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 that geometry, including the topology of ... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→In a continuous manifold, the concept of the manifold and its continuity properties can be separated from its metrical structure.

    Poincaré argued that geometry, including the topology of continuous space, is chosen by convention relative to coordinated physical laws, making pure topological facts theory-laden.

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

    No one has weighed in yet. Be the first to share reasons for or against this statement.

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

    Key Terms

    Poincaré(as the scientist whose work is being referenced)
    Henri Poincaré was a French mathematician and physicist (1854-1912) who discovered that tiny, unmeasurable changes in a system's starting conditions can lead to completely different outcomes—a key insight that helped create chaos theory.
    Theory-laden(in epistemology (theory of knowledge))
    Already shaped by or dependent on particular assumptions and theories you've already accepted, rather than being purely objective or neutral.
    Topology(as used in mathematics and philosophy)
    The mathematical study of how shapes and spaces are structured, focusing on properties that don't change when you stretch or deform something (like how a coffee mug and donut are topologically the same).
    continuous space(Islamic theological debate on the structure of space)
    Space as an open continuous expanse, not composed of discrete cells.

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    convention(Used to distinguish mere regularities from convention-governed regularities in the analysis of meaning.)
    A regularity that obtains because there is something akin to an agreement among a group of people to keep the regularity in place.
    geometry(Abstract view following the acceptance of non-Euclidean and Riemannian geometries)
    Whatever can be described within the Riemannian formalism; an abstract structure defined by a consistent metric, not necessarily tied to physical or Euclidean space.

    Connections

    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    In a continuous manifold, the concept of the manifold and its continuity propert...

    Details

    Type
    claim
    Perspectives
    0 (0 for, 0 against)
    Edits
    1 edit

    Open for perspectives

    This idea is waiting for its first supporting or challenging perspective.

    Share the first perspective