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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Convention in number-naming vindicates naturalism rather than replacing it

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.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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    • 2.If numbers are objects given by Hume's Principle, their names track abstract identity conditions, not conventionally assembled phonological parts.
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    • 3.A naming system grounded in logical objects vindicates Platonism about reference, not naturalist fit between name-sound and named nature.
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    Reason for 2 of 2
    ?
    • 1.Wittgenstein's rule-following considerations show that no finite set of conventions fixes a unique compositional rule for extending number-names.
      ?

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    • 2.If convention cannot self-interpret its own application, the descriptive power attributed to number-naming conventions is itself underdetermined and cannot ground naturalist conclusions.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.There are infinitely many numbers, so an infinite set of number-names made from a finite stock of letters cannot limit name length without agreed compositional rules
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    • 2.Agreed rules for composing number-names from smaller units (e.g., 'twenty-seven', 'two hundred and forty') allow any natural number to be named by description
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    • 3.This descriptive power of number-names is preserved through convention, not undermined by it
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