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    Quine's criterion for ontological commitment requires tha... — Carmelics
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    Challenges→TIME(n^k) is always a proper subset of TIME(n^{k+1}) for all natural numbers k

    Quine's criterion for ontological commitment requires that existential claims in formal systems carry genuine ontological weight only when the existents are specifiable, not merely provably existent.

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    Key Terms

    Existential claims(the type of claim being made within a framework)
    Statements that say something exists or is real—for example, 'numbers exist' or 'unicorns exist.'
    Formal systems(the systems Hilbert tried to use)
    A set of basic symbols and strict rules for manipulating them (like a logical language), designed to avoid ambiguity and prove statements with certainty.
    Ontological weight(whether existential claims matter for what's really real)
    How seriously we should take a claim as telling us something genuinely exists in reality, rather than being just a convenient way of speaking.
    Ontology(Carnap argues this enterprise is based on a mistake)
    The philosophical discipline that tries to answer hard questions about what there really is.
    Quine

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    (as a proper name referring to the philosopher whose theory is being discussed)
    Willard Van Orman Quine was a 20th-century American philosopher who wrote about how we know things and how language works. In this statement, we're discussing one of his specific ideas about observation.
    Specifiable(what Quine requires before something counts as really existing)
    Able to be clearly defined or described in concrete, meaningful terms rather than being vague or abstract.
    ontological commitment(Used to derive that literal truth of 'a is F' entails existence of a)
    The criterion by which acceptance of a sentence as literally true commits one to the existence of the objects referred to by singular terms in that sentence, provided the sentence cannot be paraphrased away.

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    2 topics

    Proof of definition segments1 linkedModality & Possibility1 linked

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    TIME(n^k) is always a proper subset of TIME(n^{k+1}) for all natural numbers k

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