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
    Deriving infinity as a theorem by embedding its content i... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→Infinity is a theorem of NF rather than an axiom

    Deriving infinity as a theorem by embedding its content into stratification constraints smuggles infinitary commitments into the logical syntax rather than genuinely avoiding them.

    ?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

    Commitments(as part of your mental states to review)
    Things you've decided to believe in or stand by—like moral principles or goals you're dedicated to.
    Infinity/Infinitary(as used in logic and mathematics)
    The concept of something without limits or bounds—like numbers that go on forever. 'Infinitary' means relating to or involving infinity.
    Logical Syntax(as used in logic and philosophy of language)
    The formal rules and structure of a language, focusing on how symbols and statements are arranged and combined, without worrying about what they mean.
    Smuggles in/Smuggling(as used in philosophical argumentation)
    To introduce something indirectly or hidden, rather than openly stating it—implying deception or sleight of hand.
    Stratification constraints

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    (as used in set theory)
    Special rules in NF that limit which objects can be combined into sets by requiring them to fit into strict organizational layers or ranks.
    Theorem
    A theorem is a statement that has been proven to be true through logical reasoning and evidence. It's a fact that mathematicians or scientists have carefully verified using step-by-step arguments, starting from things already known to be true. Once proven, theorems become reliable building blocks that others can use to prove even more complex ideas.
    embedding(A stronger form of homomorphism between many-sorted structures.)
    A homomorphism between structures in which all defining functions are injective and the relation-preservation condition holds in both directions.

    Connections

    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Infinity is a theorem of NF rather than an axiom

    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