An essay on philosophical method

AN ESSAY ON

PHILOSOPHICAL

METHOD :;'""__

By

R. G. COLLINGWOOD

OXFORD; AT THE CLARENDON pRESS I

::.'

o.\ford Uniursity Press, Amen HOl/se, London E.C. 4 GLASGOW

~EW

YORK TORONTO MELDOURSE \\TLLtNGTOS

nO:-IOA Y CALCUTTA J.fADRAS CArE TOWN

Gcoffrcy Cumber/cg£', Pllblisher to the University

FIRST PUBLISHED 1933

Reprinted photographically, 1950, at the UNIVERSITY PRESS, OXFORD, from sheets of the first edition PRINTED IN GREAT BRITAIN

CONTENTS 1. INTR ODUC TION § I.

§ 2.

THE PROBLEM: , I. Philosop hy must raise the question what philosop hy is. 2. Three suggeste d ways of approac hing this question 3. The way to be followed here: an account of philosop hical meth od. . . ' . • • 4. Importa nce of this subject at the present time THE METHOD 5. Necessi ty of restricti ng the subject under discussi on 6. Significance of the compari son between philosop hical and scientific thoug ht. . . • •

I

2

3 4

7 9

:;. § 3.

HISTORICAL ILLUSTRA:r~ONS 7. Socrates ~ 8. 'Plato . 9. Descart es '" 0:: 10. Ka?t . ~,

./

10 11

16 19

H. THE OVERLAP OF CLASSES § I.

THE THEORY OF CLASSIFICATION IN FORMAL LOGIC I. The tradition al theory of classification . .... 2. Its applicat ion in ~xact (mathem atical) science ::..: 3. Its' applicat ion in empirica l science . -~.

§ 2.

26 29 30

THE IMPOSSIBILITY OF APPLYING IT RIGIDLY TO PHILOSOPHICAL CONCEPTS 4. Specific classes here overlap one another 3I 5. This fact long recognized in certain cases 32 6. The case of concepts having a philosophical and a nonphilosophical phase. 33 ". 7. The overlap of classes in logic . 36 ~ 8. The overlap of classes in ethics 41 9. Significance of these facts: the reader invited to admit their genuineness-for the sake of a··lument . • 43 .

CONT ENTS § 3.

CO~SEQ1]fu~CES FOR PHILOS OPHICA L METHOD

?lIethod s proper to science (exact or empirica l) inapplicable in philosop hy, owing to the overlap of classes . I 1. The fallacy of precario us margins I::. The faUacy of identifie d coineide nts 13. Their common ground: the faUacy of false disjunct ion 14. The first rule of philosop hical method : «m I'EV 'Tb am-b ... 'A distincti on without a differe nce'. . . IS. CorolIar ies of this rule. (a) The object of philosop hical thought cannot be a classificatory syste m. . 16. (b) Nor yet an aggregat e, i.e. a whole of separabl e parts. 17. These corolIaries to be understo od only as warning s against unadvise dly assumin g the opposite 10.

46 47 48 49 49 50 SI 52

Ill. THE SCALE OF FORMS § 1.

PREU~HNARY SKETCH OF THE IDEA'I.

2.

3. 4. 5. 6.

§ 2.

The species of a philosop hical genus do not differ merely in degree Nor merely in kind Philosop hy is intereste d 10 cases where these two are combine d The scale of forms: its place in the history of philosop hy Such scales occur both in philosop hy and elsewhe re But in a philosop hical scale of forms the variable is identical with the generic essence

TWO DIFFICULTIES 7. (i) This identific ation seems nonsens ical 8. (ii) The scale, as hitherto describe d, accounts only for an overlap between opposite s, not distincts 9. It would folIow that philosop hical specifica tion is by oppositi on, non-phil osophica l by distincti on . 10. Consequ ences of this. It disintegr ates a philosop hical scale of forms, requirin g us to jettison all intermed iate tenus and keep only the extreme s I l . It requires us to jettison all distincti ons between one philosop hical concept and another . 12. It disintegr ates a non-phil osophica l scale of forms, and claims its extreme s for philo soph y.. 13. Finally it leads to a fatal dilemma concern ing the relation between oPP'osition and distinc tion. . • I

fi.D

54 55 56 57 59-

60

61 63 64 65 66 67 68

CONT ENTS

VII

§ 3.

