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    Frege's logicist program shows number-names are not descr... — Carmelics
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    Challenges→Convention in number-naming vindicates naturalism rather than replacing it

    Frege's logicist program shows number-names are not descriptive composites but logical objects fixed by abstraction principles independent of convention.

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    Reasons For

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    Reason for
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    • 1.Abstraction principles like Hume's principle derive numbers from logical relations without presupposing what numbers are.
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    • 2.Number-names refer to abstract objects whose identity conditions are entirely determined by equivalence relations, not convention.
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    • 3.If numbers were descriptive composites, their properties would depend on contingent descriptions rather than necessary logical structure.
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    Reasons Against

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    • 1.Abstraction principles like Hume's principle require a prior grasp of cardinality to be non-circular, undermining their foundational role.
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    • 2.The selection of which abstraction principle to adopt (Basic Law V vs. alternatives) appears conventional, not logically determined.
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    • 3.Logical objects without empirical instantiation face the epistemological problem of how we access their properties at all.
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    Philosophy of Language1 linked

    Related

    Abstraction principles like Hume's principle derive numbers from logical relatio...Abstraction principles like Hume's principle require a prior grasp of cardinalit...Convention in number-naming vindicates naturalism rather than replacing itIf numbers were descriptive composites, their properties would depend on conting...
    +3 moreShow less
    Logical objects without empirical instantiation face the epistemological problem...Number-names refer to abstract objects whose identity conditions are entirely de...The selection of which abstraction principle to adopt (Basic Law V vs. alternati...

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