The Methodological Structure of Kant’s Metaphysics of Science

  • Robert E. Butts
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 155)


For many of us nurtured in idealist ways inclining us to unwavering acceptance of Kantian principles, 1951 was a bad year. We read in Reichenbach’s The rise of scientific philosophy of the “disintegration of the synthetic a priori.”1 Kant had taught us that there are very general principles—each one connected to a primal category of thought—that are necessary in the formation of mathematics and physics and are expressible in nonanalytic propositions. However, since Kant’s death in 1804 both mathematics and physics have developed revolutionary traits: noneuclidian geometries, new developments in symbolic logic, relativity physics, and finally, quantum mechanics, sealed the negative fate of Kant’s high principles. Henceforth we must accept that there are no nonempty claims about reality that can be counted as necessary or indispensable to mathematics and science. Kant’s attempt to offer a new epistemological guarantee of the three-dimensionality of space, and of the Newtonian character of physical motions, thus failed in the deepest sense: As a philosophy of science it turned out to be an anthropomorphic curiosity. Kant’s epistemic formalism might well apply to macroscopic objects undergoing macroscopic movements and observed within the apparent three-dimensional limits of our human visual space. It fails to apply in any other domains. Kant’s objects of possible experience are objects too limited for purposes of recent mathematics and physics.


Physical Concept Regulative Employment Regulative Principle Fundamental Force Universal Gravitation 
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  1. 1.
    Not that this was the first philosophical expression of dissatisfaction with Kantian synthetic a prioris; for example, the Reichenbach-Einstein exchange in Schilpp (1949, pp. 289-311; 676-79) had already neatly arranged the relevant debating points.Google Scholar
  2. 2.
    The sources were rich ones: Lewis and Dewey, Mach and Schlick. It became clear by the 1950s that we were going to have to get used to very different styles of thinking about the a priori.Google Scholar
  3. 3.
    Kant mentioned the possibility of a second special metaphysics, that of “objects” of internal sense, or of the soul. However, he required of a proper science that its subject matter be mathematizable; contents of inner sense are not mathematizable; therefore a science cannot be developed on the basis of the special metaphysics of the soul. Only bodies moving in space can be objects of proper science. I argue elsewhere that this accounts for Kant’s clinical and nosological interest in psychical phenomena: He replaces the impossible science of the soul with a behaviouristic psychopathology, one whose nosology of mental disorders groups deviations from normal schematized category knowing into clinical syndromes (Butts, 1984, pp. 298-310).Google Scholar
  4. 4.
    The insistence that natural science must be essentially mathematical is clearly stated in MAN, p. 470. That all objects of possible experience must be mathematical idealizations (constructs) of appearances is a central claim of the transcendental programme. See A162-170/B202-218; A142-43/B182-83.Google Scholar
  5. 5.
    Kant is here talking about empirical natural science, not about the metaphysical foundations of natural science, as he makes clear in what follows the quoted line. Conjecture is typical of the former, a priori certainty is a feature of the latter, as we have seen.Google Scholar
  6. 6.
    This discussion necessarily bypasses what is at another level a crucial problem for Kant: What about the ontological status of moral agents? or persons? Since practical reason can only postulate such “objects” on analogy with objects resulting from schematized categories, what ontological status can be accorded them: useful fictions?.Google Scholar
  7. 7.
    Both SC and LM require that objects of proper science be mathematizable; mathematics constructs its objects; hence we must have a set of MCs (mathematical constructions) yielding the physical meaning of each LM For example, the second Kantian law of mechanics (the principle of inertia) provides part of the ontology of bodies by allowing construction of motion as an object of possible experience through provision of a “geometrical curve whose direction at each point is determined by the tangent (the geometrical representation of the first derivative, which is identical with velocity, if the horizontal axis of the coordinate system represents the time); and the physical meaning of the tangent is just inertial motion” (Pap, 1946, pp. 43-44). Constructions are of course required for each of the Kantian principles in pure physics; they provide intuitive warrant for the possibility or intelligibility of the concepts involved.Google Scholar
  8. 8.
    Kant does not list “F=ma” as a law of motion, although his discussion indicates that he accepts “ma.” Did he realize that the law of inertia is a special case of “F=ma”, where F=O? See Okruhlik (1983, pp. 252-53) for a brief discussion of Kant’s failure to mention explicitly Newton’s second law. I suspect that Kant’s failure to record acceptance of the identity has to do with his conviction that forces are not fully constructible, hence cannot be fully available for mathematical treatment. Throughout his career he wanted to retain the idea of some kind of empirical access to forces, and for him forces manifested in the motions of objects given in space and expressed as external relations between such objects were finally the best candidates. Such “transeunt” forces replaced the empirically inaccessible immanent forces of Leibniz. For my view on Kant’s treatment of the fundamental forces of attraction and repulsion, see below, Appendix.Google Scholar
  9. 9.