DEGREE AND KIND: OPPOSI TION AND DISTIN CTION 14. In philosop hy there are differen ces of degree, but we cannot measure them 69 IS. This is because they are fused in a peculiar way with differen ces of kind. . . . • 71 16. Such a fusion follows from the principl e of overlapp ing classes '74 17. There is a similar fusion of oppositi on and distinc tion. 74 18. This also follows from the overlap of classes 76 19. Summa ry: in philosop hy there is a fusion (a) of di,fferences in degree with differen ces in kind, (b) of relations of oppositi on with relations of distincti on 76

§ 4.

DEGREE AND KIND IN THE SCALE OF FORMS The fusion of degr~e and kind removes the first of the two difficult ies (§ 2. 7) 2I. Exampl e of beauty 22. Exampl e of goodnes s 23. Exampl e of pleasure 24. The fallacy of calculat ion and the fallacy of equivale nce. :;:0.

:.

§ 5.

§ 6.

OPPOSI TION AND DISJ;IN CTION IN THE SCALE OF FORMS 25. The scale begins not with zero, but with unity . 26. i.e. with a minimu m realizati on of the generic essence 27. Relative ly to higher terms, this is a negation of that essence 28. The same relation subsists between any two adjacent terms in the scale . 29. The fallacy of the false positive and the fallacy of null oppositi on THE SCALE OF FORMS AND THE OVERLAP OF CLASSES 30. Each term surpasse s the next below, not only generica lly but specifically . . . . . 31. It therefor e sums up the whole scale to that point 32. Thus it both negates and reaffirm s the next below, and this explains the overlap of classe s. . . 33. And makes the concept ion of overlap more precise

77 77

78 79

80 81 82 82 84 85

86 89 90 91

IV. DEFIN ITION AND DESC RIPTI ON The view that philosop hical concepts are definabl e. Its • difficu lties. . . . . 2. The view that they are not. Its dangers "~ I.

\

92 92

CONT ENTS

viii

3. In exact science, definitio n implies Ca) separati on of essence (expoun ded in definitions) from properti es (expoun ded in theorem s) . 4. In philosop hy this is impossi ble; here therefor e the defini. tion of a concept is coextens ive with its entire e.'(position 5. (b) An absolute differenc e between knowing the essence of a concept and not knowing it . . . 6. This too is impossib le in philosop hy, where coming to know means coming to know better . 7. The tradition al rules of definitio n must therefor e be modified in the case of philosop hical definitio n . 8. Descript ion of an empirica l concept. Its likeness and unlikeness to philosop hical definitio n 9. The principle s of philosop hical definitio n. Illustrat ions from Plato and Aristotle 10. Illustrat ion from Rant •

94

9S 96 96 98 98 100 102

V. THE PHILO SOPH ICAL JUDG EMEN T: QUAL ITY AND QUAN TITY I.

§ I.

§ 2.

Division of the subject .

AFFIRMATION AND DENIAL 2. In philosop hy we cannot deny without making a correspondin g affirmat ion. 3. Proof of the principle of concrete negation 4. Fallacy of abstract negation 5. Fallacy of abstract affirmation . 6. Proof of the principl e of concrete affirmat ion 7. Applicat ions of the principl e 8. The two principle s combine d .

104 105 106 106 107 108 IIO

THE UNIVERSALITY OF THE PHILOS OPHICA L JUDGEMENT 9, There are three elements in all universa l judgeme nts I I I 10. There are three types of thought accordin g as one or other takes preceden ce of the rest . III I I. In philosop hy each type by itself is fallaciou s I!3 12. In a philosop hical judgeme nt all three forms of structur e coexist lIS

VI. PHILOSOPHY AS CATEGORICAL THIN KING § I.

PRELIMINARY STATEMENT OF THE PRINCI PLE I. The judgeme nts composi ng the body of mathem atics are hypothe'/'cal .

fL

I17

CONT ENTS So are those of empirica l science 3. But in philosop hy the body of knowled ge consists of judgeme nts about a subject- matter conceive d as real (i.e. categori cal judgeme nts) . 2.

r-

~

lI8

121

§z:: THE EVIDENCE OF 4. 5. 6. 7. 8.

