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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Mathematics should not be conceived of as a calculus separate from other uses of language

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    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Statements
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