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    Russell's logicism differs significantly from Frege's log... — Carmelics
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    Russell's logicism differs significantly from Frege's logicism

    Philosophy of LanguageTruth & Knowledge
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    2 reasons against

    Reasons For

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    Reason for
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    • 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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    Reasons Against

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    Reason against 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 against 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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    Related

    A modification introduced to preserve the same foundational goals—deriving arith...Both Frege and Russell share the core logicist thesis that arithmetic truths are...Frege's Begriffsschrift functions and Russell's propositional functions are both...Frege's logic is based on the notion of concept, which is a function from object...
    +4 moreShow less
    Michael Dummett argues in 'Frege: Philosophy of Mathematics' that Russell's type...Reducing function to propositional function is a different foundational move tha...Russell's logic reduces the mathematical notion of function to his logical notio...Superficial technical divergences in how functions are formalized do not constit...

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    Source

    AI-extracted1/3 agreementValid
    SEP: principia-mathematica
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    Russell presented his theory of definite descriptions in “On Denoting” (1905) and it has probably been the most widely discussed application of the logic of PM. The role of the theory of definite desciptions in PM, however, is exhausted by its use in ∗30 to define what are called “Descriptive functions”. In contemporary logic it is routine to show how the notion of a “functional relation” can be used to justify the introduction of function symbols into a language with only n-place predicates. Th
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    Details

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    3 (1 for, 2 against)
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    1 edit