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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Brouwer and Dummett's anti-realism requires that mathematical existence claims be backed by constructive witness, not merely classical logical consequence.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Requiring constructive witnesses makes large swaths of established mathematics (Cantor, analysis, set theory) illegitimate without philosophical justification.
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    • 2.Constructivism conflates epistemology (how we know) with metaphysics (what exists), but logical validity shouldn't depend on knowability.
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    • 3.Even Brouwer acknowledged that constructivism cannot be formally proven within any single system, undercutting its foundational authority.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Classical logic permits existence proofs by contradiction without specifying *how* to find the object, rendering claims epistemically hollow.
      ?

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    • 2.Constructive witnesses provide computational meaning; non-constructive proofs leave mathematical claims truth-value-indefinite in practice.
      ?

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    • 3.Intuitionistic mathematics avoids the ontological extravagance of assuming infinitely many abstract objects independent of human knowledge.
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