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    The proposition 'Every German philosopher is American' is... — Carmelics
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    The proposition 'Every German philosopher is American' is universally contravalid with respect to the idea [philosopher]

    Philosophy of Language
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.No German is American
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    • 2.A proposition is universally contravalid with respect to a sequence of ideas if it fails for all substitutions of those ideas
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Bolzano's notion of universal contravalidity requires exhausting all substitutions, but the domain of substitution for 'philosopher' is not fixed or well-defined.
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    • 2.If we substitute 'philosopher' with a vacuous idea (e.g., 'round square'), the proposition becomes vacuously true, violating the contravalidity claim.
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    • 3.Frege and later Quine showed that quantification over empty domains undermines classical universal claims, making Bolzano's substitutional criterion domain-sensitive.
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    Reason against 2 of 2
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    • 1.Carnap's intensional logic holds that the truth value of universal propositions depends on the modal frame, not merely actual-world substitutions.
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    • 2.In a possible world where all German philosophers emigrate and naturalize as Americans, the proposition 'Every German philosopher is American' is true for all substitutions of 'philosopher'.
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    • 3.Therefore universal contravalidity, assessed only across actual substitution instances, conflates logical falsity with contingent falsity in a way Bolzano's framework cannot resolve.
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    Topics

    Philosophy of Language

    Related

    A proposition is universally contravalid with respect to a sequence of ideas if ...Bolzano's notion of universal contravalidity requires exhausting all substitutio...Carnap's intensional logic holds that the truth value of universal propositions ...Frege and later Quine showed that quantification over empty domains undermines c...
    +4 moreShow less
    If we substitute 'philosopher' with a vacuous idea (e.g., 'round square'), the p...In a possible world where all German philosophers emigrate and naturalize as Ame...No German is AmericanTherefore universal contravalidity, assessed only across actual substitution ins...

    Similar

    The proposition 'Every German philosopher is European' is universally ...95%All philosopher-variants of 'Every German philosopher is European' are...86%Varying only the [philosopher] idea in 'Every German philosopher is Eu...86%A proposition is logically false iff it is universally contravalid wit...81%

    Source

    AI-extracted1/3 agreementValid
    SEP: bolzano
    View source passageHide passage
    The result of applying the operation of variation to a proposition depends essentially on our choice of ideas to be varied in the proposition in question. And it can depend on matters of fact whether or not a proposition is universally valid (or contravalid) with respect to a sequence \(i\) of ideas. Thus, e.g., it is due to the fact that every German is European and no German is American that the proposition [Every German philosopher is European] is universally valid and the proposition [Every
    Extraction notes

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

    Details

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