§ 3.

TRADITIONAL PHILOS OPHY Quotatio tls from philosop hers expressi ng their recognit ion of the principl e 123 The Ontolog ical Proof, its origin and history 124 Its significa nce. The object of philosop hical thought cannot be conceive d except as existing 126 The principl e further support ed by examina tion (a) of logic • 128 (b) Of moral philosop hy 131

FINAL STATEl\1ENT ~D PROOF OF THE PRINCI PLE 9. Conclus ion from the evidenc e cited: the body of philosophical thought is essentia lly categori cal, though it contains hypothe tical element s 10. Proof of this from the principl e of overlapp ing classes II. Exclusio n of further pr~h.lems •

133 134 135

VII. TWO SCEPTICAL POSIT IONS I.

"" § I.

§ 2.

Sceptici sm as to whether a philosop hical proposit ion can be establish ed by construc tive reasonin g

CRIT,ICAL PHILOS OPHY 2. Philosop hy as the critical destruct ion of false views without assertin g or implyin g true ones 3. This induces a superfic ial, because merely formal, valuation of the views criticize d 4. It implies construc tive doctrine s on whi ...h its work is based, but neglects to formula te them

.

137

139

ANALYTIC PHILOS OPHY 5. Philosop hy as the analysis of proposit ions drawn from non-phi losophic al sourc es. . 6. Analysis of this philosop hy into three parts, only one of which is indubita bly philoso phical. . • 7. This, however , it neglects to work out . 8. But is not entitled to take it for granted 9. Both these philosop hies share the fault that they assume construc tive doctrine s while professi ng not to do so . 147 10. Both are inconsis tent with the first principl es of philosophical method as laid down in this es~ (y. .

x

CONT ENTS VIII. DEDU CTION AND INDU CTIO N

§ I.

§ 2.

§ 3.

§ 4.

§ 5.

THE IDEA OF DEDUCTIVE DEMONSTRATION 1. Demons tration in exact science. z. It implies (a) logical principle s external to the scicncc, (b) principle s belongin g to the science itself . 3. It nC\'cr chccks or criticize s, and cannot confirm, these principle s, i.c. it is irreversi ble in direction PHILOS OPHY DOES NOT CO!-."FORM TO THAT IDEA 4. The distincti on between two kinds ofprinci plcs disappea rs 5. Is its direction irreversi ble? 6. In spite of his thcory, Descartc s in practice realizcd that it is not 7. So did Spinoza and Leibniz 8. Therefo re Hegel's demand that philosop hy should justify its ~tarting-point is not ncw . PHILOS OPHY AND ITS STARTI NG-POI NT 9. Does this imply a vicious circle? 10. No, bccause its aim is not to create knowled ge e nihilo I I. The demonstra71dum is somethi ng which we in some sense already know IZ. Our demonst ration is vcrified by appcal to this previous knowled ge, and this serves to check the starting -point of the argumen t PHILOS OPHY AND INDUCT ION 13. Inductio n in empirica l science " 14. Its two kinds of principle s, and its irreversi bility IS. In philosop hy our initial knowled ge differs in three ways from the data of inductiv e thought 16, The process to which the data are subjecte d is differen t in the two cases 17. The result of the process is differen t

151 151 153

154 155 155 158 159

160 161 162

163

164

166 167 169 170

PHILOS OPHY AND EXPERIENCE 18. The continui ty of philosop hy with the e:"perienee in which it begins 170 19. This implies their homoge neity. 171 20. They are related as terms in a scale of forms 172 21. Philosop hical theory and philosop hical experien ce 173 22. Summar y, and conclusi on 173 \1,

e

CONTENTS

Xl

IX. THE IDEA OF SYSTEM §I.

OBJECTIONS AND REPLIES I.