    Some words about the word. Kant uses both Affinität and Verwandschaft in KRV. In ANTH §§. 31, 31c) he uses Verwandschaft and the Latin affinitas. Affinitas means relationship through marriage (as in the Church of England Common Prayer “Table of Kindred and Affinity”). Verwandtschaft shares these connotations; Affinität should probably be construed as Kant’s preferred technical term, although he uses Affinität and Verwandtschaft interchangeably and without distinction in KRV (for example, A657-663/B685-691). In ANTH 31c his examples are catalytic interaction of chemical substances and marriage. Affinity names a kind of relationship between dissimilars, and unites through a common ground or source. In methodological contexts the rule of affinity enjoins us to search for systematic unification achieved by a convergence of initially unrelated inductions. Shortly we will see that Kant’s favourite example of systematic unification is the inference to universal gravitation.Google Scholar
  10. 10.
    I cannot develop the point here, but what I am saying about systematic organization of classification schemes as Kant viewed it seems to me to confirm Kitcher’s (1983) claim that for Kant a scientific theory is a “projected order of nature.” Much that I argue for in (1984) depends upon accepting Kitcher’s correct insight. For a brilliant elaboration of his interpretation, see Kitcher (1986).Google Scholar
  11. 11.
    “In so far as the term’ science’ essentially connotes an activity aiming at the discovery of laws, the principle of causality, interpreted as an imperative, may, indeed, be said to be presupposed by the very possibility of science. Science is the successful response to the imperative expressed by the principle of causality. On this point philosophers as widely opposite in their attitude towards Kant’s critical idealism as Schlick and Cassirer seem to agree” (Pap, 1946, p. 68). Kant does suggest that the Second Analogy is grounded in the principle of sufficient reason: “The principle of sufficient reason is thus the ground of possible experience, that is, of objective knowledge of appearances in respect of their relation in the succession of time” (KRV A201/B246). However, as we have seen, instantiated by matter in motion, the principle of causality leads us to have strong expectations about the specific explanatory framework that will correctly explicate cases of observed motion. The agreement attributed to Cassirer and Schlick thus seems of little consequence.Google Scholar
  12. 12.
    At this stage specialists in the thought of Kant will want to remind us that the problem of property stability is important for Kant in a number of related contexts. At A90/B123 he recognizes the problem: “Appearances might very well be so constituted that the understanding should not find them to be in accordance with the conditions of its unity. Everything might be in such confusion that, for instance, in the series of appearances nothing presented itself which might yield a rule of synthesis and so answer to the concept of cause and effect. This concept would then be altogether empty, null, and meaningless”. Even empirical memory (reproductive imagination) requires stability of properties. “If cinnabar were sometimes red, sometimes black, sometimes light, sometimes heavy... my empirical imagination would never find opportunity when representing red colour to bring to mind heavy cinnabar” (A 100-101). At least some of these specialists will also want to hold that Kant’s argument in the transcendental deduction yields justified objective grounds for stability of properties. I think, however, that here we must score one for Buchdahl. Lawlikeness of empirical laws presupposes stability of properties, but the assumption of stability of properties rests on the principle of affinity—a subjectively valid regulative principle. Here there is a “messy” articulation, rather than a clinching argument. In the absence of an sich realist convictions, it is extremely difficult to argue into existence a stable and epistemologically reliable external world.Google Scholar
  13. 13.
    Both Friedman (1986) and Kitcher (1986) confirm the crucial methodological role of affinity in Kant’s philosophy of science. Shea (1986) reveals that the principle had an ancestry in Leibnizian metaphysics and played a prominent role in Kant’s early cosmological speculations.Google Scholar
  14. 14.
    My colleague Margaret Morrison reminded me of the passage in which Kant states that principles like affinity “carry their recommendation directly in themselves” (KRV, A661/B689), and warned that unless I can give an appropriate reading of Kant’s claim here, the appeal to a pragmatic justification of subjective principles is unavailing. This is a well taken point, and one worth careful development. My suggestion is that Kant is here pointing out that the success of the principles as methodological components of Newton’s (essentially correct) physics is one that can be universalized by being “represented as objective” in much the same way as are aesthetic judgements of taste. This would be consistent with Kant’s belief that Newtonian physics (including its methodology) is the best example of successful science. The suggested reading also brings judgement of the acceptability of methodologies within the ambit of judgements of taste. Thus we might say that one who rejects the described Newtonian methodology is guilty of poor “epistemic” taste. This exegetical line, one that brings Kant’s thought closer to that of Nelson Goodman and (perhaps) to that of Putnam, is one that obviously requires more extensive working out than can be accomplished here. Kant’s suggestions concerning universalizability of subjective maxims and public consensus are at (KRV, A820-22/B848-850), and at (KU, Sect. 40).Google Scholar
  15. 15.
    A different version of this material appeared in Butts (1986a). I have learned a great deal from the original commentators on the paper, Michael Friedman and Gordon Brittan.Google Scholar
  16. 16.
