Structure and Nature W. V. Quine The Journal of Philosophy, Vol. 89, No. 1. (Jan., 1992), pp. 5-9. Stable URL: http://links.jstor.org/sici?sici=0022-362X%28199201%2989%3A1%3C5%3ASAN%3E2.0.CO%3B2-7 The Journal of Philosophy is currently published by Journal of Philosophy, Inc..
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THE JOURNAL OF PHILOSOPHY VOLUME LXXXIX, NO.
1,JANUARY 1992
w
STRUCTURE AND NATURE E are familiar with three adequate but incompatible ways of modeling number theory in set theory, o r the theory of classes; and there are infinitely many more. We bandy our numbers without caring which classes we are bandying from among this wealth of alternatives. We are just content that we are operating somewhere within the ontology of classes to which we have committed ourselves anyway for other purposes. This situation, long since remarked upon by Paul Benacerrafl and others, receives formal expression in Ramsey sentence^.^ Such a sentence merely affirms that there are classes obeying the desired laws-arithmetical laws in this case-and then proceeds to apply such unspecified classes to whatever arithmetical business we had in mind. That is the structuralist treatment of number. It is just a way of eliminating an idle question-"What is number?"-and a gratuitous decision among indifferent alternatives. Ontological economy is not its point; the same old classes are presupposed. David Lewis3 has ventured the next step: a structuralist treatment of classes themselves. Now just as structuralism in number theory depended on the various ways of reducing numbers to classes, so structuralism in class theory depends on reducing classes in turn to-what? For Lewis, as for most of us, I should like to think, there are only classes and concrete individuals. So his structuralism is indeed ontologically significant. It professes a reduction of classes to individuals-hence out and out nominalism. Arithmetical structuralism, as expressed in Ramsey sentences, depended on there being classes in which the required arithmetical structures could be defined and realized, though we were freed of choosing among alternatives. Similarly for Lewis's structuralism of
' "Mathematical Truth," this JOURNAL,
LXX, 1 9 (November 8, 1973): 661-79. Frank Ramsey, T h e Foundations of Mathematics (New York: Koutledge, 1931), pp. 212-36. Parts of Classes (New York: Blackwell, 1991).
0022-362X/92/8901/5-9
O 1992 The Journal of Philosophy, Inc.
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classes; it depends, for its truth, upon there being individuals in which the desired classial structures can be defined and realized. Thus he needs a theory of individuals. What he uses is mereology, or the theory of part and whole, with atoms. By ingenious constructions he carries the day, contingently on there being enough atoms, and granted George Boolos's4 view of second-order logic as just a classless logic of plurals. If there are not enough atoms, then the higher reaches of set theory turn out meaningful but false. How much of axiomatic set theory is true comes to depend on the size of the concrete universe: on how many atoms there are. If there are only finitely many, then so much the worse for classical set theory even at its weakest. Truth in mathematics comes to depend on the richness of nature. Lewis appreciates all this. Uncertain as to the richness of nature, we can still pursue higher set theory in a conjectural spirit, finding out how it would be if nature were up to it. In any event, Lewis's construction renders the whole of set theory meaningful from his nominalistic point of view, however much of it is thereby rendered true and how much false. And, ironically enough, the scientific utility of applied mathematics is independent of all that. Structuralism for classes, hence for all abstract objects, is undeniably congenial. They are things that are known anyway only by their structural role in cognitive discourse; never by ostension. By ostension and extrapolation we do learn what individuals qualify as members of the class of cats, but that class itself is just an abstract entity to which each cat bears a cryptic epsilon relation. Your class of cats and mine can still be different things, and your membership relation and mine can be different, if it makes any sense to say so, though we see eye to eye on every cat. Such is the appeal of structuralism regarding abstract objects. Much though I admire Lewis's reduction, however, it is not for me. My own line is a yet more sweeping structuralism, applying to concrete and abstract objects indiscriminately. I base it, paradoxical as this may seem, on a naturalistic approach to epistemology. Natural science tells us that our ongoing cognitive access to the world around us is limited to meager channels. There is the triggering of our sensory receptors by the impact of molecules and light rays. Also there is the difference in muscular effort sensed in walking up or down hill. What more? Even the notion of a cat, let alone a class or number, is a human artifact, rooted in innate predisposition and cultural tradition. The very notion of an object at all, concrete or abstract, is a human contribution, a feature of our inherited apparatus for organizing the amorphous welter of neural input. "Nominalist Platonism," Philosophical Review,
XCIV,
3 (July 1985): 327-44.
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Language, the vehicle of science, is linked to our neural input by neural mechanisms of association or conditioning. Early in our learning of language we learn to associate certain expressions with certain ranges of neural input. I call these expressions observation sentences. Grammatically, some are indeed sentences, e.g., 'It's raining', and some are nouns or adjectives, e.g., 'Cat' or 'Milk' or 'White'. To begin with, they are just expressions associated holophrastically with ranges of neural input. They are as if to say, with William James, "Hello, thingumbob againH-except that even 'thingumbob' hints more of objectual reference than I could wish. The observation sentence names nothing, to begin with, neither neural input nor external object. But it is learned from adults who have learned the ways of reference, so it is indeed an expression, such as 'It's raining' or 'Cat' or 'Milk' or 'White', that is destined for eventual integration into a system of objectual reference on the child's own part as he matures. This growing system of terms and purported objects is our science of nature, our organization of the welter of neural input. Reification and implication are the key principles by which that organizing proceeds. We master implication in the course of learning to use the logical particles, such as 'not', 'and', 'or', 'if', 'every', 'some'. For instance, our learning to use 'not' and 'or' consists in part in learning to assent to 'q' whenever we have assented to 'not p' and ' p or q'. Our learning of 'every' consists in part in learning to assent to ' a is a G' once we have assented to ' a is an F and 'Every F is a G'. It is in implications of this last sort that reification makes its contribution, in our having reified the object a and the other Fs and Gs. The reification of bodies comes in stages in one's acquisition of language, each successive stage being more clearly and emphatically an affirmation of existence. The last stage is where the body is recognized as identical over time, despite long absences and interim modifications. Such reification presupposes an elaborate schematism of space, time, and conjectural hidden careers or trajectories on the part of causally interacting bodies. Such identifications across time are a major factor in knitting implications across the growing fabric of scientific hypotheses. At more sophisticated stages in the development of language and science, implications are enhanced by positing further objects, no longer observable; thus subvisible particles, also numbers and other classes. The implications thus forged are what relate our evolving scientific theory to our heterogeneous neural input and hence ultimately to the external world that our scientific theory purports to describe.
