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
    Poincaré argued in 'Science and Hypothesis' that geometri... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→Metric properties of a geometry can be defined intrinsically using projective invariants rather than by convention from a numerical manifold.

    Poincaré argued in 'Science and Hypothesis' that geometric axioms are conventions, not truths, so privileging one conic over others requires extra-projective justification.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Euclidean, hyperbolic, and elliptic geometries are all logically consistent, suggesting axioms describe possible worlds, not necessary truths.
      ?

      Think about whether this reason is strong or weak

    • 2.Within projective geometry, all conics are equivalent under projective transformations, so selecting one requires criteria external to projection itself.
      ?

      Think about whether this reason is strong or weak

    • 3.Physics required non-Euclidean geometry to describe spacetime, confirming axioms reflect conventional choices rather than absolute reality.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Some geometric properties are invariant across all consistent axiom systems, suggesting deeper truths about structure independent of convention.
      ?

      Think about whether this reason is strong or weak

    • 2.Conics possess distinct metric and topological properties (closed vs. open) that constrain which can serve equivalent roles in physical descriptions.
      ?

      Think about whether this reason is strong or weak

    • 3.Calling axioms 'conventions' conflates logical independence with epistemic arbitrariness—choice doesn't entail all choices are equally justified.
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

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

    Connections

    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Calling axioms 'conventions' conflates logical independence with epistemic arbit...Conics possess distinct metric and topological properties (closed vs. open) that...Euclidean, hyperbolic, and elliptic geometries are all logically consistent, sug...Metric properties of a geometry can be defined intrinsically using projective in...
    +3 moreShow less
    Physics required non-Euclidean geometry to describe spacetime, confirming axioms...Some geometric properties are invariant across all consistent axiom systems, sug...Within projective geometry, all conics are equivalent under projective transform...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit