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 The symmetry possessed by a geometric object F is described exactly by the subgroup of spatial automorphisms that leave F invariant

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Symmetry is an intrinsic structural property of F, not a relation between F and the ambient space of automorphisms.
      ?

      Think about whether this reason is strong or weak

    • 2.Weyl's automorphism-group account makes symmetry extrinsically dependent on the choice of background space, which can vary without any change to F itself.
      ?

      Think about whether this reason is strong or weak

    • 3.Hermann Weyl's own later work on the hole argument suggests that identifying geometric objects with their embedding space conflates intrinsic and extrinsic structure.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.A geometric object can possess continuous or approximate symmetries that no discrete subgroup of spatial automorphisms captures exactly (Nozick's objection to structural definitions).
      ?

      Think about whether this reason is strong or weak

    • 2.The subgroup description presupposes a determinate point-set identity for F, but objects individuated by their symmetries face a circularity: identity conditions presuppose the very group structure they are meant to explain.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.A geometric object F is a point set with a definite relational structure
      ?

      Think about whether this reason is strong or weak

    • 2.Those automorphisms of space that leave F invariant constitute a group
      ?

      Think about whether this reason is strong or weak

    • 3.That group captures precisely which transformations preserve all the relations constitutive of F
      ?

      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.