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This fabric of interlocking sentences hooks on to the neural input at the observation sentences. Some of these, we saw, were learned by primitive conditioning to ranges of neural input. Many further observation sentences, more sophisticated ones, are scientific sentences retroactively associated with observation through the intervention of theory; thus the chemist sees at a glance that there was copper in the solution, and perceives at a sniff that sulphur dioxide escaped. Now the way implication links theory to neural input is that a bundle of scientific hypotheses is found to imply that the fulfillment of one of two given observation sentences should always ensure fulfillment of the other. This dictates an experiment: he brings about fulfillment of the one and checks for the other. Failing the other, the bundle of hypotheses is discredited; one or another of them must be revoked. Such, in schematic caricature, is surely the evidential relation of scientific theory to the triggering of our neuroreceptors by the external world. I have ventured more detail e l ~ e w h e r e ,and ~ much more wants venturing. Perhaps a fair bit of science might be found on fuller analysis to be beyond the reach of evidence altogether. But this sketch will suffice for what I want to say about structuralism. The point I now want to make is one that over the years I have repeatedly made in terms of what I call proxy functions. The point is that if we transform the range of objects of our science in any one-to-one fashion, by reinterpreting our terms and predicates as applying to the new objects instead of the old ones, the entire evidential support of our science will remain undisturbed. The reason is twofold. First, implication hinges only on logical structure and is independent of what the objects, the values of the variables, may be. Second, the association of observation sentences with ranges of neural input is holophrastic. It is independent of reifications, independent of whatever objects the observation sentences or their parts may be taken to refer to as terms. The conclusion is that there can be no evidence for one ontology as over against another, so long anyway as we can express a one-toone correlation between them. Save the structure and you save all. Certainly we are dependent on a familiar ontology of middle-sized bodies for the inception of reification, on the part both of the individual and of the race; but once we have an ontology, we can change it with impunity. For abstract objects this is unsurprising, and quite in the spirit of Ramsey, Lewis, and Benacerraf. For familiar bodies it is less intuitive. But we must bear in mind that an observation sen"he Roots of Reference (Peru, IL: Open Court, 1974); and Pursuit of T r u t h (Cambridge: Harvard, 1990).
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tence, say, 'That's a rabbit', retains all its origmal visual associations; it is only the purported object that is gratuitously displaced. This global ontological structuralism may seem abruptly at odds with realism, let alone naturalism. It would seem even to undermine the ground on which I rested it: my talk of impacts of light rays and molecules on nerve endings. Are these rays, molecules, and nerve endings themselves not disqualified now as mere figments of an empty structure? Naturalism itself is what saves the situation. Naturalism looks only to natural science, however fallible, for an account of what there is and what what there is does. Science ventures its tentative answers in man-made concepts, perforce, couched in man-made lan\page, but we can ask no better. The very notion of object, or of one and many, is indeed as parochially human as the parts of speech; to ask what reality is really like, however, apart from human categories, is selfstultifying. It is like asking how long the Nile really is, apart from parochial matters of miles or meters. Positivists were right in branding such metaphysics as meaningless. But early positivists were wrong if and when they concluded that the world is not really composed of atoms or whatever. The world is as natural science says it is, insofar as natural science is right; and our judgment as to whether it is right, tentative always, is answerable to the experimental testing of predictions. We saw that reference could be wildly reinterpreted without violence to evidence. We see now that that is just part of a wider picture. Presumably yet more extravagant departures, resistant even to sentence-by-sentence interpretation into our own science, could conform equally well to all possible observations. If we were to encounter such a case and somehow recognize it as such, we might even proceed to master it and then switch back and forth for richer perspectives on reality. But naturalism would still counsel us that reality is to be grasped only through a man-made conceptual scheme, albeit any of various. My global structuralism should not, therefore, be seen as a structuralist ontology. To see it thus would be to rise above naturalism and revert to the sin of transcendental metaphysics. My tentative ontology continues to consist of quarks and their compounds, also classes of such things, classes of such classes, and so on, pending evidence to the contrary. My global structuralism is a naturalistic thesis about the mundane human activity, within our world of quarks, of devising theories of quarks and the like in the light of physical impacts on our physical surfaces. W. V. QUINE
Harvard University
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[Footnotes] 1
Mathematical Truth Paul Benacerraf The Journal of Philosophy, Vol. 70, No. 19, Seventieth Annual Meeting of the American Philosophical Association Eastern Division. (Nov. 8, 1973), pp. 661-679. Stable URL: http://links.jstor.org/sici?sici=0022-362X%2819731108%2970%3A19%3C661%3AMT%3E2.0.CO%3B2-V 4
Nominalist Platonism George Boolos The Philosophical Review, Vol. 94, No. 3. (Jul., 1985), pp. 327-344. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28198507%2994%3A3%3C327%3ANP%3E2.0.CO%3B2-T
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