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    The sentence 'There are infinitely many prime numbers' ca... — Carmelics
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    Home/Philosophy of Language
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    The sentence 'There are infinitely many prime numbers' can be literally true even though there are no such things as numbers.

    Philosophy of LanguageTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Philosophy of LanguageTruth & Knowledge

    Related

    Benacerraf's epistemic challenge establishes that if numbers are causally inert ...Fictionalism's attempt to preserve literal truth without ontological commitment ...If 'there are infinitely many primes' is literally true, its logical form quanti...Positing ambiguity in 'there is' without independent syntactic or semantic evide...
    +4 moreShow less
    Preserving the literal truth of mathematical sentences while denying numerical e...Quine's criterion holds that to be is to be the value of a bound variable, makin...The literal truth of a sentence containing 'there is' does not require the exist...Thin-truth-ism holds that existential expressions like 'there is' are ambiguous.

    Similar

    The set of prime numbers is infinite.83%There are infinitely many numbers80%Suppose the set of primes P is finite.79%If such a number exists, then P is incomplete and therefore not a comp...77%

    Source

    AI-extracted1/3 agreementValid
    SEP: platonism
    View source passageHide passage
    Thin-truth-ists endorse a similar view of existence claims. For instance, on their view, the sentence ‘There are infinitely many prime numbers’ is literally true, even though there are no such things as numbers. This might look like a contradiction, but it's not, because according to thin-truth-ism, existential expressions (or quantifiers) like 'there is' are ambiguous.
    Extraction notes

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

    Details

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