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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that The extensionality of classes is a derived result, not a postulate.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Quine argues in 'Set Theory and Its Logic' that contextual definitions of classes presuppose extensionality to individuate the propositional functions they quantify over.
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    • 2.If the logic of properties used in P3 already treats coextensive properties as identical, extensionality is a hidden postulate smuggled into the definiens, not derived from it.
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    Reason for 2 of 2
    ?
    • 1.Russell's substitutional theory shows that eliminating classes via propositional functions requires intensional distinctions that extensionality actively destroys, making derivation circular.
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    • 2.A definition that yields extensionality only by collapsing intensional differences between properties does not derive extensionality but stipulates it under a redescription.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.To say something G of the class of Fs is to say there exists a predicative property H coextensive with F such that H is G.
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    • 2.If F and H are coextensive, then anything true of {x: Fx} will be true of {x: Hx}.
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    • 3.Extensionality follows from this contextual definition via the logic of properties.
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