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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    321,452
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    42
    Home/Original/inverse
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    Inverse View

    It is not the case that Feferman (1960) demonstrated that the choice of provability predicate is conventional, since differently defined but extensionally equivalent predicates yield divergent unprovability results.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Divergent unprovability results from different predicates indicate they are not truly extensionally equivalent, suggesting Feferman's premise is flawed.
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    • 2.Unprovability relative to a *specific system* is objective once the system is fixed; conventionality of representation doesn't undermine this objectivity.
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    • 3.Mathematical facts about what is unprovable in PA remain invariant regardless of how we notate provability—convention affects expression, not truth.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Extensionally equivalent predicates can differ in syntactic structure, enabling different Gödel sentences with divergent provability statuses.
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    • 2.Provability is not a direct physical property but a formal relation, so its definition depends on representational choices within formal systems.
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    • 3.If two predicates prove identical sentences yet yield different unprovability results, then unprovability cannot be a purely objective mathematical fact.
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