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    If 'a > n for every natural number n' can only be verifie... — Carmelics
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    Challenges→An infinite (nonstandard) hyperreal exists

    If 'a > n for every natural number n' can only be verified schema-theoretically and never instancewise, the quantifier range presupposes what it purports to prove.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Schema-theoretic verification relies on a uniform rule, not exhaustive checking, so it cannot ground claims about infinite totalities without circularity.
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    • 2.Instance-wise verification of 'a > n' requires checking each n individually; schema-theoretic proof instead presupposes the infinity we're trying to establish.
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    • 3.Quantifying over 'every natural number' already assumes the totality of naturals exists; using only schema-theoretic methods begs this assumption.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Schema-theoretic proofs work by formal derivation rules, not by presupposing quantifier ranges—the rules generate the quantifier's legitimacy inductively.
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    • 2.Instance-wise verification of infinite claims is impossible in principle; rejecting schema-theoretic methods leaves universal quantification meaningless entirely.
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    • 3.Quantifier ranges in formal systems are defined by axioms (like Peano's), not presupposed; the claim conflates semantic interpretation with logical justification.
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    Connections

    2 topics

    Proof of definition segments1 linkedModality & Possibility1 linked

    Related

    An infinite (nonstandard) hyperreal existsInstance-wise verification of 'a > n' requires checking each n individually; sch...Instance-wise verification of infinite claims is impossible in principle; reject...Quantifier ranges in formal systems are defined by axioms (like Peano's), not pr...
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    Quantifying over 'every natural number' already assumes the totality of naturals...Schema-theoretic proofs work by formal derivation rules, not by presupposing qua...Schema-theoretic verification relies on a uniform rule, not exhaustive checking,...

    Details

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    claim
    Perspectives
    2 (1 for, 1 against)
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