Has anybody updated Kant's antinomies in view of modern physics?

In The Critique of Pure Reason (1781) he laid out the Antinomies of Pure Reason highlighting contradictions in the ideas of time and space.

Are they still valid, or how might they be updated, for example in view of Big Bang theory, relativity or quantum mechanics?

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.

The Stanford Encyclopedia comments, in 4.1 The Mathematical Antinomies:-

we may want to know, as in the first antinomy, whether the world is finite or infinite. We can seek to show that it is finite by demonstrating the impossibility of its infinitude. Alternatively, we may demonstrate the infinitude of the world by showing that it is impossible that it is finite. This is exactly what the thesis and antithesis arguments purport to do, respectively. ...

The world is, for Kant, neither finite nor infinite.

My interest here is to find out if there are still antinomies when modern ideas are applied.

PS. This question got closed on StackExchange physics because apparently it's about philosophy. It's really just about contradictions in physics.

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    Most of KrV is quite outdated now in the sense here discussed, just because Kant assumes (already in the Aesthetic) a pre-Einsteinian view of time (which doesn't mean it's a common-sensical view of time, it's just informed by XVIII-th century physics). Not really a big deal. Probably similar antinomies can be found elsewhere. The purpose of the discussion is to explain how traditional metaphysical issues arise from "recursively" applying categories from the Analytic, which have sound use within natural science etc. But obviously modern natural science uses different categories. Mar 24 at 13:54
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    I will try to give a more elaborate answer later. Kant's formulation of Antinomies draws quite a lot on terminology borrowed from Leibnizian-Wolffian mathematics, logic and metaphysics. Mar 24 at 13:56
  • In Heisenberg's intellectual autobiography The Part and the Whole, one chapter is devoted to a discussion with the neo-Kantian philosopher of the new approach and results of modern physics. It is well worth having a read. Mar 24 at 21:42

3 Answers 3


You can find some discussions of these ideas in popular books on cosmology, including

  • whether a sentence like "before the Big Bang" makes sense given our current understanding of time (maybe)

  • whether the closed spacetime manifold of a hypothetical finite universe must be embedded in some higher-dimensional space (it need not)

  • whether a hypothetical infinite spacetime, flat or curved, is consistent with observational evidence in the context of general relativity (both are, but flat is strongly favored)

Long after Kant, we discovered that information transfer has a finite speed. Observationally, then, we can only say that the universe is large enough that we cannot see evidence that it's finite: if we look far enough away, we see the universe as it was very early in its finite temporal lifetime, when it was hot and featureless. The best explanation for the featurelessness of the cosmic microwave background, "inflation," suggests that any finite size of the universe must be very much larger than we can currently see — and, because the expansion is speeding up, larger than any observer like us will ever be able to see.

I have not found much explicit mention of Kant in the physics or cosmology literature, even where the questions you raise here are discussed.

  • An important context for Kant's theory of time is the Clarke-Leibniz debate concerning these issues. One argument that Leibniz gives is that under absolute, homogeneous space it is unintelligible that God created the universe on a given day if we accept the Principle of Sufficient Reason and the Principle of Identity of Indiscernibles. I think modern theories would be closer to Leibniz in this regard and because Kant wanted to create a theory that is compatible with both Leibniz's insights and Newton's physics we find ourselves in disagreement with Kant [1/2] Mar 24 at 14:21
  • ...as we don't have to make the changes to Leibniz's theories that Kant found necessary to make them compatible with Newtonian physics (without relapsing to Newtonian absolute space). [2/2] Mar 24 at 14:22
  • @rob Cool answer +1. Kant's elegance is in making simple proofs for opposing cases. It's tricky now when the physics gets so esoteric. But I suppose even simple wave-particle dualism is such a case, in which the contradiction or indeterminacy is evident, but seems to be more accepted now we're used to the formulation. Mar 24 at 15:19
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    @ChrisDegnen Wave-particle duality becomes less of a philosophical issue as your understanding of quantum phenomena becomes more sophisticated — as the understanding across the entire literature has become over the past century, with substantial progress just in the past few decades. At least part of the problem is that the quantum mechanics we teach to undergraduates is designed for single- and few-body systems. An early paper by Mott describes one way to bridge quantum trajectories to classical ones.
    – rob
    Mar 24 at 18:03
  • 1
    In Heisenberg's intellectual autobiography The Part and the Whole, one chapter is devoted to a discussion with the neo-Kantian philosopher of the new approach and results of modern physics. It is well worth having a read. Mar 24 at 21:42

Kant was working prior to the development of special relativity (WP, nLab) and their assumptions about time and space are no longer in accord with empirical evidence. Kant's claims and axioms can be restated in ways that make them into tautologies of current-day physics, dissolving the antinomies.

Thesis (a): All geodesics appear to converge backwards towards a single point.

Thesis (b): All interactions are local; objects may be space-like separated (see this question and answers).

Antithesis (a): It is not yet ruled out whether the universe has had multiple aeons, and there exists a model for multiple aeons of time.

Antithesis (b): The observable universe is finite, but the universe appears to extend beyond it.

See also the following SEP entries: Kantian and Neo-Kantian Interpretations of General Relativity, Convention of Simultaneity, and Space and Time: Inertial Frames.


Just like all, ( Godel's incompleteness), these are based on (undefined) postulates , including presumably a flat or expanding time and space dimension. If the time dimension for example was an expanding e.g. as the time goes by, the time unit expands , then there is a beginning. E.g. think of 1 1 = 1/2 + 1/4 + 1/ 8....

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