Why does Kant say the conservation of matter is a priori rather than empirical?

Question

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.

Answer 1

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.

Answer 2

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 [...].

Answer 3

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.

Answer 4

Because Kant often identifies necessity with a priority. He thinks ("appears to think" would be perhaps a more fortunate expression; Kant's views on the matter are certainly more subtle) that all necessary principles (laws, etc.) must be a priori - not exactly in the sense that they are discoverable entirely a priori, but that they are "framework principles", constituting what Kuhn would call paradigms.

And Feynmann is correct to accuse some philosophers of a lack of imagination. Many philosophers thought that various scientific discoveries of their age were nonsensical or unintelligible. Usually they weren't great philosophers, though, and short-sightedness isn't a trait exclusive to philosophers. One late-nineteenth-century psychologist thought that imaginary numbers (invented many centuries before) were a product of our mind "going on holiday", to use Wittgenstein's phrase, like "square circles" - and that they aren't and cannot be real (in the ordinary, not in the mathematical, sense).

Kant wasn't one of these philosophers, though. It is known, for example, that he remained interested in the progress that physics and chemistry were making in the last decade of his life.

Answer 5

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).