(this is not Kant's illustration). Similarly, since you always wear spatial spectacles in your mind,
you are sure of always seeing everything in space. Thus geometry is a priori in the sense that it
must be true of everything experienced, but we have no reason to suppose that anything analogous
is true of things in themselves, which we do not experience.
Space and time, Kant says, are not concepts; they are forms of "intuition." (The German word is
"Anschauung," which means literally "looking at" or "view." The word "intuition," though the
accepted translation is not altogether a satisfactory one.) There are also, however, a priori
concepts; these are the twelve "categories," which Kant derives from the forms of the syllogism.
The twelve categories are divided into four sets of three: (1) of quantity: unity, plurality, totality;
(2) of quality: reality, negation, limitation; (3) of relation: substance-and-accident, cause-and-
effect, reciprocity; (4) of modality: possibility, existence, necessity. These are subjective in the
same sense in which space and time are--that is to say, our mental constitution is such that they
are applicable to whatever we experience, but there is no reason to suppose them applicable to
things in themselves. As regards cause, however, there is an inconsistency, for things in
themselves are regarded by Kant as causes of sensations, and free volitions are held by him to be
causes of occurrences in space and time. This inconsistency is not an accidental oversight; it is an
essential part of his system.
A large part of The Critique of Pure Reason is occupied in showing the fallacies that arise from
applying space and time or the categories to things that are not experienced. When this is done, so
Kant maintains, we find ourselves troubled by "antinomies"--that is to say, by mutually
contradictory propositions each of which can apparently be proved. Kant gives four such
antinomies, each consisting of thesis and antithesis.
In the first, the thesis says: "The world has a beginning in time, and is also limited as regards
space." The antithesis says: "The world has no beginning in time, and no limits in space; it is
infinite as regards both time and space."
The second antinomy proves that every composite substance both is, and is not, made up of simple
parts.
The thesis of the third antinomy maintains that there are two kinds