The term acquired a special significance in the philosophy of Immanuel Kant (1724-1804), who used it to describe the equally rational but contradictory results of applying to the universe of pure thought the categories or criteria of reason proper to the universe of sensible perception or experience (phenomena). Empirical reason cannot here play the role of establishing rational truths because it goes beyond possible experience and is applied to the sphere of that which transcends it.
For Kant there are four antinomies connected with
- the limitation of the universe in respect of space and time,
- the theory that the whole consists of indivisible atoms (whereas, in fact, none such exist),
- the problem of free will in relation to universal causality
- the existence of a necessary being
about each of which a thesis contradicts an antithesis. For example: in the First Antinomy, Kant proves the thesis that time must have a beginning by showing that if time had no beginning, then an infinity would have elapsed up until the present moment. This is a manifest contradiction because infinity cannot, by definition, be completed by "successive synthesis" -- yet just such a finalizing synthesis would be required by the view that time is infinite; so the thesis is proven. Then he proves the antithesis, that time has no beginning, by showing that if time had a beginning, then there must have been "empty time" out of which time arose. This is incoherent (for Kant) for the following reason. Since, necessarily, no time elapses in this pretemporal void, then there could be no alteration, and therefore nothing (including time) would ever come to be: so the antithesis is proven. Reason makes equal claim to each proof, since they are both correct, so the question of the limits of time must be regarded as meaningless.
This was part of Kant's critical program of determining limits to science and philosophical inquiry. These contradictions are inherent in reason when it is applied to the world as it is in itself, independently of our perceptions of it (this has to do with the distinction between phenomena and noumena). Kant's goal in his critical philosophy was to identify what claims we are and are not justified in making, and the antinomies are a particularly illustrative example of his larger project.