A paradox. In Kant’s first Critique the antinomies of pure reason show that contradictory conclusions about the world as a whole can be drawn with equal propriety. Each antinomy has a thesis and a contradictory antithesis.
The first antinomy has as thesis that the world has a beginning in time and is limited in space, and as antithesis that it has no beginning and no limits.
— the second proves both the infinite divisibility of space and the contrary;
— the third shows the necessity, but also the impossibility of human freedom, and
— the fourth proves the existence of a necessary being and the lack of existence of such a being.
The solution to this conflict of reason with itself is that the principles of reasoning used are not ‘constitutive,’ showing us how the world is, but ‘regulative,’ or embodying injunctions about how we are to think of it.
When regulative principles are taken outside their proper sphere of employment, as they are when theorizing about the world as a whole, contradiction results.
Kant’s 4th Antinomy
Thesis: “There belongs to the world, either as its part or as its cause, a being that is absolutely necessary.”
Demea’s a priori proof of God’s existence.
Antithesis: “An absolutely necessary being nowhere exists in the world, nor does it exist outside the world as its cause.”
Cleanthes’s counter-argument.