Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

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

    It is not the case that Internal categoricity provides a bridge between full semantics and Henkin semantics, showing that full semantics does not monopolize categoricity.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Internal categoricity proofs presuppose a metatheory in which 'all models' is itself interpreted, reintroducing the same semantic commitments.
      ?

      Think about whether this reason is strong or weak

    • 2.Väänänen and Wang (2015) demonstrate that internal categoricity results are only as strong as the background set-theoretic assumptions sustaining the metatheory.
      ?

      Think about whether this reason is strong or weak

    • 3.Therefore, internal categoricity does not escape but merely relocates the dependence on a privileged semantic framework.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Henkin semantics permits non-standard comprehension axioms, meaning 'categoricity' within Henkin models tracks structural properties relative to those axiom schemes, not an absolute notion.
      ?

      Think about whether this reason is strong or weak

    • 2.A result showing categoricity across both full and Henkin semantics conflates two distinct senses of categoricity that differ in their mathematical and philosophical import.
      ?

      Think about whether this reason is strong or weak

    • 3.Distinguishing these senses, as Shapiro's 1991 work on foundations of mathematics demands, reveals that the bridge claim equivocates rather than unifies.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Internal categoricity is defined proof-theoretically and therefore behaves the same way in both full and Henkin models.
      ?

      Think about whether this reason is strong or weak

    • 2.Full semantics is a limit case of Henkin semantics.
      ?

      Think about whether this reason is strong or weak

    • 3.Classical second-order sentences characterizing arithmetic and analysis are internally categorical under both interpretations.
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.