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    A proof that cannot be mechanically verified as syntactic... — Carmelics
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    Challenges→The above proof of the intermediate value result can be read either as a syntactic derivation from the axioms or as a semantic argument

    A proof that cannot be mechanically verified as syntactically complete conflates semantic entailment with derivability, undermining the syntactic reading.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Syntactic derivability requires explicit rule application; unverifiable proofs rely on intuitive semantic content the reader supplies.
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    • 2.Gödel's incompleteness shows formal systems distinguish derivability from truth; conflating them obscures this fundamental gap.
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    • 3.Mechanical verification is the standard for rigor in logic; proofs escaping it depend on informal interpretation, not pure syntax.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Mathematical practice accepts proofs verified by expert consensus without mechanical checking; this works because semantics guide syntax naturally.
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    • 2.The distinction between derivability and entailment is conceptual, not practical; all useful proofs eventually admit mechanical encoding.
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    • 3.Requiring mechanical completeness conflates epistemology with metaphysics; a proof can be semantically valid without being algorithmically verifiable.
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    Connections

    2 topics

    Proof of definition segments1 linkedPhilosophy of Language1 linked

    Related

    Gödel's incompleteness shows formal systems distinguish derivability from truth;...Mathematical practice accepts proofs verified by expert consensus without mechan...Mechanical verification is the standard for rigor in logic; proofs escaping it d...Requiring mechanical completeness conflates epistemology with metaphysics; a pro...
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    Syntactic derivability requires explicit rule application; unverifiable proofs r...The above proof of the intermediate value result can be read either as a syntact...The distinction between derivability and entailment is conceptual, not practical...

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    2 (1 for, 1 against)
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