In the Critique of Pure Reason Kant writes that conservation of matter is a priori synthetic:

Natural science (physics) contains a priori synthetic judgments as principles. I need cite only two such judgments: that in all changes of the material world the quantity of matter remains unchanged; and that in all communication of motion, action and reaction must always be equal. Both propositions, it is evident, are not only necessary, and therefore in their origin a priori, but also synthetic. For in the concept of matter I do not think its permanence, but only its presence in the space which it occupies. I go outside and beyond the concept of matter, joining to it a priori in thought something which I have not thought in it. The proposition is not, therefore, analytic, but synthetic, and yet is thought a priori and so likewise are the other propositions of the pure part of natural science (CPR B17ff).

Why does Kant consider such principles as a priori rather than empirical?

There is a beautiful passage in Feynman's Lectures where he argues why all kinds of principles which philosophers believe are necessary (that is, a priori), are actually empirical; in the passage he argues about the principle of relativity:

There is another school of philosophers who feel very uncomfortable about the theory of relativity, which asserts that we cannot determine our absolute velocity without looking at something outside, and who would say, “It is obvious that one cannot measure his velocity without looking outside. It is self-evident that it is meaningless to talk about the velocity of a thing without looking outside; the physicists are rather stupid for having thought otherwise, but it has just dawned on them that this is the case. If only we philosophers had realized what the problems were that the physicists had, we could have decided immediately by brainwork that it is impossible to tell how fast one is moving without looking outside, and we could have made an enormous contribution to physics.” These philosophers are always with us, struggling in the periphery to try to tell us something, but they never really understand the subtleties and depths of the problem.

Our inability to detect absolute motion is a result of experiment and not a result of plain thought, as we can easily illustrate. In the first place, Newton believed that it was true that one could not tell how fast he is going if he is moving with uniform velocity in a straight line. In fact, Newton first stated the principle of relativity, and one quotation made in the last chapter was a statement of Newton’s. Why then did the philosophers not make all this fuss about “all is relative,” or whatever, in Newton’s time? Because it was not until Maxwell’s theory of electrodynamics was developed that there were physical laws that suggested that one could measure his velocity without looking outside; soon it was found experimentally that one could not.

Now, is it absolutely, definitely, philosophically necessary that one should not be able to tell how fast he is moving without looking outside? One of the consequences of relativity was the development of a philosophy which said, “You can only define what you can measure! Since it is self-evident that one cannot measure a velocity without seeing what he is measuring it relative to, therefore it is clear that there is no meaning to absolute velocity. The physicists should have realized that they can talk only about what they can measure.” But that is the whole problem: whether or not one can define absolute velocity is the same as the problem of whether or not one can detect in an experiment, without looking outside, whether he is moving. In other words, whether or not a thing is measurable is not something to be decided a priori by thought alone, but something that can be decided only by experiment. Given the fact that the velocity of light is 186,000 mi/sec, one will find few philosophers who will calmly state that it is self-evident that if light goes 186,000 mi/sec inside a car, and the car is going 100,000 mi/sec, that the light also goes 186,000 mi/sec past an observer on the ground. That is a shocking fact to them; the very ones who claim it is obvious find, when you give them a specific fact, that it is not obvious.

Finally, there is even a philosophy which says that one cannot detect any motion except by looking outside. It is simply not true in physics. True, one cannot perceive a uniform motion in a straight line, but if the whole room were rotating we would certainly know it, for everybody would be thrown to the wall—there would be all kinds of “centrifugal” effects. That the earth is turning on its axis can be determined without looking at the stars, by means of the so-called Foucault pendulum, for example. Therefore it is not true that “all is relative”; it is only uniform velocity that cannot be detected without looking outside. Uniform rotation about a fixed axis can be. When this is told to a philosopher, he is very upset that he did not really understand it, because to him it seems impossible that one should be able to determine rotation about an axis without looking outside. If the philosopher is good enough, after some time he may come back and say, “I understand. We really do not have such a thing as absolute rotation; we are really rotating relative to the stars, you see. And so some influence exerted by the stars on the object must cause the centrifugal force.”

