According to the Encyclopedia Britannica article on Immanuel Kant, in the section discussing the Critique of pure reason:

In the Transcendental Analytic, the most crucial as well as the most difficult part of the book, he maintained that physics is a priori and synthetic because in its ordering of experience it uses concepts of a special sort. These concepts—“categories,” he called them—are not so much read out of experience as read into it and, hence, are a priori, or pure, as opposed to empirical. But they differ from empirical concepts in something more than their origin: their whole role in knowledge is different. For, whereas empirical concepts serve to correlate particular experiences and so to bring out in a detailed way how experience is ordered, the categories have the function of prescribing the general form that this detailed order must take. They belong, as it were, to the very framework of knowledge. But although they are indispensable for objective knowledge, the sole knowledge that the categories can yield is of objects of possible experience; they yield valid and real knowledge only when they are ordering what is given through sense in space and time.

This view that physics provides the general form of this detailed order seems to be incorrect because physics is now done differently. Before, physics was the development of equations to predict events (classical mechanics). Now, physics is the development of equations to determine probabilities of events (quantum mechanics). Furthermore, spacetime is no longer considered static. So how can physics be a priori then?


Neo-Kantian philosophers, wishing to take into account that physics and mathematics had undergone deep changes in the decades after Kant, proposed a historicized a priori. Fundamental principles frame what we take to be our experience, but these principles are subject to change. Ernst Cassirer's Determinism and Indeterminism in Modern Physics is an important example of such work, which takes up the challenge presented by quantum mechanics.

For current accounts of such a historicized a priori, take a look at Michael Friedman's work, such as The Dynamics of Reason, and his contribution to Discourse on a New Method.

  • Hi David. I feel inclined to highlight that implicit in the reply that I gave (hidden behind the last link) is the claim that even if nobody thought about it beforehand, the analysis following Lawvere (with "categories of thought" formalized as actual (co-)reflective subcategories of the ambient topos) shows that quantum mechanics is as a priori as Riemannian geometry is, both having natural and elegant formalizations in terms of such axiomatics. That at least is the claim of "Quantization via Cohesive homotopy types" ncatlab.org/schreiber/show/… – Urs Schreiber Mar 4 '15 at 9:49

There is a remarkable proposal by William Lawvere, for connecting transcendental philosophy and theoretical physics. Lawvere proposes that the categories in the version in which Hegel presents them in the Science of Logic are faithfully and usefully formalized in categorical logic (a mathematical term! which happens to fit well the use in philosophy) as systems of (co)-reflective subcategories (in the mathematical sense! of category theory) of some ambient topos.

The resulting structure Lawvere called a cohesive topos (following Hegel's discussion of "cohesion" in the Philosophy of Nature), and he indicates how such "gros toposes" may serve as Toposes of laws of motion for physics.

It is possible to refine this a little more to arrive at a concept of cohesive infinity-toposes. In a book-in-progress titled Differential cohomology in a cohesive infinity-topos (web, pdf) I claim to work out how a considerable chunk of modern physics naturally finds its formalization in terms of such categories, see in particular the introductory section 1.2 on Classical field theory via Cohesive homotopy types (web, pdf).

See here for pointers to Lawvere's proposal for formalizing idealistic philosophy in terms of categorical logic.

See here for pointers to Lawvere's work on building a foundation of (classical continuum) physics based on this.

See here for details on how the mathematical formalization of "the categories" according to Hegel's Science of Logic proceeds.

For more background and survey see also the beginning of my lecture slides on Synthetic Quantum Field Theory.

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    But notably and you're eliding this, Kant's categories are not Hegel's categories. (Though we might be able to say Hegel's categories are Kant's categories) – virmaior Mar 4 '15 at 10:08
  • That's true, I am following here Hegel in thinking that "his" categories are the proper way to look at Kant's categories. – Urs Schreiber Mar 4 '15 at 14:24

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