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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
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    Perspectives
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    42
    Home/Original/inverse
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    Inverse View

    It is not the case that Category theory faces foundational problems similar to those of comprehension in set theory, making inconsistent solutions applicable to category theory as well.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Category theory's foundational issues are resolved by Grothendieck universes, which avoid self-reference without requiring inconsistency toleration.
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    • 2.The comprehension problem in set theory arises from unrestricted self-membership, but categorical foundations use arrows and functors, not extension-based membership.
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    • 3.Mac Lane and Eilenberg designed category theory to sidestep set-theoretic paradoxes structurally, not to replicate the conditions that generate them.
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    Reason for 2 of 2
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    • 1.Lawvere's Elementary Theory of the Category of Sets (ETCS) provides a consistent categorical foundation that does not inherit Cantorian comprehension vulnerabilities.
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    • 2.Applying paraconsistent or inconsistent solutions to category theory presupposes a disanalogy-obscuring equivalence between membership-based and morphism-based ontologies.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Category theory has been proposed as an alternative foundation for mathematics.
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    • 2.Such generality in foundational theories inevitably runs into problems similar to those of comprehension in set theory.
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    • 3.Inconsistent solutions have been applied to comprehension problems in set theory.
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