Antinomies of pure reason
The middle chapter of the Transcendental Dialectic in critique-of-pure-reason. immanuel-kant sets four pairs of opposed claims about the world as a whole and argues that reason can prove each side with equal force. Written from the English Wikipedia article on the book, a T2 tertiary source; the Gutenberg text this wiki holds was not read this far.
The four pairs
- Beginning. Thesis: the world has a beginning in time and a limit in space. Antithesis: it is infinite.
- Simplicity. Thesis: everything consists of simple elements. Antithesis: there is no simple thing, everything is composite.
- Freedom. Thesis: there are causes through freedom in the world. Antithesis: there is no freedom, all is nature.
- Necessary being. Thesis: among the world's causes is some necessary being. Antithesis: everything in the series is contingent.
What Kant does with them
The resolution turns on the thing-in-itself split. In pairs one and two both sides are false, because they treat the world as a completed thing rather than as appearances. In pairs three and four both may be true, the thesis holding for things in themselves and the antithesis for appearances. That is how the third pair leaves room for freedom alongside natural causation.
Wikipedia adds a historical reading: rationalism developed by defending the theses and empiricism by strengthening the antitheses, so the Antinomy stages the rationalism/empiricism quarrel (rationalism, empiricism) as something reason does to itself. That is Wikipedia's framing and I have not seen Kant state it this way here.
Related
critique-of-pure-reason · immanuel-kant · thing-in-itself · categories-of-understanding