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 Hume's Principle is consistent (can be consistently added to second-order logic), unlike Basic Law V

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Hume's Principle, while consistent, is not logically innocent: it carries substantial ontological commitments to infinitely many abstract objects.
      ?

      Think about whether this reason is strong or weak

    • 2.A principle that entails the existence of infinitely many objects cannot be treated as a mere logical truth or analytic definition.
      ?

      Think about whether this reason is strong or weak

    • 3.Frege's Neo-Logicist program fails if its foundational principle is synthetic rather than analytic, undermining the epistemological motivation for the consistency result.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.George Boolos argued that second-order logic is itself ontologically committal, smuggling set-theoretic assumptions into the metatheory.
      ?

      Think about whether this reason is strong or weak

    • 2.Demonstrating consistency of Hume's Principle within second-order logic inherits whatever foundational problems afflict second-order logic itself.
      ?

      Think about whether this reason is strong or weak

    • 3.The consistency proof thus presupposes a mathematical framework of comparable strength to what it aims to ground, making the result epistemically circular.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Hume's Principle only requires a many-to-one correlation between concepts and numbers, not a one-to-one correlation
      ?

      Think about whether this reason is strong or weak

    • 2.Basic Law V's requirement of a one-to-one correlation between concepts and extensions is problematic (leads to contradiction)
      ?

      Think about whether this reason is strong or weak

    • 3.Several authors have independently developed models demonstrating that Hume's Principle can be consistently added to second-order logic
      ?

      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.