges and universities Ronchi, Vasco 471 Rose, Cipriano de 294 Roshdi Rashed 470 Rossi-Monti, Paolo 267n Rousseau, Jean Jacques 461 Royal Society Catalogue of Scientific Papers 436 The Royal Society 258, 460, 461 Rudolph II, Emperor 331, 494 Rushworth, William 381 Russell, Gul 470 Sabra, A.I. 471 Sacrament of the Eucharist 489 Sacrobosco, Johannes de 60, 486 'Sagredo' (and Galileo) 226, 244, 251 salamander 411 'Salviati' as Galileo 226, 243-5, 247-8, 250-3, 261 Santillana, Giorgio de 257 Santorio Santorio 485 Sarpi, Pietro 176 Saturn 185 Saumaise, Claude 287, 289 Savoy 125 Scaliger, Joseph-Juste 278, 288 Scaliger, Julius Caesar 153 scepticism 20, 72, 128, 167 —, see also Stoics/Stoicism Scheiner, Christopher 180 and history of optics 345-7 science: —, and Clavius 181-3, 184, 185, 187

—, experimental 89-114 —, history of 31-8, 263-70, 440, 443-4, 451-64 —, and Islam 54 —, language of 3, 439-42 —, of music 107-10 —, and nature 1, 19, 54, 165-229 —, new science 35, 36, 279, 459 —, quantitative 20 —, of vision 302 —, —, see also optics —, Western visions of 1-12 scientific language 439-42 scientific method of Darwin 429-37 scientific method of inquiry 10, 11, 12, 467-8 scientific objectivity, Western experience of 13-30 scientific revolution 451-64 scientific style 159, 229, 270, 467-8, 472 scientific thought of R. Bacon 53-63 scorpion 412 Scriptures, Holy 41, 53, 182, 470 sculpture, Galileo's interest in 173 Sedgwick, Adam 433 Semitic groups and origins of language 278 Seneca, Lucius ('the Younger') 34, 51, 60 Sextus Empiricus 218, 365, 366, 379 Shakespeare, William 105, 416 Shea, William 157, 158 shell, tropical, at Shrewsbury 433 Shirley, John 473 Siculus, Diodorus 275 Silvestris, Bernard 33 Simon de Montfort 41, 59 'Simplicio' —, as Aristotle 243, 247, 250, 252, 253 —, and undated writings of Galileo 226 Simplicius 183, 221 Siraisi, Nancy 471 Smith, Adam 392, 394, 396 Snel, Willebrord 349 social responsibility 99 —, see also virtu Socrates 32, 200, 233-6, 466 solar eclipses 329-30, 332 solar radiation 43 Soto, Domingo de 126 sound 42, 108-9, 219, 292, 296, 297-8 —, see also hearing; music South America 431, 434 Spain 110, 284

Index species, classification of 413 Speculum astronomic, authorship question of 61 Speroni, Sperone 126 Sprat, Thomas 461 stars 43, 57, 177, 178, 179 —, see also astronomy; cosmology; planets statistics 11, 385-8, 399, 447, 448 —, and economy 392 —, and evolution 398 —, and Maupertuis 390 Stoffler, Johannes 62 Stoics/Stoicism 21, 68, 71, 72, 128 —, see also scepticism Straker, Stephen 471, 473 Sturm, Johann Christoph 347 Suarez, Francisco 83, 84 submarines 33, 57 sulpher drugs 448 sun 179, 186, 211, 213 sunspots 207, 269 —, Galileo on 211 —, —, First Letter 87, 150, 180, 186, 215, 216 —, —, Second Letter 213 —, —, Third Letter 215 Swammerdam, Jan 414 Sweden 125 Sydenham, Thomas 446 Taccola (Mariano di Jacopo) 106, 320 Tartaglia, Niccolo 132 Tartars 54 Tasso, Torquato 223 taxonomy and scientific style 11, 467-8 technology, modern 448-9 Tedeschi, Leonardo 177 telescope 87, 91, 186, 207, 217, 494 —, discoveries 177, 185, 214 —, of Kepler 343 —, observations 106, 179, 217, 286-7 Telesio 249 Tempier, Bishop Stephen 53, 61, 80 Thabit ibn Qurra 62 Thales 130 Themistius 239, 292 Theodoric of Freiberg 38, 471-2 Theodosius 59 theological letters of Galileo 229 theology 23, 34, 54, 151 —, and Archimedes 470 —, and Aristotle 22, 151, 470 —, Christian 5, 72, 79, 99, 469

