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I know of open problems in model theory, but would like to know about philosophical problems (philosophy of language, Husserl's phenomenology ) that have relevance in set theory or type theory.

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    A central problem of metaphysics is reducing the Many to the One. In this task Russell's paradox raises its ugly head and it has to be solved for any progress. It is solved in some philosophies, and the solution would have relevance in set-theory. Hence Russell acknowledges the solution presented by GS Brown, which is a metaphysical solution for the emergence of form from formlessness. The connection between mathematics and metaphysics is also crucial for an analysis of the space-time continuum. I sometime think that metaphysics is mathematics and it is certainly inextricably related. . . .
    – user20253
    Commented Feb 5, 2018 at 12:48
  • Mathematics is arguably nothing more than symbolic manipulation, so one question would be: why can't a symbolic manipulation system be both complete and consistent (Godel proved "why" in a mathematical sense, but it seems philosophically annoying). A more tangible problem: is infinity "real"? If so, it creates several seeming paradoxes.
    – user935
    Commented Feb 5, 2018 at 19:00
  • Did you mean open problems in set or type theory that have philosophical significance? It does not make much sense the other way, all problems in philosophy are "open", phenomenology is generally not susceptible to mathematization (but can be applied to mathematics), and philosophy of language may use formal semantics, etc., but that simply applies logic/set theory.
    – Conifold
    Commented Feb 6, 2018 at 1:38

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