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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that 'Every' can be treated as a predicate satisfied by ordered pairs ⟨X, Y⟩ such that the extension of X includes the extension of Y.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Frege argued that quantifiers are fundamentally second-order functions mapping first-order concepts to truth-values, not predicates of any ordered pairs.
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    • 2.Treating 'every' as a predicate of pairs collapses the Fregean type-distinction between object-level predication and concept-level quantification.
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    • 3.This type-collapse generates systematic ambiguities in sentences like 'Every property is instantiated,' where the quantifier must range over its own domain.
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    Reason for 2 of 2
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    • 1.Generalized quantifiers like 'every' exhibit logical properties (conservativity, monotonicity) absent from ordinary relational predicates like 'likes'.
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    • 2.Assimilating quantifiers to predicates of pairs obscures these structural asymmetries that explain cross-linguistic quantifier universals (Barwise & Cooper 1981).
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    Reasons Against

    1 perspective
    Reason against
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    • 1.'Likes' can be described as a predicate satisfied by ordered pairs ⟨x, y⟩ such that x likes y.
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    • 2.The same predicate-of-ordered-pairs treatment can be extended from relations between individuals to relations between predicates.
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