515

—, and Galileo 229 —, Hebrew 27, 70, 469 —, Islamic 5 —, and Jesuit education 118 —, and modern science 16, 461 —, Muslim 79 —, see also belief and doubt; Catholicism; Creator; God Theon of Smyrna 219, 293 Theophratus 467 thermometers 111, 203, 485 Thierry of Chartres 31, 32 Thomas Aquinas see Aquinas, St Thomas Thomas de Vio see Cajetan Thorndike, Lynn 59-60 Thucydides 13, 14, 27 tides 43, 47, 160, 179, 185-6, 211 Times Literary Supplement 479, 484, 489-91 Toledan tables 60 Toledo, Francisco de (Toletus) 119, 126, 153, 158 —, written work 168, 172, 269-70, 484 Toletus see Toledo, Francisco de Torres, Balthassar 119 Torricelli, Evangelista 118 Toscanelli, Paolo dal Pozzo 59, 99 Tournefort, Joseph Pitton de 413 Tractationes de mundo et de caelo (Galileo) 151-60, 167, 194 transmutation of species 434 —, see also Darwin, Charles; evolution; natural selection Tribunal of the Holy Office 490 true/false premise 182 truth 23, 24, 53, 381 —, and bulverisation 28 —, and communism 29 —, in modern science 25 Turks' invasion of Greek churches 456 Tuscany 139 Tuscany, Grand Dukes of 134, 159, 247, 492-3 Tycho see Brahe, Tycho Tyndall, John 3 Tyson, Edward 413, 415, 418 United States 59, 264, 476 universal language 277, 278, 282 universities see colleges and universities Urban VIII, Pope 489, 490-1 Valerio, Luca 116, 207 Valla, Giorgio 100, 102, 131

516


Valle see Vallius Vallesius (Francisco Valles) 126, 177, 284 Vallius, Paulus (Paolo della Valle) 169, 479 —, and Galileo's writings 484 —, and Pererius 485 —, and Zabarella's tracts compared 480-4 Valori, Baccio 134, 139 Vasari, Giorgio 453 Vatican Library 294 Venice 48, 133, 153, 155, 271, 293 —, see also under colleges and universities —, Vincenzo Galilei studies in 294 Venus 185,186 Vere, William de 39 Vesalius, Andreas 320, 324, 325, 328 Vick, Henri de 82 Vickers, Brian 232-3 Vico, Giovanni Battista (Giambattista) 461 Vieri, Francesco 134-9 —, background 134, 138 —, and astrology 136 —, on perspective 137-8 —, Platonic philosophy —, written work 135, 138, 139 Viete, Francois 225, 442, 485, 487 Villalpando, Juan Batiste 132n Villani, Filippo 34, 453 Villard de Honnecourt 97, 473 Vinta, Belisario 179, 224, 227 Vio, Tommaso de see Cajetan Virgil 75 virtu 89-91, 98-9, 104, 112, 113 —, and the Renaissance 89, 453, 477 Vitelleschis, Mutius 485 Vitelo see Witelo Vitruvius 101, 132, 212, 223

Vitry, Philippe de 293 Viviani, Vincenzo 103, 156, 203, 224, 225, 259 Voltaire 258, 408, 409 —, on Maupertuis 409, 410, 411, 417, 427 —, and scientific revolution 451-2, 456, 457, 461, 462-3 Waard, Cornelis de 270, 287 Wallace, Alfred Russel 431, 432, 435 Wallace, William 156, 158, 172-4n, 479, 484, 485 Walter of Odington 293 watermarks on Galileo's paper 156, 157, 162-3 weather 43, 387 weather glass 111 weather, prediction of 52, 136 Welser, Mark 126 Whewell, William 3, 258, 260, 441, 463 William of Auvergne 52 William of Conches 31 William of Ockham 77-8, 80-1 Willis, Thomas 299, 353 Wisan, Winifred 208, 215, 270 witchcraft 372 Witelo 63, 132, 316, 330-1, 342, 344, 471 —, critics 331, 333, 334 —, Ptolemy's tables 332 —, and rainbows 472 Witt, Jan de 379, 384, 387 world, conceptions of 21, 22 Wotton, Henry 343 Young, Thomas 463 Zabarella, Giacomo 140n —, and Vallius tracts compared 480-4 Zarlino, Gioseffe 131, 293, 294, 295, 296 Zonca, Vittorio 320 Zorzi, Benedetto 134

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