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    Quine and Boolos both argue that ontological commitments ... — Carmelics
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    Challenges→The Cantor-Lawvere principle (CL) is a theorem of first-order logic, not dependent on set-theoretic axioms

    Quine and Boolos both argue that ontological commitments are smuggled into logical frameworks through comprehension-like principles implicit in predicate abstraction.

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    1 reason for
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    Reasons For

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    Reason for
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    • 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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    Reasons Against

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    • 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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    Related

    Boolos demonstrated that second-order logic with standard semantics presupposes ...Modern type theory and stratified comprehension avoid paradox without assuming f...Predicate abstraction allows formation of sets from any formula without restrict...Predicate abstraction can be interpreted proof-theoretically as syntactic rules ...
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    Quine showed that naive comprehension commits us to entities (classes/sets) not ...The Cantor-Lawvere principle (CL) is a theorem of first-order logic, not depende...The distinction between logical framework and ontological commitment is clearer ...

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