Are there any such things as category theories where the category is an indeterminist/postdeterminist form of free will? Let's say, maybe it is a category where each object is an object of choice, there are initial choices and terminal choices, etc.

Or, this concept of free will actually requires going between subsidiary categories. So it involves metacategories or what are called "n-categories," maybe? I tried looking for an essay where they work something out along these lines, but the sort-of closest I got was an essay about category theory being applied to an analysis of the deontic logic implicit in the Canadian legal system. I'll try Googling something like "deontic logic and category theory" and see what that gets me.

Alt./specified formulation of the issue: talk of "nontrivial automorphisms" is given in category theory, incl. where this intersects higher set theory. Now Kant says that the three main phrasings he expresses the categorical imperative in are at heart equivalent/enter into some sort of equivalence relation with each other. So perhaps we could speak of nontrivial automorphisms of the category of categorical imperatives. Since Kant has autonomian free will and moral concepts as integrally linked, perhaps he could be construed as allowing that deontic categories could be repurposed as categories of free will. (Or, then, his own "categories of freedom" are such things, except insofar as his use of the word "categories" is not identical in meaning to modern use in the higher-mathematics context.)

  • Once you have a category theoretic representation for that problem, what will you do with it?
    – Frank
    Feb 2 at 20:32
  • @Frank one set theorist, Penelope Maddy, has proposed an in re realism about mathematical objects, but I think it was uncertain whether the surrogates she selected from the physical world (arbitrary subregions of spacetime) are plentiful enough to satisfy the reference maps from ante rem realism. I wonder if the range of the sheer will-to-refer, however, then, could allow for an in re realism (where mathematical objects exist as encoded into free will, which will is capable of referring to whatever it wills to refer to as such). Feb 2 at 22:51
  • I think in re realism, and even realism tout court, are fool's errands.
    – Frank
    Feb 3 at 2:21
  • @Frank my idea at an angle from that is that the distinction between realism and fictionalism can be undermined, and the question of existence itself negated (perhaps) on every level, including the mathematical one. But before Quine/category theory, the schools of philo-o-math were evidentialism-minded. Each portrays its evidence base as the evidence base (semiotic formalists: physical symbols; intuitionists: formal physical intuitions; predicativists, noncircular intensions; Platonists, intellectual intuition), and in a foundationalist vein. Feb 3 at 2:36
  • So I think it is not really a "coincidence" that Quine's set theory has circular sets, including a circular universal set, and that he was so fundamentally involved in the matter of the indispensability argument for mathematical realism. The holism of his reasoning, here, is of a piece with the coherentism of category theory. If we switch to a logic that doesn't use the concept of existence at all, then, we could evaporate the question of realism (but also of fictionalism), maybe. Feb 3 at 2:39


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