2.

3. 4.

5. 6.

§2.

§ 3·

Reasons for the common prejudice against system 176 This prejudice as the expression of a legitimate demand • 178 (a) No system can be final 179 (b) No·single philosopher can do all the work required to 181 construct a system 182 (c) Any system is merely personal (d) Any system does violence to the diversity of philo184 sophical problems

4

EXPOSITION OF THE IDEA 7. The idea of system i~ indispensable to philosophy 1. 8. The divisions of ifS· subject-matter form overIapph classes • . . . . 9. And fall into a scale of forms. Systematic philosophy as~ a scale of philosophies 10. This conception clears up ·the difficulties stated in § I

18 9 190

EXAMPLES OF ITS PARTIAL:P.EALIZATION II. The idea constantly tends to realize itself: e.g. 12. (a) In the relation between the philosophical sciences 13. (b) In the history of philosophy 14. (c) In the philosophy of a single age IS. (d) In the philosophy of a single man

193 194 194 195 197

18 5

188

X. PHILOSOPHY AS A BRANCH OF LITERATURE § (:;. PROSE AND POETRY The two elements in prose The relation between them 3. In poetry there is only one 4. Prose is poetry with a difference 5. Prose and verse I.

2.

§ 2.

199 199 200 200

201

PHILOSOPHICAL PROSE AND SCIENTIFIC PROSE

6. Technical terms are sought in science and avoided in philosophy . 201 "';,7· What they are. Symbolism and language 20 3 8. Why they are needed in science and not in philosophy 2)5 9· The needs of philosophy can only be met by ordinary • • 'Z06 (literary or non-technical) language.

CONT ENTS

xii

§ 3.

§ 4.

PHILOSOPHICAL STYLE AND HISTORICAL STYLE 10. Historic al style is didactic I I. Philosop hical style is the opposite 12. 'Ve 'consult ' historian s, but 'follow' philosop hers

208 209 211

PHILOS OPHY AND POETRY 13. They are alike in the intimate relation between writer and reader 212 14. Philosop hy as the point at which prose comes nearest to being poetry. 213 IS. The philosop her uses language as the poets use it, but . what he writes must be prose . . . 213

§ 5. Tn.E READER'S

RELATION TO THE WRITER (a) As understa nding him. The reader must (i) read ,• philosop hy as pure literatur e. /17. (ii) Come to it prepared for the special philosop hical -problem of that special work. 'l8. (b) As criticizin g him. This is necessar y to compreh ension, but logically posterio r to it 19. It has a positive and a negative side 20. The critic as pupil C:"

215 215 217 218 219

XI. CONCLUSION Does the view hitherto stated agree with experienc~? 221 2. This question has been already asked pieceme al as the argumen t proceed ed. Justifica tion of this method 222 3. Whose experien ce? That of all philosop hers, ourselve s included 223 4. Does this not rest on an unprove d assumpt ion? . 224 5. If it is an assumpt ion, it is one of those assumpt ions which are not only legitima te but obligato ry • • 225 I.

INDE X.

I INTRODUCTION §I THERE are some things which we can do witho ut understanding what we are doing ; not only things which we do with our bodies, like locomotion and digestion, but even things which we do wit~ur minds, like making a poem or recognizing a \ ce. But when that which wc do is in the nature of th king, it begins to be desirable, if we are to do it ~ 1, that we should under stand what we are trying to do. Scientific and historical thoug ht could never go very far unless scientists and historians reflected on their own work, tried to under stand what they were aiming at, and asked themselves how best to attain it. Most of all, this is true of philosophy. It is possible to raise and solve ph~losophical problems with no very clear idea of what philosophy is, what it is trying to do, and how it can best do it; but no great progress can be made until these questions have been asked and some answer to them given. Philosophy, moreover, has this peculiarity, that reflection upon it is part of itself. The theory of poetry mayo r may not be of service to a poet opinions on that question have differ ed-bu t it is no part of poetry. The theory of science and the theory of history are not parts of science and of his- , tory; if scientists and historians study these things, they study them not in their capacity as scientists I.

