Kant’s Third Antinomy seems to be about the possibility of freedom. But his arguments apply much more widely; if he had never published anything else, the few pages of the Third Antinomy would have made Kant the most important philosopher since Aristotle.
An “antinomy,” according to Kant, is a pair of propositions which contradict each other, yet can both be proven. According to the Third Antinomy’s thesis, if there is no such thing as freedom, then everything that happens, happens according to causal laws, and so by modification of a previous state of affairs. So any event E must come from a previous event D, and must have done so according to a law of nature. But then that previous event D must have come from a still earlier event C, and so on—to infinity. The number of events which must have already occurred prior to any given event is therefore infinite; but infinity is precisely that which can never be reached in this way. Therefore, at some point, we must accept an event which springs from no prior events—a free act.
According to the antithesis, let us suppose that there are such free acts. Such an act must be produced by the will at a specific time. This means that there must be a change in the will itself, by which it begins to cause that act: in Kant’s parlance, the will must “determine itself to produce the act.” So we have one thing—the will—in two successive states: not-yet-determining itself to produce some given act, and actually determining itself. But these two states cannot be connected to each other by any law, for then the will’s producing of the act would be determined, not free. So the will’s “determination of itself” must be a wholly random change. But such randomness (in addition to being mere spontaneity, not true freedom) would reduce nature to, at bottom, a series of random, disconnected events.
These arguments are not very plausible, either in my short summaries or in Kant’s cumbersome German; whether they can be made plausible is a huge question. But I am after their structure, which is that of a reductio: each side of the contradiction is proved out of the other side. The thesis begins by assuming that no act is free and proves that some must be; the antithesis begins with the view that some acts are free and proves that none can be. P implies not-P, which implies P.
This has metaphysical implications far beyond issues of freedom. For the thesis is Platonic (#11): it argues that if you claim that everything has the principle of its being in a cause other that it, you must eventually, to avoid accepting a completed infinite series of causes, posit something that has no principle of being beyond itself: the free act plays a role akin to that of Plato’s Form of the Good.
Unsurprisingly, the antithesis is Aristotelian (also #11), positing that there are things which, like Aristotelian ousiai, have their principle of being within themselves; in free acts, the moral law plays a role akin to that of Aristotelian immanent forms. But any given form, for Aristotle, comes into its matter at a certain time and place—its beginning is an event, such as the arrival of a seed in a particular patch of soil—and this must be explained by something beyond that thing. But this in turn requires the existence of things like the sun warming the earth, the alternation of night and day, the change of seasons, and other features of the natural order.
And where does the natural order, the kosmos, come from? For Aristotle, it comes from the Prime Mover—pure Form, existing apart from matter. For Kant the natural order is the causal sequence of the entire universe, in which every event is caused by previous events.
Kant has thus revealed, for the first time, the structure of the Metaphysical Barn. He has shown, in about ten pages, how Platonists and Aristotelians have been chasing one another around that barn for 2000 years—and that neither approach provides a way out.