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    If concepts F and G are distinct concepts, then F and G a... — Carmelics
    Home/Philosophy of Language
    HistoryEditSee Inverse

    If concepts F and G are distinct concepts, then F and G are not materially equivalent.

    Modality & Possibility
    ?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.In an extensional model of concepts, material equivalence of F and G is both a necessary and sufficient condition for the identity of F and G.
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    • 2.F = G if and only if for all x, Fx if and only if Gx.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Frege himself distinguished concept identity from co-extensionality: 'the morning star' and 'the evening star' share extension but differ intensionally.
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    • 2.Material equivalence is an extensional relation, but concepts individuated by sense (Sinn) can diverge even when their extensions are necessarily identical.
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    • 3.Therefore, F and G can be materially equivalent yet remain distinct concepts, falsifying the claim that distinct concepts cannot be materially equivalent.
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    Reason against 2 of 2
    ?
    • 1.Necessarily co-extensive concepts like 'triangular' and 'trilateral' are materially equivalent across all possible worlds yet are paradigmatically treated as distinct concepts in intensional semantics.
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    • 2.If material equivalence sufficed for concept identity, hyperintensional contexts—where substitution of co-extensive terms fails—would be semantically unintelligible, but they are not.
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    Topics

    Philosophy of LanguageModality & Possibility

    Related

    F = G if and only if for all x, Fx if and only if Gx.Frege himself distinguished concept identity from co-extensionality: 'the mornin...If material equivalence sufficed for concept identity, hyperintensional contexts...In an extensional model of concepts, material equivalence of F and G is both a n...
    +3 moreShow less
    Material equivalence is an extensional relation, but concepts individuated by se...Necessarily co-extensive concepts like 'triangular' and 'trilateral' are materia...Therefore, F and G can be materially equivalent yet remain distinct concepts, fa...

    Similar

    If concepts F and G are not materially equivalent, then F and G are di...100%Most Fregeans deny that properties are identical to concepts.82%Therefore, although idea and material object are not identical, they a...82%If concepts F and G differ, then the extensions of F and G differ.82%

    Source

    AI-extracted1/3 agreementValid
    SEP: frege-theorem
    View source passageHide passage
    To analyze the inconsistency in more detail, consider an extensional model of concepts, in which the material equivalence of concepts \(F\) and \(G\) serves as both necessary and sufficient conditions for the identity of \(F\) and \(G\), i.e., in which \(F = G \equiv \forall x(Fx \equiv Gx)\). So, given this understanding, if it is not the case that \(F\) and \(G\) are materially equivalent, then \(F\) and \(G\) are distinct concepts; and if \(F\) and \(G\) are distinct concepts, then they are
    Extraction notes

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

    Details

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