,A

;, \ i

I

, I

2

INTR ODU CTIO N

or historians, but in their capacity as philos opher s. But the theory of philos ophy is itself a proble m for philos ophy; and not only a possible proble m, but an inevitable proble m, one which soone r or later it is bound to raise. For these two reasons, both because it is among his prope r subjects of study and because witho ut it his chance of success in his other subjec ts is diminish& : the philos opher is under an obligation to stud( the nature of philos ophy itself. Towa rds that stud1r the presen t essay is intend ed as a contri bution j its ~Jrimary purpo se being to consid er the questi on \Vila~ philos ophy is. 2. There are various lines by which that questi on might be approached. One of these would depen d upon the relation between an object and the thoug ht of it. Any special science, we might argue, must have somet hing special to study , and whate ver peculiarities it presen ts in aim and metho d must be due to peculiarities in its objec t; from this point of view it would appea r that the most hopef ul way of appro aching our questi on is first to define the prope r object of philosophical thoug ht, and then to deduce from this definition the prope r metho ds it should follow. But this line of appro ach would offer no hope of success except to a person convinced that he already possessed an adequate conception of this objec t; convinced, that is, that his philosophical tJlOught had already reached its goal. To me at least, d~refore, this path is closed ; for thoug h I believe th( certain ways of philosophizing are more fruitful

INTR ODU CTIO N

3

than others , I know of no p1;lilosophy fhat is not· a voyage of explo ration whose end, the adequ ate knowledge of its prope r object, remains as yet unrea ched. A secon d way, which might be open .even if the first were closed, depen ds on the relation betwe en means and end. We might ask what kind of result s philos ophy hopes or desires to achiev e; and, havin g thus laid down its progr amme , consid er what means can be found of realizing it. But althou gh every philos opher has some idea of what he hopes to achieve, this idea varie::J from perso n to perso n and in the same perso n from time to time; nor could it be otherwise, for any progress in thoug ht must bring with it a certai n change in the conception of its own end, the goal of one stag~ .being the startin g-poin t of the next. If I followed this metho d, therefore, I could not hope or even desire to comm and the assent of my readers, or even my own assent hereafter. 3. There remains a third line of approach. Philosophy never with any of us reaches its ultima te goal; and with its tempo rary gains it never rests conte nt; e pur si muo've: it is an activity which goes on in our minds, and we are able to distinguish it from amon g others, and to recognize it by certain peculi ar marks. These marks characterize it as an activity or proce ss; they are, theref ore, peculiarities of proce dure; and accordingly it is possible to answer the questi on what philos ophy is by giving an account of philosophical metho d. This suggests taking philosophical thoug ht as a special kind of fact, scruti nizing it, and describing

4

INTRODUCTION

the procedure which it is found to exhibit. But that would not be enough. The question what philosophy is, cannot be separated from the question what philosophy ought to be. When we distinguish philosophy from the other activities of our minds, we do not think of it as something that merely happens in us like the circulation of the blood; we think of it as something we try to do, an activity which we are trying to bring into conformity with an idea of what it ought to be. Consequently, when we set out to give an account of philosophical method, what we are trying to describe is not so much a method actually followed by ourselves or anyone else, as a method which in our philosophical work ,ve are trying to follow, even if we never entirely succeed. Hence an account of philosophical method must attempt to satisfy two conditions. First, to avoid a kind of philosophical utopianism, it must keep in touch with facts, and never lose sight of the question what methods have actually been used by philosophers of the past. Secondly, to avoid replacing a philosophical question by an historical one, it must treat all such precedents as mere preliminaries to the main question: the final appeal must be to our own experience of philosophical work, and to our consciousness that when we are engaged in it these are the principles which we are trying to follow. 4. The problem of method is one which has exercised philosophers from the earliest times; but there are reasons for thinking it a problem of peculiar