Now, for all we know, that is true; we have no way, at the present time, of telling whether there would have been centrifugal force if there were no stars and nebulae around. We have not been able to do the experiment of removing all the nebulae and then measuring our rotation, so we simply do not know. We must admit that the philosopher may be right. He comes back, therefore, in delight and says, “It is absolutely necessary that the world ultimately turn out to be this way: absolute rotation means nothing; it is only relative to the nebulae.” Then we say to him, “Now, my friend, is it or is it not obvious that uniform velocity in a straight line, relative to the nebulae should produce no effects inside a car?” Now that the motion is no longer absolute, but is a motion relative to the nebulae, it becomes a mysterious question, and a question that can be answered only by experiment.

  • I think there's an interesting question here, but right now it's mostly two quotes stapled together. Do you see Feynman as raising the objection to Kant's view in its best (or a good) form?
    – virmaior
    Oct 9, 2015 at 8:17
  • I see Feynman as raising an objection to claims such as that particular claim of Kant; but I am not sure how far such an objection can be applied (for example, I personally cannot conceive a timeless world), and I am not sure why Kant made that particular claim about conservation of matter; was he just wrong or do I misunderstand him? how do Kantian scholars explain this?
    – nir
    Oct 9, 2015 at 8:30
  • 2
    I think you (and Faynman) misunderstand (like most people do) the notion of a priori: Kant was (in some aspects) Humean, he agreed that every empirical judgement is in fact inductive and therefore not necessary (in the strict, logical sense). Necessity like the one thought in "a priori" is always between concepts. But this does not mean that these concepts and their relation could ever be thought without intuition. And intuition needs empirical input. A priori is abstract, between concepts, that must be "feeded" by concrete perceptions.
    – Philip Klöcking
    Oct 9, 2015 at 9:41
  • @Philip Klöcking Until now I thought a priori means before and hence without experience. What do you mean in your last sentence by concepts, that must be "feeded" by concrete perceptions? And which role do you ascribe to the term intuition in Kant's epistemology? References to CPR would be helpful. Thank you in advance.
    – Jo Wehler
    Oct 9, 2015 at 9:52
  • @JoWehler: The central piece of text could be "Thoughts without content are empty, intuitions without concepts are blind." (A51|B75), (taken from Wikipedia about Kant), but this is a bad translation. In the original, it is more like "Intuitions (Anschauungen) without concepts (Begriffe) are empty, concepts without intuitions are blind." Taking this seriously, we cannot even think anything (this needs Begriffe) without Anschauung (and they need sensual input, as they are the manifold under concepts)...a priori therefore should be understood as before in a logical sense, a necessary condition
    – Philip Klöcking
    Oct 9, 2015 at 10:11

4 Answers 4


The Copernican Shift of Kants philosophy actually was, in reference to Hume, that not the empirical facts themselves are true knowledge (episteme, "Erkenntnis"), because they are arbitrary; they depend on our ability to percept at all and our factual experiences.

True knowledge lies in transcendental knowledge: What we can get necessary knowledge of are the necessary conditions of our experience. As necessary conditions they lie in every experience possible to humans. In this sense they are a priori. Every knowledge a priori is transcendental and therefore necessary (in a strict sense).

For a reference and some argument on this, see the comments of the question and this answer.

Transferred to the quotes in the question: Kant would say that the conservation of matter isn't anything we can actually experience: We can measure in several moments and therefore infer this as necessary in form of a condition of what we experience. But in a strict sense, we do not experience this itself, we think it as necessary, which includes a further judgement of reason.

To add a general note: Nature = the sum of all experience. Laws of nature are the regularities in experience (Hume) thought as necessary. We do not experience this necessity, we think it. The necessity is of the rule for the relation expressed by the law, not for the truth or validity of the law itself. Therefore it is no problem for the necessity that laws of nature are falsifiable.

