Kant's Antinomies of Pure Reason

Philosophy 272: Handout K1

1st Antinomy: Thesis: The world is limited with regard to (a) time and (b) space.

Proof (a):

1. If the world has no beginning, then for any time t an infinite series of successive states of things has been synthesized by t.
2. An infinite series cannot be completed through successive synthesis.
3. The world has a beginning (is limited in time).

Proof (b):

1. If the world has no spatial limitations, then the successive synthesis of the parts of an infinite world must be successively synthesized to completion.
2. The parts of an infinite world cannot be successively synthesized to completion.
3. The world is limited with regard to space.

Antithesis: The world is unlimited with regard to (a) time and (b) space.

Proof (a):

1. If the world has a beginning, then the world was preceded by a time in which the world does not exist, i.e. an empty time.
2. If time were empty, there would be no sufficient reason for the world.
3. Anything that begins or comes to be has a sufficient reason.
4. The world has no beginning.

Proof (b)

1. If the world is spatially limited, then it is located in an infinite space.
2. If the world is located in an infinite space, then it is related to space.
3. The world cannot be related to a non-object such as space.
4. The world is not spatially limited.

2nd Antinomy: Thesis: Every composite substance in the world is made up of simples.

Proof:

1. If composite substances are not composed of simple parts, then if we imagine the absence of composition, nothing remains, i.e. no substance is given.
2. Either we cannot imagine the absence of composition or composite substances are composed of simple parts.
3. If we cannot imagine the absence of composition in composite substances, then the composites would not be substances.
4. Every composite substance is made up of simples.

Antithesis: No composite substance in the world is made up of simples.

Proof:

1. If a composite is made of simples, then all simples in composites occupy space.
2. Every object that occupies space contains in itself a manifold of constituents and so is composite.
3. No composite is made of simples.

3rd Antinomy: Thesis: There is freedom in the world.

Proof:

1. If there were no freedom in the world, then each state would presuppose a previous state upon which it follows according to the laws of nature.
2. If each state presupposes a previous state, then there is no absolute, but only a relative, beginning.
3. If there is only a relative beginning, then there is no sufficient cause for any event.
4. Nothing happens without a sufficient cause.
5. There is freedom in the world.

Antithesis: There is no freedom in the world.

Proof:

1. If there were freedom, then some state of a free cause would itself have no causal antecedent.
2. If some state of a cause has no causal antecedent, then it has no sufficient cause.
3. Nothing happens without a sufficient cause.
4. There is no freedom in the world.

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.

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.

Proof (b):

1. If a necessary being is cause of the world then it exists outside the world.
2. If a necessary being is a cause of the world, then it is in time and so not outside the world.
3. A necessary being is not cause of the world.