INTRODUCTION

5

.importance to-day. Since the close of the Middle Ages there have been two great constructive movements in philosophy: the Cartesian, following upon the scepticism that dissolved the medieval systems of thought, and the Kantian, following upon the scepticism of the eighteenth century. Each was . marked by a general agreement, such as must always exist in any period of achievement and. progress, concerning the principles of method; and each was opened, and its main principles were laid down, by a methodological tieatise. The movement of the seventeenth century is called Cartesian because its constitution and code of law were given to it by Descartes in the Discours de la M etlzode; that of the late eighteenth and early-nineteenth century stands in a similar relation to the Critique of Pure Reason. The Kantian movement, as ~ philosophical movement, had worked itself out within fifty years from the publication of the Critique, and its influence passed into the sphere of historical and humanistic studies, as that of the Cartesian had passed into the sphere of natural science. Throughout the greater part of the nineteenth century, the attention of active minds was chiefly taken up by these two branches of knowledge, science and history; there seemed nothing left for philosophy to do, and it sank into complete neglect, except as an appendage of natural science or as a part of history. Late in the century a few men appeared in whom once more philosophy found its proper shape as a distinct and living form of thought. These men heralded the dawn of a new 4033

B

6

IN TR OD UC TIO N

generation, tha t in which we now live, for which philosophy is am ong the universal inte res ts of the mind. Th e fer me nt of a new gro wth is at work. In the qua ntit y and qua lity of the phi losophical books now issuing fro m the press of this cou ntr y alone, our tim e can bea r comparison wit h any oth er; jud ged by the num ber of writers, the ser iousness of the ir aims, and the ir resolution in explor ing new ways of tho ugh t, this gen era tion has already reached a level in philosophical wo rk wh ich no one cou ld have anticipated fifty years ago, and see ms to promise a fur the r advance which ma y even lea d to a new con str!lctive movement. Bu t in ord er tha t this promise sho uld be red eem ed, one thin g is needed above all oth ers : a pat ien t and tho rou gh reconsideration of the pro ble m of me tho d. Th e pre sen t is a time of crisis and chaos in phi losophy. Th e exceptional difficulty wh ich mo der n philosophers find in accepting eac h oth er's conclusions, and even in und ers tan din g each oth er's arg uments, is a necessary consequence of the ir failure to agree upo n principles of me tho d, or even to find out exactly how the y differ; this only is clear, tha t the old methods are no longer followed, and eve ryo ne is free to inv ent a new one of his own. Th is is a state of things nat ura l and pro per to an age when new movements are in the ma kin g; b:ut if it lasts too long discouragement arid ind ifference will take the place of enterprise, and the new mo vem ent will be rot ten before it is ripe. Th ere is a widespread inte res t in the pro ble m of

INTRODUCTION

7

method; but it has not yet been directly faced as a distinct problem, as Descartes faced it in the DisCOW"S or Kant in the Critique. Consequently philosophers of all schools are still in varying degrees, however ,little they may recognize it, under the domination of methodological ideas inherited from the nineteenth century, when philosophy was in v.arious ways assimilated to the pattern of empirical science. If the state of philosophy at present is chaotic, that is beca~,se the rubbish left on the ground by the decayed systems of the last century is an impediment to sight and an obstacle to progress. The aim of this essay is to clear some of this rubbish from the ground, or at least to call attention to the need of doing so 'and invite others to go on with the work. To those who are busy constructing systems of their own, an invitation to take part in such elementary and menial work may seem an impertinence; but at least it betokens a conviction that beneath the apparent chao~ there is unity of purpose and spirit, and that beyond the present crisis the future of philosophy is full of hope.

