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    The claim that Rosser's predicate is unsuitable conflates... — Carmelics
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    Challenges→Rosser's provability predicate cannot be used to formalize the consistency claim in the second incompleteness theorem.

    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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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Rosser's predicate captures consistency by formalizing the absence of contradictory proofs, which is the core philosophical content of consistency.
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    • 2.Multiple formal systems can express the same consistency property through different predicates, so formal derivability details don't determine philosophical validity.
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    • 3.Rosser's construction avoids Gödel's self-reference diagonalization, offering a coherent alternative interpretation of what consistency formally requires.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Rosser's predicate requires complexity assumptions (like provable totality of a fast-growing function) that standard consistency doesn't require philosophically.
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    • 2.The philosophical content of consistency is independent of formal machinery; conflating formal devices with philosophical meaning inverts the explanatory direction.
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    • 3.Rosser's predicate is strictly stronger than classical consistency and proves different theorems, suggesting it captures something philosophically distinct.
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    Key Terms

    Coherent interpretation(as used in philosophy of language and logic)
    A way of understanding or reading a concept that makes sense together as a whole, without internal conflicts or confusion.
    Formal derivability(mathematical logic)
    The ability to prove something is true by following the strict rules and step-by-step logical steps of a formal system, like solving a math proof.
    Rosser's predicate(as used in mathematical logic)
    A logical tool created by mathematician J. Barkley Rosser that defines consistency (the quality of having no contradictions) in a different way than the standard definition, while still capturing the same essential idea.
    consistency(Syntactic concept in many-sorted logic)
    The syntactic counterpart of satisfiability; corresponds to satisfiability in the same sense as ⊢ corresponds to ⊨

    Connections

    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Multiple formal systems can express the same consistency property through differ...Rosser's construction avoids Gödel's self-reference diagonalization, offering a ...Rosser's predicate captures consistency by formalizing the absence of contradict...Rosser's predicate is strictly stronger than classical consistency and proves di...
    +3 moreShow less
    Rosser's predicate requires complexity assumptions (like provable totality of a ...Rosser's provability predicate cannot be used to formalize the consistency claim...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    The philosophical content of consistency is independent of formal machinery; con...