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 a formal system avoids paradox only by prohibiting gra... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→A type-theoretical formal property theory can be constructed that avoids Russell's paradox

    If a formal system avoids paradox only by prohibiting grammatically well-formed and intuitively meaningful propositions, it has not solved Russell's paradox but merely quarantined it.

    ?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

    Formal system(as used in logic and mathematics)
    A set of rules and symbols (like mathematical axioms) that you use to prove whether statements are true or false, similar to how a chess game has specific rules that determine what moves are legal.
    Russell's paradox(Independently discovered by Zermelo and Russell)
    The paradox of the 'set' of all sets that are not members of themselves
    grammatically well-formed(as a quality of propositions)
    A statement that follows all the proper rules of grammar and structure, so it's put together correctly even if it might not make sense.
    intuitively meaningful(as a quality of propositions)
    Something that makes sense to us naturally and obviously, without needing a complicated explanation.
    paradox

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    (R. M. Sainsbury's definition, presented as a target of criticism)
    An apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises
    quarantined(as what happens when paradoxes are prohibited rather than solved)
    Isolated or blocked off to prevent spread, like putting a sick person in isolation—here, it means hiding the problem rather than truly fixing it.

    Connections

    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    A type-theoretical formal property theory can be constructed that avoids Russell...

    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