§2 5. The different parts of philosophy are so related among themselves that none of them can be discussed without raising problems belonging to the rest. The subject of this essay is the nature of philosophy; and it w~uld be both easy and agreeable to expand this subject ,so as to include the place of philosophy among the other forms of thought, ;

s

INTR ODU CTIO N

the place of thoug ht amon g the other activities of the mind, and the relation of mind to the world. There are two reasons against yielding to this tempt ation. First, as a matte r of princi ple: .if the discussion of a special proble m is allowed to expan d until it becomes a discussion of the most general problems, no special proble m will ever receive adequate attent ion; whatever question is raised will come to be regarded merely as a variant of the one ultimate question, and its special features will be neglected. The result will be a philosophy where all distinctions are swallowed up in a blank and colourle~s unIty; a result no less fatal to the unity than to the distinctions, because the unity, which ought to be the articulated unity of an ordered system, has now become a mere undifferentiated chaos. Secondly, as a matte r of expediency. The purpo se of this book is to call attent ion to a certain problem. There are plenty of books on the marke t in which the general problems of philosophy are ably and attractively dealt with, and I should hesitate to add to them; but there does seem to be a place for an essay on philosophical metho d; and the utility of such an essay can only be impaired if it expands into a general philosophical treatise. For these reasons, thoug h no doubt the thoug hts here expressed have implications in metaphysics, logic, and the theory of knowledge, these implications will not be discussed. The reader will find that, in order to bring into relief the special characteristics of philosophy, it is constantly compared and

INTR ODU CTIO N

9

contrasted with science, and in partic ular with two kinds of science, empirical and exact. He will also find references to history and to poetry. But he will find no sketch, however brief, of a general scheme in which 'poetry, history, science, and phi~osophy have each its own place. 6. Anoth er warning is due to the reader at this point. I have illustrated the idea of exact science from elementary mathematics, and the idea of empirical science from zoology, botany, and othet: natural sciences. Perhaps a :mathematician, if I am fortunate enough to numb er mathematicians among my readers, may say to me: 'Your account of the metho d used in exact science is altogether beside the mark; modern mathematical theory has changed all that, and you are tilting at a man of straw.' If so, I shall reply that my contentions, so far from being invalidated, are confirmed in precisely that quarte r where confirmation is most welcome. For what I am discussing~ when I distinguish philosophical metho d from that of exact science, is not mathematics itself but a certain method, often mistakenly used in philosophy, which is believed to be that of mathematics. Even if it is right in mathematics I believe it to be wrong in philos ophy; but my attem pt to combat it as a philosophical metho d may, I fear, be opposed by the reply: 'This metho d is so brilliantly successful in mathematics that philosophy canno t do wrong to imitate it.' That is ~n argument, I contend, in which the conclusion does not follow from the premi ss; but my objection to it is only streng thene d if the

10

INTR ODU CTIO N

premiss is prono unced untru e. A corres pondi ng answer would apply to a scient ist who objected to my account of induc tive science.

§3 The scope of this essay does not requir e that it should be prefaced by even the briefest histor y of its probl em; but it will be of service to consider a few points in that history, as especially instru ctive for my purpo se. I propo se to take four philosophers, Socrates, Plato, Descartes, and Kant, and to discuss their contri bution s to the theory of philosophical metho 'd; not asking what metho ds they actually used in their work, which is an entire ly distin ct question, but only what metho ds they explicitly claimed to be using or recom mend ed for the use of others. 7. The central positi on in the histor y of Greek philosophy occupied by Socrates was undou btedly connected with his contri bution s to metho d. The very existence of the word dialectic, ,vhich from his time down to the prese nt day has stood for an impor tant group of methodological conceptions, owes its origin to his techn ique in philosophical discus sion; and when Aristotle asked himself what contri bution Socrates had made to philosophy, he answered in terms imply ing that, in his opinion, Socrates was essentially the inven tor of a metho d. Socra tes stated his own theory of his inven tion by saying that knowledge was to be sough t within the mind, and broug ht to birth by a process of

