Kant's antinomies

Immanuel Kant's Antinomies, from the Critique of Pure Reason, are contradictions which he believed follow necessarily from our attempts to conceive the nature of transcendent reality.

Kant thought that certain of his Antinomies (God and Freedom) could be resolved as "Postulates of Practical Reason". He used them to describe the equally rational-but-contradictory results of applying the universe of pure thought to the categories or criteria, i.e. applying 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.

These antinomies are four: two "mathematical" and two "dynamical". They are connected with (1) the limitation of the universe in respect of space and time, (2) the theory that the whole consists of indivisible atoms (whereas, in fact, none such exist), (3) the problem of free will in relation to universal causality, and (4) the existence of a necessary being.

The first two antinomies are dubbed "mathematical" antinomies, presumably because in each case we are concerned with the relation between what are alleged to be sensible objects (either the world itself, or objects in it) and space and time. The second two are dubbed "dynamical" antinomies, presumably because the proponents of the thesis are not committing themselves solely to claims about spatio-temporal objects.

Geoff Goddu (https://facultystaff.richmond.edu/~ggoddu/Modern/272h-k1.html) offers this version:

4th Antinomy: Thesis: A necessary being is either part of or cause of the world.

Proof: 1. The sensible world contains a series of alterations. 2. Every alteration requires a condition without which that alteration would not be possible. 3. Every condition presupposes a complete series of conditions up to the unconditioned which is itself, absolutely necessary. 4. A necessary being is part or cause of the world.

4th Antinomy: Antithesis: A necessary being is not (a) part of the world or (b) cause of the world.

Proof (a): 1. If a necessary being is part of the world, then either the beginning of the series of alterations is absolutely necessary or the series has no beginning and the whole series is absolutely necessary. 2. The series of alterations can have no beginning. 3. The whole series of alterations cannot be absolutely necessary. 4. A necessary being is not part of the world.

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