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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
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    42
    Home/Original/inverse
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    Inverse View

    It is not the case that Rosser's provability predicate cannot be used to formalize the consistency claim in the second incompleteness theorem.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Rosser's provability predicate satisfies Hilbert-Bernays derivability conditions, which are the standard criteria for legitimate provability predicates.
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    • 2.If a predicate meets the canonical technical criteria for provability, its associated consistency statement is a genuine formalization of consistency.
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    • 3.Therefore, the unprovability of Rosser consistency constitutes a substantive, not merely nominal, consistency result within the second incompleteness framework.
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    Reason for 2 of 2
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    • 1.Feferman (1960) demonstrated that the choice of provability predicate is conventional, since differently defined but extensionally equivalent predicates yield divergent unprovability results.
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    • 2.If the second incompleteness theorem's scope is predicate-relative, then Rosser's predicate reveals the theorem's dependence on representational choices, not a defect in the predicate itself.
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    • 3.The claim that Rosser's predicate is unsuitable conflates a system's formal derivability facts with the philosophical content of consistency, which Rosser's construction legitimately captures under one coherent interpretation.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Using Rosser's provability predicate, one can prove the 'consistency' of a formal system F within F itself.
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    • 2.A provability predicate that allows a system to prove its own consistency is not a suitable formalization of the genuine consistency claim.
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