  • What do you think: Was Kant wrong when claiming that conservation of matter is an a priori knowledge? E.g. we know that particle and antipartice annihilate to pure energy. Of course Kant could not know about these features of matter and the insight E = m * c**2. But should we conclude, that conservation of matter cannot be knowledge a priori?
    – Jo Wehler
    Oct 9, 2015 at 10:56
  • I think it actually shows the problems of the whole concept of knowledge a priori: It is in the end based on experience. And things one cannot conceive cannot be considered. Kant couldn't possibly conceive what we think now to be true, therefore he would, today, say it is conservation of energy what is knowledge a priori. And perhaps, as it is equated, it doesn't even matter.
    – Philip Klöcking
    Oct 9, 2015 at 11:28
  • do you mean that for Kant something can be necessary and false at the same time?
    – nir
    Oct 9, 2015 at 11:40
  • necessary only considering all that we know, therefore falsiable. If there were good reasons to consider something as false, it can in no sense be necessary anymore
    – Philip Klöcking
    Oct 9, 2015 at 11:44
  • @Philip Klöcking Stating that the concept of knowledge a priori in the end is based on experience seems to me to seal the fate of the idea of knowledge a priori.
    – Jo Wehler
    Oct 9, 2015 at 12:12

The philosophy of science is always a tricky battle between empiricism and a priori beliefs. Consider an example case:

You observe 10 women. All of them have long hair. You make the statement "All women have long hair."

In such a case, we can see how easy it is to err with empiricism. Just because 100% of samples show a behavior doesn't mean that every entity shows that behavior. It looks a bit silly with 10, lets make the experiment more powerful

You observe 10,000,000 women. All of them have long hair. You make the statement "All women have long hair."

Is this an a priori statement, or an empirical one?

I believe Kant is arguing that, unless you can prove that you have observed every woman in the universe, you cannot make any empirical statement about "all women," because you simply cannot know. You must make an a priori claim because you are assuming truth about "all women" without actually observing them. Meanwhile, Feynman is arguing that no philosopher makes an a priori statement of truth without some empirical evidence to back up their claim. It may be faint, but some how the philosopher's experience works its way into the choice to make a declaration.

Which point of view you agree with depends mostly on which direction you want to take the topic. If you find that empiricism is overstepping its bounds, making claims about things it should not claim, you may side with Kant, arguing such claims are a priori. If you find that philosophers are making things up that do not match with the world view your experiences are developing, you may side with Feynman, arguing that experience is essential in any such claim.


Kant deals with the statement in Chapter 3 (= 3. Hauptstück) Metaphysical Foundations of Mechanics, Proposition 2 of his Metaphysical Foundations of Natural Science. This passage presupposes the principle of conservation of substance. Kant calls this principle a theorem from General Metaphysics.

So what Kant really does in his Metaphysical Foundations of Natural Science, is no more than to specialize a general principle about substance to a special principle about matter.

It is interesting that Kant here simply refers to the philosophical tradition and quotes one of the fundamental metaphysical principles. He makes no attempt to argue why conservation of substance is a valid principle. Neither does he give any argument why the abstract, and at best qualitative concept of substance equates with the quantitative concept of matter. Did Kant consider it not necessary?

As @Conifold comments, one year later in the first analogy (Critique of Pure Reason B224f) Kant makes up for a proof of the metaphysical principle of conservation of substance. He uses the equation

Now, the substratum of all that is real, that is, of all that belongs to the existence of things, is substance [...].

