To reconstruct Kant's theory of science, the author identifies unifying themes of his philosophy of mathematics and philosophy of physics, both undergirded by his distinctive logical doctrines, and shows how they come together to form a relatively consistent system of ideas. A new analysis of the structure of central arguments in the Critique of Pure Reason and the Prolegomena draws on recent developments in logic and the philosophy of science.
Professor Brittan's unified account of the philosophies of mathematics and physics explores the nature of Kant's commitment to Euclidean geometry and Newtonian mechanics as well as providing an integrated reading of the Critique of Pure Reason and the Metaphysical Foundations of Natural Science. Contemporary ideas help both to illuminate Kant's position and to show how that position, in turn, illuminates contemporary problems in the philosophy of science.
Originally published in 1978.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Related collections and offers
Read an Excerpt
Kant's Theory of Science
By Gordon G. Brittan Jr.
PRINCETON UNIVERSITY PRESSCopyright © 1978 Princeton University Press
All rights reserved.
the anti-reductionist Kant
Almost everyone follows Hegel in thinking that the history of modern philosophy has a nice symmetry about it. Rationalist thesis ("knowledge is based on reason") gives way to empiricist antithesis ("knowledge is based on sense experience"), which in turn gives way to Kantian synthesis ("knowledge is a product jointly of understanding and sensibility"). For those who play the numbers game, the impression of symmetry is heightened by the fact that there are as many empiricists (Locke, Berkeley, Hume) as rationalists (Descartes, Spinoza, Leibniz), and one Kant, a magical seventh, to reconcile both traditions.
This characterization is oversimplified, of course, but there is nothing essentially wrong with it. The history of modern philosophy, writ large, does have just this sort of dialectic. No one was more aware of the dialectic than Kant himself, as the closing paragraphs of the Critique of Pure Reason indicate. It continues to provide a useful framework for the discussion of his ideas. Yet, at the same time, there is another fundamentally important and, it seems to me, largely overlooked way in which what Kant wrote constitutes not so much a reconciliation of "rationalism" and "empiricism" as the rejection of a feature they share in common. This rejection is connected with what I am going to call, somewhat ponderously, the "anti-reductionist" theme in Kant's thought. The present chapter is concerned with developing the theme in some detail. In my view, Kant's theory of science is best approached by first appreciating its anti-reductionist motives.
Return for a moment to our rhetorical version of the history of modern philosophy. We begin with Descartes. One of the characteristic claims he wants to make is that the sentences that comprise the various sciences all follow from a few basic propositions, perhaps ultimately the "Cogito," which reason discovers by reflecting on itself. Thus, to retrace briefly a very well-known route, from the fact of his existence Descartes "proves" the existence of God, then, a little further along, that the essence of matter is extension, that momentum is conserved, and eventually Galileo's laws of motion. Similarly, Leibniz claims that, given the principles of contradiction and sufficient reason, all of "natural philosophy" can be "demonstrated." To choose but one example, Leibniz derives Snell's Law ("sin i/sin r is constant for any pair of media," where i is the angle of incidence of a light ray and r is its angle of refraction) from the innately given principle of simplicity, a corollary of the principle of sufficient reason, for the law describes the least path through a pair of media. The role of sense experience in acquiring scientific knowledge, of which physics is the paradigm, is apparently limited to prompting reason to self-reflection. In other words, the whole of scientific knowledge can be spun out a priori, by following up the deductive implications of those basic principles which reason originally discloses to itself.
This is only a very rough sketch, but it indicates two important aspects of the view I am attributing to Descartes and Leibniz. First, that physics in its entirety can be derived from a few basic logical and metaphysical principles and, second, that these principles are discovered and their truth guaranteed by reason. If the second aspect of their position is primarily what makes Descartes and Leibniz "rationalists" (in perhaps a not quite standard sense of the word), the first makes them — to coin a term — "reductionists." Provisionally, a "reductionist" is someone who claims that a deductive relationship obtains between sentences of one kind and sentences of another, "kinds" to be made clearer by way of examples. Descartes' attempted derivation of physical laws from metaphysical principles is an attempted reduction of the former to the latter. So too would be the derivation of biology from physics that he forecasts. In the same way, mathematics reduces to logic if the propositions of mathematics can be derived from the laws of logic and definitions, as Leibniz believed.
Classical empiricists do not, to my knowledge, claim that a deductive relationship obtains between the propositions of physics and sentences reporting or describing certain sorts of primary sense experience. This is not to say that there are no texts that at least superficially claim an empiricist reduction. Among the most striking of these is the general Scholium added to the second edition of Principia, where Newton declares: "I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena...." There is also the equally celebrated Query XXXI at the end of the second edition of Newton's Optics: "To tell us that every species of things is endowed with an occult specific quality by which it acts and produces manifest effects is to tell us nothing; but to derive two or three general principles of motion from phenomena, and afterwards to tell us how the properties and activities of all empirical things follow from these manifest principles, would be a very great step in philosophy...." The difficulty with such texts is that the significance of the words "deduced," "derived," and "inferred," even "phenomena," is far from clear, however we might broaden our characterization of reductionism.
