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
    If axiom choice itself depends on conventions shaped by s... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→After geometric axioms are established, it is no longer necessary to resort to sense perceptions in geometric proofs.

    If axiom choice itself depends on conventions shaped by sensorimotor experience, sense perception is never fully expelled from geometric reasoning.

    ?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.Mathematical axioms are chosen by human mathematicians whose conceptual frameworks evolved through embodied interaction with physical space.
      ?

      Think about whether this reason is strong or weak

    • 2.The parallel postulate's historical rejection in some cultures correlates with different spatial intuitions shaped by environmental affordances.
      ?

      Think about whether this reason is strong or weak

    • 3.Even abstract set theory uses spatial metaphors (membership, containment) that originate in sensorimotor schemas of physical objects.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Formal proofs in geometry succeed precisely because they suspend sensory dependence through explicit axiomatization and logical derivation rules.
      ?

      Think about whether this reason is strong or weak

    • 2.Alternative axiom systems (non-Euclidean geometries) are proven consistent despite contradicting sensory intuitions, showing reasoning transcends perception.
      ?

      Think about whether this reason is strong or weak

    • 3.The origin of axiom choice (evolutionary or embodied) is causally distinct from whether those axioms yield objective mathematical truths.
      ?

      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 linkedSkepticism1 linked

    Related

    After geometric axioms are established, it is no longer necessary to resort to s...Alternative axiom systems (non-Euclidean geometries) are proven consistent despi...Even abstract set theory uses spatial metaphors (membership, containment) that o...Formal proofs in geometry succeed precisely because they suspend sensory depende...
    +3 moreShow less
    Mathematical axioms are chosen by human mathematicians whose conceptual framewor...The origin of axiom choice (evolutionary or embodied) is causally distinct from ...The parallel postulate's historical rejection in some cultures correlates with d...

    Details

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