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.
