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    Extensional sentences containing numerical singular terms... — Carmelics
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    Extensional sentences containing numerical singular terms, if true, are ontologically committed to numbers.

    Philosophy of LanguageTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.Numerical singular terms are genuine singular terms.
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    • 2.Genuine singular terms, when occurring in true extensional sentences, refer to objects.
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    • 3.Numbers are the objects referred to by numerical singular terms in true extensional sentences.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Numerical singular terms function as nominalizations of predicates or quantifiers, not as genuine referring expressions that pick out objects.
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    • 2.Frege's context principle permits number-words to contribute to sentence truth conditions without requiring corresponding objects in the domain.
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    • 3.A sentence like '2+2=4' can be fully explained by its role in inferential practice without positing abstract objects as referents.
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    Reason against 2 of 2
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    • 1.Paraphrase strategies (Field, Hellman) can restate all true arithmetic claims using second-order logic over physical regions, eliminating numerical singular terms entirely.
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    • 2.If true numerical sentences admit of nominalistically adequate paraphrases that preserve all empirical content, then ontological commitment to numbers is not mandatory but merely one interpretive choice.
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    Related

    A sentence like '2+2=4' can be fully explained by its role in inferential practi...Frege's context principle permits number-words to contribute to sentence truth c...Genuine singular terms, when occurring in true extensional sentences, refer to o...If true numerical sentences admit of nominalistically adequate paraphrases that ...
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    Numbers are the objects referred to by numerical singular terms in true extensio...Numerical singular terms are genuine singular terms.Numerical singular terms function as nominalizations of predicates or quantifier...Paraphrase strategies (Field, Hellman) can restate all true arithmetic claims us...

    Similar

    Fregean arguments for ontological commitment to numbers depend on the ...94%Fregean ontological commitment arguments can be challenged by denying ...89%Appropriate sentences involving numerical singular terms are sometimes...83%Therefore, numerical singular terms refer to objects.83%

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    SEP: ontological-commitment
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    This argument might be challenged in two different ways. First, one might deny that sentences containing numerical singular terms are (literally) true; one might, for example, endorse a fictionalist account of mathematics (Field 1980). For our purposes, we can sidestep this objection and focus on the other premise of the argument, that extensional sentences containing numerical singular terms, if true, refer to numbers—which is to say, in other words, that such sentences, whether true or not, a
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    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit