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
    Thus the argument establishes only that no *symmetric* pr... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→A symmetric function defined on a set of pairs cannot be a choice function on that set

    Thus the argument establishes only that no *symmetric* procedure suffices, which is precisely what motivates AC as an independent axiom, not a refutation of choice functions per se.

    ?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

    Axiom of Choice (AC)(as used in mathematics and logic)
    A fundamental rule in mathematics that says if you have a collection of non-empty sets, you can always pick one item from each set, even if there's no specific rule for how to pick.
    choice functions(Formal semantics of indefinites)
    Functions that select a member from a set, used as a semantic mechanism to account for the scopal behavior of indefinites without syntactic movement
    independent axiom(as used in logic and mathematics)
    A basic assumption or rule that cannot be proven true or false using other axioms—it has to be accepted on its own.
    refutation(SR 6 168a37)
    A proof of the contradictory of the thesis maintained by the answerer
    symmetric procedure

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    (as used in logic and set theory)
    A method or process that treats all options or cases equally, without favoring one over another.

    Connections

    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    A symmetric function defined on a set of pairs cannot be a choice function on th...

    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