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In category theory, there are self-dual objects, where AA (A is isomorphic to its dual), with the strict, but possibly non-coherent, case being when A equals A (see Selinger[??]). In some traditions of metaphysics, there is talk of a primal unity or advaita, which is a composite of a- (for "non-") and -dvaita (for "-duality"), i.e. non-duality. The former is represented in a highly discursive manner; the latter is meant to be apprehended by intuition (in roughly both the Kantian and common senses of that word "intuition").

But so are there analyses where an overlap between self-duality and non-duality is looked for? Either seems to involve concepts X such that X is not differentiable from its opposite, or then it has no conceivable opposite. For example, if there are all things, then no thing y is different from every thing, because then y would be equal to something that isn't anything, which is pointless to say (on the other hand, if there are all-things-thought-in-one, then what is different compared to that is just anything-not-as-that-one). So there seems to be at least one class of representation which nothing can be differentiated from, or in, as such; c.f. Kant on Zeno's universe:

Again, if the universe contains in itself everything that exists, it cannot be similar or dissimilar to any other thing, because there is, in fact, no other thing with which it can be compared. If two opposite judgements presuppose a contingent impossible, or arbitrary condition, both—in spite of their opposition (which is, however, not properly or really a contradiction)—fall away; because the condition, which ensured the validity of both, has itself disappeared.

Are category theorists, Advaita Vedantists, and Kant more or less all talking about a similar conceptual phenomenon?

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  • Indeed self-duality is related to metaphysical nonduality if not sufficiently, up to isomorphism or homotopy, and its autonomous category has identity morphisms, dual twisted or braided morphisms and tensor products of objects such as the category of finite-dimensional real inner product vector spaces with linear maps. This insinuates nonduality if exists ought to be some tortile categorical structures or processes. If the objects therein are Frobenius algebra, their co/product is the functor from the category of cobordism to the category of vector spaces as topological quantum field theory... Commented Nov 3, 2023 at 6:56
  • There is definitely an affinity between Kant's observation and non-duality. Indeed, Kant's phrasing is reminiscent of Hegel's later sublation, or a "common sense" variant of it that a non-Hegelian would give. In both cases, we have a failure of language, but in Kant's case it is a failure within language, only in a fragment of it, which is explained and resolved once embedded into broader language. Non-dualists (and, arguably, Hegel) have in mind a more drastic failure. When we are pushing the outer limits of language and conception, the ones we cannot get outside of to embed and resolve.
    – Conifold
    Commented Nov 3, 2023 at 7:08
  • And this is why intuitive intellect (which Kant ascribes to the Divine only) is needed for discursive one must fail. But is categorical duality really the paradigm of opposition? Is OR the "opposite" of AND (I would have thought NAND). Are points in projective geometry the "opposites" of lines? Duality in categories seems to capture more of affinity or symmetry than opposition. Does self-duality really signal a failure of no meaningful opposition rather than a success of meaningful self-symmetry? Do we really feel like it needs to be resolved by removing some condition to break the symmetry?
    – Conifold
    Commented Nov 3, 2023 at 7:27
  • @Conifold I had trouble seeing whether self-duality held in cases where some category C was isomorphic/equal to its opposite category, but then I've hardly scratched the surface of what I'm reading. I think there's supposed to be a connection; but I also wonder how much/little the word "opposite" in "opposite category" is being used for opposition in the sense relevant to non-duality. If there are multiple flavors of contrariety, there could be non-contrariety in one sense but not another, etc. Commented Nov 3, 2023 at 11:45
  • Nonduality is the non-distinction of self and other, it is not about self-similarity. "All is One. One is None. None is All."
    – Scott Rowe
    Commented Nov 4, 2023 at 3:31

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