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    Interpretability is a good criterion for fixing a compari... — Carmelics
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    Home/Philosophy of Language
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    Interpretability is a good criterion for fixing a comparison between theories T and T'

    Philosophy of Language
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Interpretability is characterized either in terms of uniform definability of models or the existence of an interpretation map which preserves logical form and provability
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    • 2.Interpretability is helpful for proving consistency, as T' is proved consistent when interpreted in a consistent T
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Interpretability is not symmetric: T interpreting T' does not imply T' interprets T, so it cannot ground mutual comparison.
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    • 2.Quine argued that ontological reduction via proxy functions shows interpretability preserves structure but not ontological equivalence.
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    • 3.Two theories can be mutually interpretable yet be fundamentally different in their ontological commitments, undermining interpretability as a neutral comparator.
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    Reason against 2 of 2
    ?
    • 1.Visser and Lindström demonstrated that mutual interpretability strictly weaker than synonymy, so interpretability underdetermines theoretical identity.
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    • 2.Consistency preservation via interpretation conflates proof-theoretic strength with truth, a distinction central to Gödel's incompleteness results.
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    Topics

    Philosophy of LanguageTruth & Knowledge

    Connections

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    Proof of definition segments1 linked

    Related

    Consistency preservation via interpretation conflates proof-theoretic strength w...Interpretability is characterized either in terms of uniform definability of mod...Interpretability is helpful for proving consistency, as T' is proved consistent ...Interpretability is not symmetric: T interpreting T' does not imply T' interpret...
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    Quine argued that ontological reduction via proxy functions shows interpretabili...Two theories can be mutually interpretable yet be fundamentally different in the...Visser and Lindström demonstrated that mutual interpretability strictly weaker t...

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    SEP: logic-many-sorted
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    Interpretability is a good criterion for fixing a comparison between theories \(T\) and \(T^{\prime }\), for it is characterized either in terms of “uniform definability of models” or of “the existence of an interpretation map which preserves logical form and provability” (Mceldowney 2020: 15). It is also helpful for proving consistency, as \(T^{\prime }\) is proved to be consistent when interpreted in a consistent \(T\). However, interpretability between theories of a many-sorted signature does
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    Details

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