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 nominalist is unable to account for the common features of certain rearrangements that can only be explained by reference to a common mathematical structure.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.There exist simple game examples between two players where certain rearrangements share common features.
      ?

      Think about whether this reason is strong or weak

    • 2.These common features can only be explained by reference to a common mathematical structure of the rearrangements.
      ?

      Think about whether this reason is strong or weak

    • 3.The realist, unlike the nominalist, can appeal to mathematical structures as real entities to ground such explanations.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Hilary Putnam's indispensability argument shows mathematical structures appear in the best explanations of physical phenomena across multiple domains.
      ?

      Think about whether this reason is strong or weak

    • 2.Nominalist paraphrase strategies (Field 1980) cannot preserve the explanatory unity that identical mathematical structures provide across structurally isomorphic physical systems.
      ?

      Think about whether this reason is strong or weak

    • 3.When two distinct physical arrangements share identical symmetry properties, only appeal to a common abstract structure explains why the same invariants appear in both.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Structural explanation requires that the explanandum be derivable from features shared across instances, which abstract mathematical structures uniquely supply.
      ?

      Think about whether this reason is strong or weak

    • 2.Alan Baker's enhanced indispensability argument demonstrates that mathematical objects do genuine explanatory work irreducible to nominalist metalinguistic or modal reformulations.
      ?

      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.