The categories which are of importance in Kant's argument are quantity, quality, substance, causation, and reciprocity, and necessity, possibility, and actuality. The last three are less important than the others, and we shall not deal with them.
To the first five of these categories correspond the following principles:
(1) Quantity. "All phenomena are, with reference to their perception, extensive quantities."
(2) Quality. "In all phenomena the real, which is the object of a sensation, has intensive quantity, that is, a degree."
The last three are classed under a general heading of Analogies of Experience, whose principle is: "Experience is possible only through the representation of a necessary connection of perceptions." They are
(3) The principle of the permanence of substance. "In all changes of phenomena the substance is permanent, and its quantum is neither increased nor diminished in nature."
(4) Principle of the succession of time, according to the Law of Causality. "All changes take place according to the law of connection between cause and effect."
(5) Principle of co-existence, according to the law of reciprocity or community. "All substances, so far as they can be perceived as co-existent in space, are always affecting each other reciprocally."
These principles, Kant points out, are assumed in the sciences of applied mathematics. The application of geometry to the world we experience assumes that all phenomena are extensive quantities; physics assumes that quantitative expression can be given to the qualities of objects other than their size, their weight, e.g., and all scientific determination of change assumes the three principles which Kant calls analogies of experience: the permanence or conservation of amount in changes, the necessary connection of things in time, and the reciprocal interdependence of things which exist at the same time. These principles are not proved by science; their validity is assumed in all scientific investigation. On what, then, does it rest?
We shall follow Kant's argument more easily if we take his account of one of these principles--the principle of causation. For what is said of that will hold, with necessary changes, of the others, and, as we have noticed, it was Hume's criticism of causation which first led Kant to formulate the critical problem. Hume had pointed out that we had never such insight into causal connection as to be able, from mere inspection of a cause, to foretell the effect without any reference to experience. He declared, on the contrary, that there was no difference between observed succession and causation so far as concerned the objects observed. In each case we see first one thing and then another. The difference, then, between mere succession and causal connection can only be in us, in the way we come to feel about certain successions we observe. In technical language, the necessity of causation is subjective.