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    Therefore, F ≠ G implies the extension of F ≠ the extensi... — Carmelics
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    Supports→If concepts F and G differ, then the extensions of F and G differ.

    Therefore, F ≠ G implies the extension of F ≠ the extension of G.

    Modality & PossibilityPhilosophy of Language
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    Related propositions within the same area of thought.
    Basic Law V (Vb) states that the extension of F equals the extension of G if and...If concepts F and G differ, then the extensions of F and G differ.Material equivalence of F and G is a sufficient condition for the identity of F ...The contrapositive of Vb asserts that if F and G are not materially equivalent, ...

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    Divisibility is of the essence of extension.91%EXP and NEXP both properly extend P.89%EXP and NEXP both properly extend P88%If meanings determine extensions, then expressions with multiple disti...84%

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    SEP: frege-theorem
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    So the contrapositive asserts that if \(\neg \forall x(Fx \equiv Gx)\) then \(\epsilon F \neq \epsilon G\). But in the case where the material equivalence of \(F\) and \(G\) is a sufficient condition for \(F = G\), i.e., in the case where \(F \neq G\) implies \(\neg \forall x(Fx \equiv Gx)\), then Vb implies \(F \neq G \to \epsilon F \neq \epsilon G\), i.e., that if concepts \(F\) and \(G\) differ, the extensions of \(F\) and \(G\) differ. So, the correlation that Basic Law V sets up between co

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