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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
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    42
    Home/Original/inverse
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    Inverse View

    It is not the case that Quine and Boolos both argue that ontological commitments are smuggled into logical frameworks through comprehension-like principles implicit in predicate abstraction.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Modern type theory and stratified comprehension avoid paradox without assuming full ontological commitment to abstract entities.
      ?

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    • 2.Predicate abstraction can be interpreted proof-theoretically as syntactic rules rather than positing new objects into reality.
      ?

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    • 3.The distinction between logical framework and ontological commitment is clearer than Quine-Boolos analysis suggests; framework ≠ commitment.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Predicate abstraction allows formation of sets from any formula without restriction, mirroring unrestricted comprehension.
      ?

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    • 2.Quine showed that naive comprehension commits us to entities (classes/sets) not explicitly postulated in logical axioms.
      ?

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    • 3.Boolos demonstrated that second-order logic with standard semantics presupposes a domain of properties/relations ontologically.
      ?

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