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 R can be reconstructed under stratified comprehension ... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→The Russell class R cannot be a member of any class (i.e., R must be a proper class).

    If R can be reconstructed under stratified comprehension as a legitimate set within NF, then labeling R a 'proper class' reflects one axiomatic choice, not an ontological necessity.

    ?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

    Axiomatic choice(as used in logic and philosophy of mathematics)
    A decision about which basic rules or assumptions to accept as the foundation of a logical system (like choosing which game rules to play by).
    NF (New Foundations)(a formal mathematical framework)
    A system for organizing mathematical objects (like numbers and sets) that uses special rules to avoid logical contradictions that plagued earlier systems.
    Ontological necessity(contrasted with things that exist but didn't have to)
    Something that must exist by its very nature, as opposed to something that just happens to exist; a thing that could never fail to exist.
    Ontology(Carnap argues this enterprise is based on a mistake)
    The philosophical discipline that tries to answer hard questions about what there really is.

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    Reconstructed(as used in describing how consciousness works)
    Built or put back together again, often after the fact—suggesting the memory or awareness is being reassembled rather than being directly available.
    Stratified comprehension(as used in set theory, particularly in the NF system)
    A rule for creating sets that arranges elements in layers or levels to avoid logical contradictions (think of it as a safety system to prevent broken definitions).
    proper class(If the iterative process never terminated, the union of all generated chains would form a proper class, contradicting the assumption that P is a set.)
    A collection of sets that is too large to itself be a set in the relevant set-theoretic framework.
    set(von Neumann's class theory)
    A class that is a member (of some class).

    Connections

    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    The Russell class R cannot be a member of any class (i.e., R must be a proper cl...

    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