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

    It is not the case that Internal categoricity proofs presuppose a metatheory in which 'all models' is itself interpreted, reintroducing the same semantic commitments.

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

    Reasons For

    1 perspective
    Reason for
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    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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