    That which is fundamental cannot be conceived because it is empirically unconditioned, and Kant insists (MAN, p. 534) that no force laws can be licensed a priori, but must “be concluded from data of experience.”.Google Scholar
  17. 17.
    For details of Kant’s theory of hypotheses in science see Butts (1984, Ch VIII).Google Scholar
  18. 18.
    Kemp Smith’s translation of “Kraft” as “power” in this passage is adequate, because Kant’s examples here are wit, memory, etc (mental “powers”) However, I think Kant would have had some difficulty accepting the English “power” as a good translation of his “Kraft”, partly because it may be taken as suggesting an occult quality. Moreover, Kant had been discussing forces since “True Estimation,” even when “psychical” forces were at issue. And so “Grundkraft” is better rendered “fundamental force”. In MAN, p. 534, Kant writes “Kräfte und Vermögen”, suggesting a distinction between “forces” and “powers.” The passage from KRV should be compared with MAN, p. 534 “Grund,” by the way, is much more expressive of Kant’s meaning than is the feeble English “fundamental.” “Grounding” is the principal function of reason; and a “ground” is a reason. Baumgarten, one of Kant’s sources of philosophical terminology, translates the Latin ratio as Grund (Baumgarten, 1779, p. 5).Google Scholar
  19. 19.
    Several of the authors of papers in Butts (1968b) stress the importance of the idea of the focus imaginarius in Kant’s discussion of methodology in the Appendix to the Transcendental Dialectic. It may be worthwhile, therefore, to point out that Kant’s application of the analogy between the optical and the methodological imaginary focus derives from optical speculations which appear to have fascinated him because of their application to certain epistemological problems. Kant discusses the physiology of vision in (of all places!) Träume (Ak II, pp. 344-48). Kant here presents the focus imaginarius as that point in a visual representation at which the lines of direction from the impressed sensation converge. This is not literally the point of their source. A similar focus imaginarius can be assigned to that point where impressions of sound waves, which travel in straight lines emanating from the oscillating system of nerves in the brain, converge. Kant remarks that similar considerations apply with respect to the other three senses, except that the senses of touch, taste and smell come into direct contact with sensory objects, so that the lines of direction of such sensory stimuli converge in the sense organs themselves. (Much of what Kant says about these optical and physiological matters could easily have been derived from Newton’s Opticks, Book III, Part I Queries 12, 13, 14, 23.) Kant also suggests that there is a technical problem he cannot solve, and which generates an empirically inadequate explanation of the place of sight. The focus imaginarius marks an apparent position of seen nearby objects, and this postulated point agrees with our experience of objects as outside us. However, if we assume, as seems required, that the lines of direction from the visual stimulus must travel to the optic nerve, they can only do so by first being refracted by the humid eyeball, which would put the point of convergence (the imaginary focus) not outside the body, but “on the floor” of the eyeball. The problem, as Kant rightly sees, arises because of the requirement that the sensation take place in a single nerve. This optical problem of insuring that the theory capture the externality of the virtual image is of more than passing interest for Kant. For he concludes that in normal wakeful vision the focus imaginarius is a point outside us where the lines arriving from the oscillating nerve organs of the brain converge. In dreams, however, the focus imaginarius is literally in the brain, a thesis that Kant thinks entails that even when awake the dreamer will be unable to distinguish his dream delusions from real perceptions received from external sources. Furthermore, this conclusion about different points of focus (external to the brain/in the brain) is one Kant goes on to use to distinguish normal perception from mentally deranged perception in the condition he calls “Wahnsinn” (dementia). The spiritualist dreamer (Swedenborg) is therefore in an aberrant physiological state indistinguishable from that form of severe mental derangement that makes it impossible to assign an external place of origin to sensations. An unfocused imagination in this physiological sense is one that violates the conditions of external sensibility. However defective Kant’s understanding of optics, physiology, and related matters may have been, his conclusion about spiritualism in Träume is entirely compatible with the methodology attendant upon the critical philosophy: Responsible method always directs us back to the point of focus that is the phenomenal, the ever-enlarging accumulation of theoretically well-managed (systematically unified) empirical observations. (For more on Kant’s physiological and psychiatric speculations, see Butts, 1984, especially pp. 282-318.).Google Scholar
  20. 20.
    Although, as we have seen, the postulated fundamental forces are themselves the basis for representation of diverse empirical forces as systematically connected. The postulated forces are equivalent to principles of reduction; they are not themselves discoverable realities.Google Scholar
  21. 21.
    I am not denying that Kant held a kind of scientific realism. He did accept, after all, that physics and mathematics yield fully reliable knowledge. This brute factness of science ought not to obscure the decisive fact that Kant provided an idealist reconstruction of this scientific realist base. And that, of course, is one of the reasons why the unconstructibility of fundamental forces was not an issue for him. To deny that Kant is a metaphysical realist about science is also to deny that he thought of the fundamental forces as theoretical constructs, concepts pointing to entities existing beyond the threshold of observation.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Robert E. Butts
    • 1
  1. 1.Department of PhilosophyThe University of Western OntarioCanada

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