INTRODUCTION

11

questioning. The contrast bere insisted upon is the contrast between perceiving (a'LaB1]aLS) , regarded as the observation of things outside oneself, and think... ing (V01]aLS) , regarded as the discovery of what is within. Socrates showed that this second activity was common to two kinds of inquiry, which he does not seem to have distinguished in his theory of method: mathematics and ethics. His revolt against the study of nature was essentially a, revolt against observation in favour of thought; and whereas mathematical methgg, as an example of thought, had already been discovered by his predecessors, his own discovery was that a similar method, for which he invented an appropriate technique, could be applied to ethical questions. This technique, as he himself recognized", depended on a principle which is of great importance to any theory of philosophical method: the principle that in a philosophical inquiry what we are trying to do is not to discover something of which until now we have been ignorant, but to know better something which in some sense we knew already; not to know it better in the sense of coming to know more about it, but to know it 'better in the sense of coming to know it in a different and better way-actually instead of potentially, or explicitly instead of implicitly, or in whatever terms the theory of knowledge chooses to express the difference: the difference itself has been a familiar fact ever since Socrates pointed it out. 8. It is true that philosophical thought resembles mathematical in the manner asserted by Socrates;

12

INT RO DU CT ION

each is essentially not a way of obs erving facts, but a way of thinking. Bu t a closer com parison between the method of mathematics and his own new me tho d of dialectic would have shown him tha t, tho ugh similar up to a poi nt, beyond tha t poi nt the y differ in an imp ort ant wa y; and the evidence bef ore us suggests tha t Socrates himself did not explici tly recognize this difference. No thi ng is said abo ut it in any writing earlier tha n Pla to's Republic, where it is developed with unw ont ed explicitness in a we ll-known passage at the end of the sixth boo k; there is not hin g abo ut it in the Phaedo, where the intellectua l autobiography of Socrates not only per mit s but ·on e mig ht almost say de"mands a reference to it, had such an imp ortan t conception been Socratic in origin. Wi tho ut dogmatizing, therefore, I propos e to regard this doctrine as a Platonic development of the conceptions inherited from Socrates. Th e passage in question is tha t in which a line is divided into four par ts so tha t a: b :: c : d:: a + b : c + d. He re a + ban d c + d are the wo rlds of tho ugh t (Ta v01]ra) and perception (here called 'Ta opara), whose relation has been ,expounded in the Phaedo; so far we are doubtless on familiar Socrati c ground. Wh at Plato now wishes to poi nt out is tha t a similar relation exists wit hin the world of tho ugh t, between two orders of objects and two ' forms of tho ugh t corresponding to them, these forms of tho ugh t being dialectic and mathematics. Whatever may be the unsolved obs curities of this famous passage, one thin g is cle ar: tha t it expresses

INTR ODU CTIO N

13

a view according to which dialectic and mathematics differ in method. The difference is stated by saying that in mathematics the mind 'goes from hypotheses not to a principle but to a conclusion', whereas in dialectic it 'goes from hypotheses to a non-h ypothetical principle'; and this is furthe r explained by saying that geometricians posit triangles and so forth as hypotheses, and admit no argum ent about them, , but proceed on this basis to demonstrate their conclusions ; whereas in dialectic we use hypotheses not as principles, but as tbe hypotheses which they are, employing them as stepping-stones to reach something which is not an hypothesis but the principle of everything. I Mathematics and dialectic are so far alike that each begins with an hypot hesis: 'Let so-and-so be assumed .' But in mathematics the hypothesis formg a barrier to all furthe r thoug ht in that direct ion: the rules of mathematical metho d do not allow us to ask 'Is this assumption true? Let us see what would follow if it were not.' Henc~ mathematics, although intellectual, is not intellectual aoutrance; it is a way .of thinking, ~ut it is also a way of refusing to think. r Rep. 509 D seqq. The passages paraphrased are : !fovx~ ~7]T€LV

;g ao ) . e'

dvay«a~€TaL tmoelcT €wv, 0?J« €TT' dpx~v 1TopwoJ LlvTJ, dM' ;1Tl T€AWTl} V, TO 8' ET€POV ;1T' dpX~v aVV1TOefTOV tmOelUf WS '~( Lovua 510 B. V1TO €JL€VOt TO T€ 1T€PLTTOV «aL TO apTLOV «TI\ • ••• o?Jolva Aayov oirrf aUTO'S ot1T€. MAOLS ET, dgLouuL 1TfP~ a?JTwv