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
    A general choice function over all non-empty sets require... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→A choice function exists in constructive mathematics

    A general choice function over all non-empty sets requires selecting from collections with no computable or definable structure.

    ?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.The Axiom of Choice applies to arbitrary collections, including those lacking definable well-orderings or computable selection rules.
      ?

      Think about whether this reason is strong or weak

    • 2.Many infinite sets (e.g., uncountable ordinals) have no recursive structure enabling mechanical selection from their powersets.
      ?

      Think about whether this reason is strong or weak

    • 3.If choice functions required computability, they'd fail for most transfinite collections—contradicting AC's logical independence from ZF.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.For practical or constructive mathematics, choice functions only need apply to sets we can actually describe or enumerate.
      ?

      Think about whether this reason is strong or weak

    • 2.The claim conflates logical existence (via AC) with epistemological availability—a choice function needn't be constructible to exist abstractly.
      ?

      Think about whether this reason is strong or weak

    • 3.Many standard choice functions (lexicographic, cardinality-based) *do* rely on definable structure, weakening the necessity claim.
      ?

      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 linkedPhilosophy of Language1 linked

    Related

    A choice function exists in constructive mathematicsFor practical or constructive mathematics, choice functions only need apply to s...If choice functions required computability, they'd fail for most transfinite col...Many infinite sets (e.g., uncountable ordinals) have no recursive structure enab...
    +3 moreShow less
    Many standard choice functions (lexicographic, cardinality-based) *do* rely on d...The Axiom of Choice applies to arbitrary collections, including those lacking de...The claim conflates logical existence (via AC) with epistemological availability...

    Details

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