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Atrium > Mathematics, Physics & Philosophy: Dialectics and Duality

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  1. Has anyone ever made a connection between category theoretic duality and dialectics (not necessarily Hegelian dialectics, but dialectics in general (such as that found in Taoism))? A canonical example of dialectical reasoning follows:

    Thesis: The Absolute is Being.
    Antithesis: The Absolute is Non-Being.
    Synthesis: The Absolute is Becoming.

    Polarity (opposites) and negations are recurrent in dialectics.
    Is there a natural way to categorify general dialectical reasoning? Is there a categorical analogue of thesis-antithesis-synthesis dialectics?
    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 16th 2010

    Maybe some people here would enjoy that question (I don’t know), but I’d urge you to take your question to Lawvere, who has spent his life thinking about such things. Certainly dialectical materialism plays an explicit role in some of his early writings. I have a feeling that he might have some interesting responses if you were to write him an email.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 16th 2010

    Yes, Google “Lawvere”, “unity and identity of opposites”, “dialectical”. There are other papers than those at his site, like ’Adjointness in Foundations’ available here.

  4. Thanks.

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