Early in the Prolegomena, Kant says that both pure mathematics and pure physics are examples of a priori cognition. What exactly did he mean by "pure physics"?

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    What we today call Mathematical physics. May 12, 2023 at 7:28
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    Pure physic consists of propositions which, as Kant puts it, "are commonly treated at the commencement of proper (empirical) physical science". By analogy with mathematics, those come from "pure intuition", synthetic activity of understanding and productive imagination without any empirical input. Since those faculties also process empirical sensations what they produce on their own is supposed to apply universally to all of physics. What Kant identifies as such is a vague version of Newtonian mechanics, including the conservation of matter, the action-reaction law and the law of causality.
    – Conifold
    May 12, 2023 at 8:49
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    Superb! Kant was, as some have pressed upon me, a genius of the highest order. These men ... and women ... are what we've truly lost, oui mes amies? 🥀
    – Hudjefa
    May 12, 2023 at 10:33
  • But the propositions provided by today's mathematical physicists are theoretical and contingent and must be empirically verified. In that sense, they are not a priori propositions. Kant implies that such mathematical conclusions do not need confirmation, that the experimental physicist MUST RELY on the math theory, not confirm it.
    – Gerry
    Jan 18 at 21:06

3 Answers 3


The clue is in the fact that he called it a priori. Pure physics is physics that can be done a priori without relying on experimentation. Here is an example from one of Kant's other works.

All matter is subject to both attracting and repelling forces. If there were no attracting forces between the particles of an object, the object could not hold together. Any disturbance would send the particle all flying off independently. If there were no repelling forces, then the attracting forces would cause all of the particles to converge to a point. Therefore, order for a solid object to exist, the particles of the object must both attract and repel each other.

Note that there is no experimentation here, it's all a priori reasoning.

  • According to Kant intuition is a priori. I'm not sure what you mean by "Hume's theory". Hume claims that our expectation that patterns we have seen in the past will be repeated in the future is wholly unjustified. Kant does not agree with that. May 12, 2023 at 4:20
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    This is a good start but I'd say some clarity is at hand. Maybe I'll have a bit of time later on.
    – Philip Klöcking
    May 12, 2023 at 5:34
  • And... is he not erring right there already by assuming that "all matter is subject to both attracting and repelling forces" a priori? For example, there is no repulsion in the force of gravity. It seems very vague and maybe related to some idea of cosmic balance, but Nature may not comply...
    – Frank
    May 12, 2023 at 15:07
  • @Frank, it's a priori. That means that unless there is an error in the reasoning, you can know it's true without experimenting. Your gravity counter-example isn't a count-example. The claim isn't that every identifiable force both attracts and repels; the claim is that there is an attracting force and a repelling force. May 12, 2023 at 16:53
  • Thank you David. Kant is infamous for being short on examples, this helps a lot. Now would the a priori assertion that there exist repellant and attractive forces be "analytic" or "synthetic"? I ask because there seem to be at least two ways in which Kant uses the term "analytic: 1) in the sense of being true by definition and 2) in the sense of inference or implication. For example, the existence of solid objects in experience implies attractive forces, and separation of said objects in space implies existence of the opposite force.
    – Gerry
    May 13, 2023 at 11:04

Now we are nevertheless actually in possession of a pure natural science, which, a priori and with all of the necessity required for apodictic propositions, propounds laws to which nature is subject. Here I need call to witness only that propaedeutic to the theory of nature which, under the title of universal natural science, precedes all of physics (which is founded on empirical principles). Therein we find mathematics applied to appearances, and also merely discursive principles (from concepts), which make up the philosophical part of pure cognition of nature. (Kant, Prolegomena, §15)

In other words: Pure natural science is the canon of conditions under which the study of nature (as lawful unity) is possible mathematically.

  • +1 I think this bolsters exactly the comments of Mauro above.
    – J D
    Jan 22 at 15:35

You're sure to get a better response from Klocking than this, but one should preface any response by saying that Kant's views are open to interpretation. According to the SEP article on Transcendental Idealism:

In the Critique of Pure Reason Kant argues that space and time are merely formal features of how we perceive objects, not things in themselves that exist independently of us, or properties or relations among them. Objects in space and time are said to be “appearances”, and he argues that we know nothing of substance about the things in themselves of which they are appearances. Kant calls this doctrine (or set of doctrines) “transcendental idealism”, and ever since the publication of the first edition of the Critique of Pure Reason in 1781, Kant’s readers have wondered, and debated, what exactly transcendental idealism is, and have developed quite different interpretations. (my emphasis)

It appears you are quoting:

One need only attend to the various propositions that appear at the beginning of proper (empirical) physics, such as those of the permanence of the same quantity of matter, of inertia, of the equality of action and reaction, and so on, in order to be soon convinced that they constitute a pure (or rational) physics, which well deserves, as a science of its own, to be isolated and established in its entire extent, be it narrow or wide. (my emphasis)

According the SEP article on Kant and Hume:

[Kant believed] empirical laws owe their status as “necessary and universally valid” to their relationship with the a priori “pure or universal” laws (principles) of the understanding. (my emphasis)

According to this article on Kant and Science, one interpretation of Kant's views on the sciences, and in particular physics is:

At the top of the hierarchy is physics, which is both proper and rational. Physics, McNulty explains, is rational for Kant because it has laws, and proper because these laws are necessary and can be derived independently of experience. Kant holds that the laws of motion, for example, are derivable from the essential, conceptual nature of matter. We do not, then, infer through observation that matter is subject to Newton’s laws of motion so much as come to realize that matter must be subject to such laws in order to be observed at all. (my emphasis)

Thus, pure physics is the physics that serves as a metaphysical basis for empirical observation. According to WP's article on Kant's use of the term a priori:

Space, time and causality are considered pure a priori intuitions. Kant reasoned that the pure a priori intuitions are established via his transcendental aesthetic and transcendental logic. He claimed that the human subject would not have the kind of experience that it has were these a priori forms not in some way constitutive of him as a human subject. (my emphasis)

Thus, the intuitions of physics, the 'pure physics', particularly the physics of Newton which are known through logic and mathematics, come prior to empirical experience as Hume advocated, and we come to know the universal laws of physics through the a priori (as reformulated by Kant) intuitions about physics that are perceived by the mind.

  • So JD, are you saying that an example of an a priori, or "pure," statement of physics would be Newton's law that an object at rest is still or moving at a constant velocity?
    – Gerry
    May 13, 2023 at 11:18
  • Okay, with the caveat that I'm not a Kant scholar, and even his English translations are dense reading for me (i.e., I profess no authority whatsoever), my interpretation is that pure physics is the a priori intuitions that arise from the basics of experience of the forms of times and space that can be made as modal statements, and so, wherein Newton can express a Law of Nature, according to Kant, he is expressing pure physics as conditions of possibility.
    – J D
    May 13, 2023 at 14:30
  • So, on my reading, Netwon's laws are not a paradigm of pure physics, but the CULMINATION of pure physics which is more about the intuition that give way to logic. My belief is that pure physics once equations and measurements begin to be bandied about transitions into a special logic that appeals to physics-specific principles.
    – J D
    May 13, 2023 at 14:39
  • But beyond that, I'm ill-equipped to argue the point, sorry.
    – J D
    May 13, 2023 at 14:40
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    S'okay. My fault. I should have included the quote in the first place instead of the paraphrase. What you say makes sense, it's just difficult for me to grok given the science age in which we live. I can't help but think about Parmenides in the Socratic dialogue who essentially does attempt something like pure physics, not necessarily with good results.
    – Gerry
    May 19, 2023 at 22:16

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