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Kant proves the limits of human reason by providing 4 antinomies, pairs of rational but contradictory statements, which he claims pure reason can never help us decide which one of the pair is correct.

But for his idea to hold, shouldn't it be shown that the antinomies are contradictions or paradox in formal logic, not just colloquially? Is there a chance that they can be dissolved upon formal logical analysis? Has anyone tried to formalize Kant's antinomies?

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    I suppose that Kant's antinomies can be formalized. Because I remember a similar enterprise: Gödel formalized the ontological proof of Anselm from Canterbury. But apparently, Gödel's formalization did not evoke much interest.
    – Jo Wehler
    Commented Jan 20, 2016 at 7:25
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    Having reviewed the time antinomy, it seems to be based on two premises "built in" to our human faculties/reasoning: 1) that infinities can never be completed, and 2) any "point in time" when considered locally necessarily has points in time preceding it ("what came before?" is an answerable question regarding any point in time). By #1 there must be a beginning point of time finitely in the past because an infinity of time could not have been completed before the evidently-existing now. By #2, there must have been time before any such supposed "beginning point". Not sure how to formalize it.
    – Jeff Y
    Commented Jan 20, 2016 at 16:21
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    @ Jeff Y I think the formalization can be put in a kind of temporal logic.But I just think in some part,Kant fails,in some parts,Kant presuppose the conclusion. Commented May 10, 2020 at 10:15
  • Logic, as the claim goes, is meant to extract and capture the cognitive content, which I presume are the propositional components of discourse. Not all the implicatures are successfully rendered in logic, the famous example being "but". Nevertheless, these are of no inferential significance and we may reinsert them at the right loci (post argument) and restore, to some degree, the original intent.
    – Hudjefa
    Commented May 26 at 15:29

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Kant's antinomies are quite straightforwardly understandable so I don't see the need for formalization. It should however be noted that the way Kant formulates these antinomies often relies on various notions borrowed from mathematics of Kant's times (that's why some are confused about Kant's formulations). Patrick Suppes has written about this, here.

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