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    Internal categoricity proofs presuppose a metatheory in w... — Carmelics
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    Challenges→Internal categoricity provides a bridge between full semantics and Henkin semantics, showing that full semantics does not monopolize categoricity.

    Internal categoricity proofs presuppose a metatheory in which 'all models' is itself interpreted, reintroducing the same semantic commitments.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Quantifying over 'all models' requires fixing a domain; any domain choice imports semantic assumptions into the metatheory.
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    • 2.Internal categoricity proofs cannot avoid mentioning models; mentioning models requires a language interpreted in some structure.
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    • 3.The regress problem: explaining 'all models' requires a metatheory; explaining that metatheory requires a meta-metatheory, ad infinitum.
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    Reasons Against

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    Reason against
    ?
    • 1.A metatheory can treat 'all models' syntactically (proof-theoretically) without semantic commitment to any particular domain.
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    • 2.Reintroduction of commitments is not vicious if the metatheory's commitments are weaker or different in kind from the object theory's.
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    • 3.Internal categoricity succeeds if it establishes uniqueness up to isomorphism; semantic grounding of the metatheory is orthogonal to this result.
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    Connections

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    Proof of definition segments1 linkedTruth & Knowledge1 linked

    Related

    A metatheory can treat 'all models' syntactically (proof-theoretically) without ...Internal categoricity proofs cannot avoid mentioning models; mentioning models r...Internal categoricity provides a bridge between full semantics and Henkin semant...Internal categoricity succeeds if it establishes uniqueness up to isomorphism; s...
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    Quantifying over 'all models' requires fixing a domain; any domain choice import...Reintroduction of commitments is not vicious if the metatheory's commitments are...The regress problem: explaining 'all models' requires a metatheory; explaining t...

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    2 (1 for, 1 against)
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