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    Convention in number-naming vindicates naturalism rather ... — Carmelics
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    Convention in number-naming vindicates naturalism rather than replacing it

    Philosophy of Language
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 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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    Reasons Against

    2 perspectives
    Reason against 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 against 2 of 2
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    • 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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    Philosophy of Language

    Related

    A naming system grounded in logical objects vindicates Platonism about reference...Agreed rules for composing number-names from smaller units (e.g., 'twenty-seven'...Frege's logicist program shows number-names are not descriptive composites but l...If convention cannot self-interpret its own application, the descriptive power a...
    +4 moreShow less
    If numbers are objects given by Hume's Principle, their names track abstract ide...There are infinitely many numbers, so an infinite set of number-names made from ...This descriptive power of number-names is preserved through convention, not unde...Wittgenstein's rule-following considerations show that no finite set of conventi...

    Similar

    Convention is invoked for number-names not to replace naturalism but t...92%For the preceding natural numbers to be numbered by Frege's trick, tho...78%This descriptive power of number-names is preserved through convention...77%The nature in the particular is only denominatively (accidentally) num...76%

    Source

    AI-extracted1/3 agreementValid
    SEP: plato-cratylus
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    The difficult question about these two moves, on which scholarship is divided, is how far the pendulum has now swung back towards conventionalism. There are reasons for being wary of exaggerating the swing. As regards the first argument, it is significant that Socrates nowhere in the dialogue admits any case in which the inappropriate elements in a name outnumber the appropriate ones (hence item 19 in the list of etymological principles, section 3 above). The test case, that of sklêrotês, is one
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit