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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Russell's logicism differs significantly from Frege's logicism

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Both Frege and Russell share the core logicist thesis that arithmetic truths are analytic and reducible to purely logical laws.
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    • 2.Frege's Begriffsschrift functions and Russell's propositional functions are both second-order devices mapping arguments to logical values, differing only in notation.
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    • 3.Superficial technical divergences in how functions are formalized do not constitute a significant foundational difference when the overarching reductive program is identical.
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    Reason for 2 of 2
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    • 1.Michael Dummett argues in 'Frege: Philosophy of Mathematics' that Russell's type theory is best understood as a technical repair of Frege's own logicist system rather than a departure from it.
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    • 2.A modification introduced to preserve the same foundational goals—deriving arithmetic from logic—counts as a continuation of a program, not a significant divergence from it.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Frege's logic is based on the notion of concept, which is a function from objects to truth values
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    • 2.Russell's logic reduces the mathematical notion of function to his logical notion of propositional function
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    • 3.Reducing function to propositional function is a different foundational move than grounding logic in concepts
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