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 A disjunction lacking a constructive witness—where we cannot currently prove any single disjunct—fails to constitute genuine mathematical knowledge by intuitionist standards, even if classically valid.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Classical mathematics has successfully solved concrete problems for centuries; restricting knowledge to constructive proofs excludes proven effective methods.
      ?

      Think about whether this reason is strong or weak

    • 2.A disjunction can be mathematically meaningful and knowable without a witness—e.g., we know 'p or not-p' is true by logical principle, not construction.
      ?

      Think about whether this reason is strong or weak

    • 3.Intuitionism conflates epistemology with metaphysics; non-constructive truths may exist independently of our ability to produce witnesses for them.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Mathematical knowledge requires understanding *how* a result holds, not merely that it holds; constructive proof provides this explanatory content.
      ?

      Think about whether this reason is strong or weak

    • 2.A disjunction without a witness leaves us unable to specify which claim is true, making our assertion epistemically incomplete.
      ?

      Think about whether this reason is strong or weak

    • 3.Classical logic's law of excluded middle adds no computational or constructive information, so it shouldn't ground genuine mathematical knowledge.
      ?

      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.