But it is worth adding that if classical empiricists are not explicit about claiming that a deductive relationship obtains between the propositions of physics and sense-experience sentences, many of their more recent successors have insisted on it. Ernst Mach for one, C. I. Lewis for another, Rudolf Carnap for a third have claimed that the propositions of physics can be "translated" or "transformed" into sense-experience sentences, and, while the notion of translation involved here is not always clear, at the very least it must mean that sentences, or sets of sentences, of the two kinds are deductively equivalent. Once again, to the extent that the propositions of physics can be derived from sense-experience sentences, physics has been reduced to them.
As I have formulated them, "rationalism" and "empiricism" share a reductionist feature, although they differ sharply concerning the character of the sentences to which the reduction is to be made. They also share a common motive. In both cases a reduction is typically carried out with the purpose of providing physics with a firm epistemological foundation. If physics can be reduced to ideas innate to reason, whose truth and necessity is thereby guaranteed, then physics will have been shown to be epistemologically secure. For those of empiricist persuasion, the demand is that physics be reduced to sense experiences that are themselves incorrigible; only in this way can the knowledge claims that science makes be justified. Or, if such a reduction cannot be carried out, we should in conscience become skeptics.
reductionism rejected: "the Copernican Revolution"
It is just at this point that I want to locate Kant's break with the philosophical tradition. The break has several different aspects, all of which can be brought together under the very general heading of "the Copernican Revolution" Kant hoped to bring about in philosophy. For the moment, it is not so much a question of giving arguments as of sketching a changed perspective.
In the first place, the reductionist program, and even more strikingly its epistemological motive, is abandoned. Kant begins with the security of physics. It is the point of departure, not the end of a long demonstration. There is no need to justify the propositions of physics, individually or collectively, or to reduce them to something more basic or secure. We are not to ask whether we do in fact have genuine knowledge of nature, but rather, granting from the outset that we do have such knowledge, what conceptual abilities are presupposed. Or, as Kant himself preferred to put it, not "Is knowledge possible?" but "How is it possible?"
I have suggested that for both empiricists and rationalists the epistemological security of physics typically motivated reductionist programs. Why the worry? For one thing, there were traditional problems about the reliability of sense perception, most of them pointed up by one version or another of the "argument from illusion." For another thing, and for my purposes the more important, two fundamental theses of 17th- and 18th-century science were taken to imply that our knowledge of the world could never be more than inferential. The first of these theses had to do with a physiological account of perception. On this account, physical objects impinge on the various sense organs, giving rise to sensations that are in turn the immediate objects of perception. The second thesis was that, in reality, the world is composed of imperceptible particles or corpuscles. The two theses were combined in the claim that these imperceptible particles had merely spatial properties, and that the color, taste, and smell we ordinarily attribute to the objects in our environment are in some sense subjective, dependent on peculiarities of human physiology. Both theses apparently open up a gap between the world as it presents itself to our senses and untutored intelligence, and the world as it actually is, in the light of scientific investigation. If physics is taken to describe the world as it actually is, then it would appear, possibly with some additional assumptions, that its epistemological security can be guaranteed only if this gap is bridged or closed. A central aim of reductionist programs, of both empiricist and rationalist varieties, is to provide the appropriate closure or bridge. Talk about the world as it emerges in the scientific picture of things, and in particular talk about imperceptible particles, is legitimized only insofar as it can be translated into talk about sense experiences, on the one hand, or shown to follow from necessary first principles, on the other.
Kant subscribed to the theses of 17th- and 18th-century science just mentioned, but he denied that an epistemological gap opened as a result, a gap that philosophers had to close or bridge. We can begin with the second thesis, that the world is composed of imperceptible particles. In a passage at B226/B273 of the Critique of Pure Reason the following point is made: "Thus from the perception of the attracted iron filings we know of the existence of a magnetic matter pervading all bodies, although the constitution of our organs cuts us off from all immediate perception of this medium (dieses Stoffs). For in accordance with the laws of sensibility and the context of our perceptions, we should, were our senses more refined, come also in an experience upon the immediate empirical intuition of it. The grossness of our senses does not in any way decide the form of possible experience in general."
The point is complex, but it seems to have at least two aspects. One is the explicit denial that the imperceptibility of the medium (the magnetic matter) creates an epistemological gap. The other is an intended contrast, made clearer in the paragraphs following the passage quoted, between this type of inference, made within the limits of possible experience, and a pretended inference from what is given in experience — sensations, for example — to what is beyond experience, those objects lying on the other side of the veil of perception. The latter sort of inference, Berkeley rightly saw, can never be justified, not even by an appeal to God's benevolence. We must distinguish the former, legitimate (and properly scientific) inference from the latter, illegitimate (and metaphysical) one, the contingent imperceptibility that depends on the grossness of our senses from the non-contingent imperceptibility that has to do with the limits of possible experience. If we do not make the distinction, and we do take seriously the scientific picture of things, then there would seem to be no option to idealism, "the theory which declares the existence of objects in space outside us either to be merely doubtful and indemonstrable or to be false and impossible." On the other hand, Kant goes on to argue, in the Refutation of Idealism that immediately follows the quoted passage in the Critique, not only is the existence of objects in space outside us in general not doubtful, hence no inference and, a fortiori, no "reduction" is needed, it is in some sense more certain than awareness of private sense experiences or the fact of one's own existence. The motives that prompt reductionist accounts inevitably lead to idealism. Kant's rejection of the one is of a piece with his rejection of the other.
