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    Brouwer and Dummett's anti-realism requires that mathemat... — Carmelics
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    Challenges→A polynomial time algorithm for any single NP-complete problem would entail the existence of polynomial time algorithms for all problems in NP.

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

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    1 reason for
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    Reasons For

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    Reason for
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    • 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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    Reasons Against

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    Reason against
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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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    Proof of definition segments1 linkedModality & Possibility1 linked

    Related

    A polynomial time algorithm for any single NP-complete problem would entail the ...Classical logic permits existence proofs by contradiction without specifying *ho...Constructive witnesses provide computational meaning; non-constructive proofs le...Constructivism conflates epistemology (how we know) with metaphysics (what exist...
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    Even Brouwer acknowledged that constructivism cannot be formally proven within a...Intuitionistic mathematics avoids the ontological extravagance of assuming infin...Requiring constructive witnesses makes large swaths of established mathematics (...

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    2 (1 for, 1 against)
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