  • Unfortunately it is true of substance and false of matter, since matter can become energy.
    – user9166
    Oct 9, 2015 at 19:37
  • @jobermark I cannot grasp the meaning of a statement about conservation of substance. How do I measure the quantum of substance which should be conserved? What could an increase or decrease of substance mean? - Concerning conservation of matter please have a look at the discussion subsequent to the answer of Philip Klöcking.
    – Jo Wehler
    Oct 9, 2015 at 19:54
  • But matter does not vanish, it is converted into "energy," a term which establishes a measurable, mathematical continuum between the two. This in itself would not be a bad defintion of "substance," that very underlying relation which is conserved between the two. Feynman uses a nice story to describe "energy" using a set of children's blocks. When we see some missing, we know they will be found somewhere, and we know how many will be found. Whether Feynman likes it or not, this is not far from metaphysical "substance," which in Kant's case becomes active or "subject." Oct 10, 2015 at 18:11
  • The first analogy in the Critique is the deduction of the conservation of substance, which is one of the a priori categories, an unchangeable substrate that is necessary to contextualize change in a unified account of experience. Matter for Kant is an empirical concept, and identification of substance with matter is an empirical judgement. Kant could not know about E=mc2 but in light of it his substance now should be identified with energy, not matter. There is another empirical premise to all deductions of the Critique, that knowledge with certainty is possible.
    – Conifold
    Oct 10, 2015 at 19:59
  • For the first analogy see here philarete.s3-website-us-east-1.amazonaws.com/kant.html A very good source on Kant's a priori arguments and their relation to science is Friedman's Kant and Exact Sciences. We may today reject his premise that unified account of experience (knowledge) is possible, but his analysis of the logical structure of Newtonian mechanics based on them is quite penetrating. In particular, like Einstein he rejects absolute space and insists on physical identification of reference frames, and points to the link between 3D space and the inverse square law.
    – Conifold
    Oct 10, 2015 at 20:07

Why does Kant consider such principles as a priori rather than empirical?

The short answer is that he doesn't: he says that they are synthetic a priori; that is they are both (synthetic meaning being derived from experience is related quite closely to the notion of the empirical).

To be fair, he admits the difficulty of positing both - he asks:

how are synthetic a priori propositions possible

Before going into demonstrating how this is in fact possible (one might then accept its possibility and intelligibility without then proceeding to its neccessity).

I'm not sure Feynman for all his deserved fame as a physicist should be taken as an authority on the history of physics, never mind that of philosophy or the interaction of the two; he did once point out I recall reading somewhere in one of his popular accounts that atomism was the pre-eminent idea of modern physics having not realising its actual origins in antiquity, and also how both argument and observation were marshalled to make the case.

The passage quoted by him rather looks like using philosophy as a straw-man - after all he mentions no-one by name, but a generic armchair philosopher; it's rather like Galileos Dialogue on two world systems where he pits two philosophers against each other, and the philosopher he chooses to present the weaker argument he calls simplicio ie simple-minded (in Italian semplice).

  • 1
    Nicely put at the beginning, that's something I wanted to express in the comments above but weren't able to grasp as I am deeper into the later text at the moment, and far from deep into English expressions of it ;)
    – Philip Klöcking
    Oct 15, 2015 at 16:38
  • I think that the part of your answer about Feynman should be removed, since it seems like an ad hominem attack against him, instead of his argument; I think that his argument is actually philosophical and a good one at that; in fact his lectures are full with such beautiful philosophical insights and arguments.
    – nir
    Oct 16, 2015 at 5:44
  • Can you explain in what way being synthetic a priori is closely related to being empirical? it seems to me that Kant presents these two ideas as polar opposites; for example in B3, and also in "But in a priori synthetic judgments this help is entirely lacking. [I do not here have the advantage of looking around in the field of experience.]" (B13)
    – nir
    Oct 16, 2015 at 6:15
  • I am sure that a philosophical argument against Feynman's argument can be made, and if you have one, please share it; but claiming that he is no authority in matters of philosophy does not count as such an argument; Kant begins the Critique by writing that "there can be no doubt that all our knowledge begins with experience." in what sense does your answer go beyond that statement to explain my question?
    – nir
    Oct 16, 2015 at 8:43
  • Feynman's thought experiment invites his readers into a trap, to shake them off the natural belief that the principle of relativity is (synthetic) a priori, and to generally stress the scope of the scientific method; you can think of his sarcastic opinion of philosophers as a purposeful distraction, as magician waving his hands; it is not the philosophers who are his victims, but the reader. if you believe his argument is missing the subtleties of philosophy, please explain in what way.
    – nir
    Oct 16, 2015 at 11:06

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