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    Structural parity in a semantic framework is insufficient... — Carmelics
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    Part of a larger discussion

    Challenges→The fact that toposes support closed set logic as readily as open set logic is an argument that inconsistent theories are equally reasonable as items of mathematical study.

    Structural parity in a semantic framework is insufficient for philosophical parity without an independent account of what cognitive or mathematical practice the logic is answerable to.

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    Key Terms

    Answerability (or 'answerable to')(in epistemology)
    Being responsible to or accountable to something; a system is 'answerable to' practice if it must match up with what actually happens in the real world.
    Cognitive practice(in philosophy of mind and epistemology)
    The actual ways our minds work when we think, learn, and solve problems in the real world.
    Logic (formal logic)(as used in mathematics and computer science)
    A system of rules for determining what conclusions definitely follow from given starting statements, used to avoid mistakes in reasoning.
    Mathematical practice(describes how mathematics develops historically)
    The actual work mathematicians do—developing new ideas, proving theorems, and building on existing knowledge over time.
    Philosophical parity

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    (in epistemology and metaphysics)
    When two things deserve equal status or weight in serious philosophical thinking—meaning one isn't just a copy of the other but genuinely stands on its own.
    Semantic framework(as the type of framework substitutional quantification represents)
    A system that explains what words and logical symbols actually mean and how they connect to reality or ideas.
    Structural parity(describing when cases appear similar in form)
    When two situations have the same basic structure or pattern—meaning they're organized or arranged in the same way.

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    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

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    The fact that toposes support closed set logic as readily as open set logic is a...

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