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    Frege's context principle permits number-words to contrib... — Carmelics
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    Challenges→Extensional sentences containing numerical singular terms, if true, are ontologically committed to numbers.

    Frege's context principle permits number-words to contribute to sentence truth conditions without requiring corresponding objects in the domain.

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    Reasons For

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    • 1.Sentence meaning is semantically fundamental; reference to objects is derivative and explanatorily secondary to sentential context.
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    • 2.Numbers demonstrably affect truth-conditions of sentences without requiring platonist commitment to abstract objects.
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    • 3.The context principle dissolves traditional ontological puzzles by shifting analysis from terms to whole sentences.
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    Reasons Against

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    • 1.If number-words contribute to truth-conditions, compositional semantics requires assigning them content independent of sentential context.
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    • 2.The context principle, taken literally, makes it mysterious how sentences about numbers have determinate truth-values at all.
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    • 3.Mathematical discourse presupposes quantification over numbers; truth-conditions require such objects exist in the domain.
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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Extensional sentences containing numerical singular terms, if true, are ontologi...If number-words contribute to truth-conditions, compositional semantics requires...Mathematical discourse presupposes quantification over numbers; truth-conditions...Numbers demonstrably affect truth-conditions of sentences without requiring plat...
    +3 moreShow less
    Sentence meaning is semantically fundamental; reference to objects is derivative...The context principle dissolves traditional ontological puzzles by shifting anal...The context principle, taken literally, makes it mysterious how sentences about ...

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