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    Mathematics should not be conceived of as a calculus sepa... — Carmelics
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    Mathematics should not be conceived of as a calculus separate from other uses of language

    Philosophy of LanguageTruth & Knowledge
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    2 reasons for
    1 reason against

    Reasons For

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    Reason for 1 of 2
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    • 1.Frege's logicist program demonstrates that arithmetic truths are derivable from logical laws governing ordinary predication and concept-application.
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    • 2.Logical laws are not domain-specific calculi but constitutive of rational discourse across all linguistic contexts.
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    • 3.Therefore, arithmetic inherits its normative force from the same inferential practices that govern non-mathematical language use.
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    Reason for 2 of 2
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    • 1.Quine's indispensability argument shows mathematical entities are posited within the same holistic web of belief as empirical claims.
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    • 2.If mathematics were a separate calculus, it could not play its explanatory role in scientific theories expressed in natural language.
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    • 3.The semantic continuity between mathematical and non-mathematical discourse is a precondition for mathematics having any epistemic authority.
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    Reasons Against

    1 perspective
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    • 1.Parts of arithmetic can be seen as grounded in non-mathematical uses of language
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    • 2.Wittgenstein attempts to show that arithmetic connects to broader linguistic practice rather than existing as an isolated formal system
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    Philosophy of LanguageTruth & Knowledge

    Related

    Frege's logicist program demonstrates that arithmetic truths are derivable from ...If mathematics were a separate calculus, it could not play its explanatory role ...Logical laws are not domain-specific calculi but constitutive of rational discou...Parts of arithmetic can be seen as grounded in non-mathematical uses of language
    +4 moreShow less
    Quine's indispensability argument shows mathematical entities are posited within...The semantic continuity between mathematical and non-mathematical discourse is a...Therefore, arithmetic inherits its normative force from the same inferential pra...Wittgenstein attempts to show that arithmetic connects to broader linguistic pra...

    Similar

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    SEP: formalism-mathematics
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    Care must be taken, however. Wittgenstein distinguishes utterances which are sinnlos, which lack sense (including logical tautologies and contradictions here) from those which are unsinnig, nonsensical; it is not clear into which class mathematical utterances fall. One might well think that the game formalist should treat mathematical utterances, on that view just strings of meaningless marks, as unsinnig, not just sinnlos. One clear difference from game formalism however is this: for Wittgenste
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    claim
    Perspectives
    3 (2 for, 1 against)
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