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    'Every' can be treated as a predicate satisfied by ordere... — Carmelics
    Home/Philosophy of Language
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    'Every' can be treated as a predicate satisfied by ordered pairs ⟨X, Y⟩ such that the extension of X includes the extension of Y.

    Philosophy of Language
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 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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    Philosophy of Language

    Related

    'Likes' can be described as a predicate satisfied by ordered pairs ⟨x, y⟩ such t...Assimilating quantifiers to predicates of pairs obscures these structural asymme...Frege argued that quantifiers are fundamentally second-order functions mapping f...Generalized quantifiers like 'every' exhibit logical properties (conservativity,...
    +3 moreShow less
    The same predicate-of-ordered-pairs treatment can be extended from relations bet...This type-collapse generates systematic ambiguities in sentences like 'Every pro...Treating 'every' as a predicate of pairs collapses the Fregean type-distinction ...

    Similar

    'Likes' can be described as a predicate satisfied by ordered pairs ⟨x,...90%Quantifiers can be represented as functions on ordered pairs of predic...84%Therefore, F ≠ G implies the extension of F ≠ the extension of G.82%The same predicate-of-ordered-pairs treatment can be extended from rel...79%

    Source

    AI-extracted1/3 agreementValid
    SEP: logical-form
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    Just as we can describe ‘likes’ as a predicate satisfied by ordered pairs \(\langle x, y \rangle\) such that \(x\) likes \(y\), so we can think about ‘every’ as a predicate satisfied by ordered pairs \(\langle X, Y \rangle\) such that the extension of \(X\) includes the extension of \(Y\). (This is compatible with thinking about ‘every boy’ as a restricted quantifier that combines with a predicate to form a sentence that is true iff every boy satisfies that predicate.) One virtue of this notatio
    Extraction notes

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

    Details

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