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 Frege's Basic Law V cannot be true

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Frege's Basic Law V commits to the existence of a set for every predicate
      ?

      Think about whether this reason is strong or weak

    • 2.The predicate 'x is not a member of itself' is a well-formed predicate
      ?

      Think about whether this reason is strong or weak

    • 3.If Basic Law V holds, there must exist a set R of all sets that are not members of themselves
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Frege's own logicism required extensions to be logical objects, but Russell's paradox shows no coherent domain of logical objects can satisfy unrestricted comprehension.
      ?

      Think about whether this reason is strong or weak

    • 2.Dummett's analysis in 'Frege: Philosophy of Mathematics' demonstrates Basic Law V cannot be rescued by restricting extensions without abandoning the logicist program entirely.
      ?

      Think about whether this reason is strong or weak

    • 3.Any consistent fragment of Basic Law V (e.g., New Foundations or Hume's Principle) requires abandoning the universality that made Basic Law V philosophically significant to Frege.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Boolos showed in 'The Consistency of Frege's Foundations of Arithmetic' that arithmetic can be recovered from Hume's Principle without Basic Law V, confirming Basic Law V is the locus of contradiction.
      ?

      Think about whether this reason is strong or weak

    • 2.If Basic Law V were true, the formal system of Grundgesetze would be consistent, but Frege himself conceded in his appendix to Grundgesetze Vol. II that Russell's paradox destroys the system's foundations.
      ?

      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.