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    Formalist positions of Goodman and Quine's persuasion are... — Carmelics
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    Formalist positions of Goodman and Quine's persuasion are refuted by reductio ad absurdum

    Philosophy of LanguageTruth & Knowledge
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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Wittgenstein's rule-following considerations show that meaning requires communal practice, not abstract objects, so truth must be grounded in actual human inferential activity.
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    • 2.Goodman and Quine's nominalism entails that unbounded ideal reasoners are themselves abstract posits, making 'ideal provability' an illicit platonist commitment.
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    • 3.A mathematical sentence with no possible concrete proof-token has no determinate inferential role in any actual linguistic community, and therefore lacks cognitive content by verificationist standards.
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    Reason for 2 of 2
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    • 1.Field's fictionalism demonstrates that classical mathematics can be conservatively dispensed with for physical applications, so preserving 'current mathematical practice' is not a decisive philosophical constraint.
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    • 2.The reductio only lands if mathematical practice has normative authority over metaphysical positions, but Quine's own revisability thesis holds that no statement is immune from revision on theoretical grounds.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Under Goodman and Quine's formalism, a sentence is true or false only if a concrete proof or refutation exists
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    • 2.There exist sentences (such as the Fermat-like primality claim) that are decidable in the formal sense but for which no concrete proof or refutation exists or could be manipulated by any human
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    • 3.Under Goodman and Quine's formalism, such sentences would be neither true nor false
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    Topics

    Philosophy of LanguageTruth & Knowledge

    Connections

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    Related

    A consequence that destroys current mathematical practice constitutes a reductio...A mathematical sentence with no possible concrete proof-token has no determinate...Field's fictionalism demonstrates that classical mathematics can be conservative...Goodman and Quine's nominalism entails that unbounded ideal reasoners are themse...
    +6 moreShow less
    The reductio only lands if mathematical practice has normative authority over me...There exist sentences (such as the Fermat-like primality claim) that are decidab...Treating decidable mathematical sentences as neither true nor false would requir...Under Goodman and Quine's formalism, a sentence is true or false only if a concr...Under Goodman and Quine's formalism, such sentences would be neither true nor fa...Wittgenstein's rule-following considerations show that meaning requires communal...

    Similar

    Paraconsistentists may reject reductio ad absurdum83%By reductio ad absurdum, anything that entails a contradiction is fals...82%Fitch's reasoning relies on reductio ad absurdum to establish that K(p...81%Opponents of Bergson and Samuelson misunderstood their position rather...77%

    Source

    AI-extracted1/3 agreementValid
    SEP: formalism-mathematics
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    (That is—with ‘2^\(n\)’ representing ‘2 to the power \(n\)’—‘[2^(2^(2^(2^(2^2))))]\(+1\) is prime’; cf. Tennant, 1997 p. 152.) They cannot deny the sentence exists, for there is the token before our very eyes. But there are strong grounds for thinking that no concrete proof or disproof will exist, for the only methods available may use up more time, space and material than any human could have at her disposal, perhaps than actually exists. There are countless sentences with this property: concre
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit