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    The correlation between concepts and extensions establish... — Carmelics
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    Home/Philosophy of Language
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    The correlation between concepts and extensions established by Basic Law V must be a function — no concept gets correlated with two distinct extensions.

    Philosophy of LanguageProof of definition segments
    ?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.Basic Law V asserts (via its Va direction) that if the extensions of F and G differ (εF ≠ εG), then F ≠ G.
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    • 2.The material equivalence of F and G (∀x(Fx ≡ Gx)) is a necessary condition for F = G, meaning ¬∀x(Fx ≡ Gx) implies F ≠ G.
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    • 3.A mapping is a function if and only if no input is correlated with two distinct outputs.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Basic Law V is inconsistent (Russell's paradox), so any functional property derived solely from it inherits this inconsistency and cannot be asserted as a genuine logical truth.
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    • 2.A principle that entails contradiction does not establish a well-defined mapping; it establishes no mapping at all, making the claim vacuously grounded.
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    Reason against 2 of 2
    ?
    • 1.On an intensional conception of concepts (Frege's own Begriffe), distinct concepts with identical extensions remain distinct objects, leaving the direction of correlation from concept to extension under-determined.
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    • 2.If multiple co-extensive concepts are candidates for a single extension, the Va direction alone does not rule out a non-functional one-to-many correlation at the level of senses rather than references.
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    Topics

    Philosophy of LanguageProof of definition segments

    Connections

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    Related

    A mapping is a function if and only if no input is correlated with two distinct ...A principle that entails contradiction does not establish a well-defined mapping...Basic Law V asserts (via its Va direction) that if the extensions of F and G dif...Basic Law V is inconsistent (Russell's paradox), so any functional property deri...
    +3 moreShow less
    If multiple co-extensive concepts are candidates for a single extension, the Va ...On an intensional conception of concepts (Frege's own Begriffe), distinct concep...The material equivalence of F and G (∀x(Fx ≡ Gx)) is a necessary condition for F...

    Similar

    The correlation that Basic Law V sets up between concepts and extensio...92%The correlation between concepts and extensions is one-to-one (distinc...91%Basic Law V's requirement of a one-to-one correlation between concepts...90%Va only entails that distinct extensions are correlated with distinct ...88%

    Source

    AI-extracted1/3 agreementValid
    SEP: frege-theorem
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    So the contrapositive asserts that if \(\epsilon F \neq \epsilon G\), then \(\neg \forall x(Fx \equiv Gx)\). But in the case where the material equivalence of \(F\) and \(G\) is a necessary condition for \(F = G\), i.e., in the case where \(\neg \forall x(Fx \equiv Gx)\) implies \(F \neq G\), then Va implies that if \(\epsilon F \neq \epsilon G\), then \(F \neq G\), i.e., that whenever the extensions of \(F\) and \(G\) differ, the concepts with which they are correlated, namely \(F\) and \(G\),
    Extraction notes

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

    Details

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