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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
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    42
    Home/Original/inverse
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    Inverse View

    It is not the case that The sentence 'There are infinitely many prime numbers' can be literally true even though there are no such things as numbers.

    ?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.Quine's criterion holds that to be is to be the value of a bound variable, making existential quantification inseparable from ontological commitment.
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    • 2.If 'there are infinitely many primes' is literally true, its logical form quantifies over numbers, thereby committing the speaker to their existence.
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    • 3.Positing ambiguity in 'there is' without independent syntactic or semantic evidence is an ad hoc maneuver that violates theoretical parsimony.
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    Reason for 2 of 2
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    • 1.Benacerraf's epistemic challenge establishes that if numbers are causally inert abstract objects, reliable mathematical knowledge becomes inexplicable.
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    • 2.Fictionalism's attempt to preserve literal truth without ontological commitment collapses the distinction between true and merely useful fictions, undermining the normative force of mathematical proof.
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    • 3.Preserving the literal truth of mathematical sentences while denying numerical existence creates an unexplained asymmetry between mathematical and ordinary empirical discourse.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Thin-truth-ism holds that existential expressions like 'there is' are ambiguous.
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    • 2.The literal truth of a sentence containing 'there is' does not require the existence of the entities quantified over, given the ambiguity of existential expressions.
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    Strongest counterpoint
    Explore the most compelling reason on the other side.