In the same way, Kant denies that an epistemological gap between ourselves and the world opens as a result of the first thesis, that perception is causally mediated. As he puts it in the General Observations on Transcendental Aesthetic, at A45/B62: "We commonly distinguish in appearances that which is essentially inherent in their intuition and holds for sense in all human beings, from that which belongs to their intuition accidentally only, and is valid not in relation to sensibility in general but only in relation to a particular standpoint or to a peculiarity of structure in this or that sense. The former kind of knowledge is then declared to represent the object in itself, the latter its appearance only." But, Kant adds at once, this distinction is merely empirical. It is a distinction made within experience, not between experience and that which lies beyond or behind it. It is, in fact, only if we assume the existence of physical objects impinging on our sense organs from the outset that a physiological account of perception is coherent.
With regard to both theses, Kant often makes his point in terms of a distinction between transcendental and empirical questions. Kant uses the word "transcendental" in several different ways, often carelessly. On one of these uses, the distinction between transcendental and empirical questions is a distinction between questions about experience and questions asked within experience, a distinction, we might put it today, between the kinds of questions philosophers ask and the kinds of questions scientists ask. Both the physiological theory of perception and the corpuscular hypothesis are empirical or scientific hypotheses, and the distinction they suggest between the world as it is and the world as it appears is empirical. It is when this distinction is taken as a transcendental distinction, between what lies within our experience and what beyond it, that an epistemological gap is created, attempts at reduction initiated, and idealism produced. Part of Kant's break with his predecessors (and, I think, with certain aspects of his own pre-Critical writings on science) involves his claim that they confused empirical with transcendental questions.
Kant's claim that the propositions of physics stand in no need of justification is connected in another way with his view of what it is to do theory of science or, more generally, of what it is to do philosophy. On the traditional view, to do theory of science is to re-do science, to reconstruct it rationally so that it is clear how its content may be guaranteed against skeptical attack. This is also the view of many of the more recent logical positivists: philosophy consists in the analysis of the propositions of science, and to analyze a scientific proposition is to show how it can be "reduced" to immediate sense experience. But Kant rejects this view of what it is to do theory of science. In his view, theory of science is not concerned so much with the justification of phycics — indeed, physics stands in no need of justification — as with the isolation and examination of the a priori and conceptual elements in it and the role they play in making physics "possible," that is, in guaranteeing its application to objects that in an important sense are independent of us. Not the epistemological security of physics but its "objectivity" is what is at stake. This changed conception is still another aspect of "the Copernican Revolution."
These claims about Kant's position are, of course, very general and so far largely unsupported. They are intended merely as a suggestive preamble to what follows. Even so, they run counter to two standard ways in which Kant's position has been interpreted. One of these interpretations bases itself on passages in the Critique of Pure Reason, where a kind of phenomenalism is suggested, and on a particular reading of the doctrine of "synthesis," a reading associated with the picture of the mind "putting together" sensations to "form" objects. This interpretation derives some additional support from W. V. Quine's well-known thesis that classical empiricism turns on two inseparable dogmas: the analytic/synthetic distinction and empiricist reductionism. Kant insists on the analytic/synthetic distinction. If Quine is right, it would follow naturally (if not logically) that he is committed to a reductionist view of the empiricist variety. The other interpretation mentioned again bases itself on passages in the Critique, this time where the mind is pictured as laying down the law to nature, and on a particular reconstruction of Kant's central argument. It is to the effect that Kant is a "reductionist" in the rationalist tradition, attempting to derive, inter alia, the whole of Newtonian physics from certain necessary propositions about human sensibility and understanding.
Excerpted from Kant's Theory of Science by Gordon G. Brittan Jr.. Copyright © 1978 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.
Table of Contents
- Frontmatter, pg. i
- Preface, pg. vii
- Contents, pg. xi
- Chapter 1: the anti-reductionist Kant, pg. 3
- Chapter 2: Kant's philosophy of mathematics, pg. 43
- Chapter 3: geometry, Euclidean and non-Euclidean, pg. 68
- Chapter 4: the axioms of intuition, pg. 90
- Chapter 5: Kant and Newton, pg. 117
- Chapter 6: the substance of matter, pg. 143
- Chapter 7: time and causality, pg. 165
- Chapter 8: the problem of induction and its "solution", pg. 188
- Selected Bibliography, pg. 209
- Index, pg. 211