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
    The two theories have different axioms — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Truth & Knowledge
    HistoryEditSee Inverse

    Part of a larger discussion

    Supports→PM's no-classes theory and ZF set theory cannot simply be compared in terms of their theorems

    The two theories have different axioms

    Proof of definition segmentsTruth & Knowledge
    ?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.

    Topics

    Truth & KnowledgeProof of definition segments

    Connections

    1 topic

    Philosophy of Language3 linked

    Related

    Next step

    Based on where you are in your exploration

    Browse more in Truth & Knowledge
    Related propositions within the same area of thought.
    PM's no-classes theory and ZF set theory cannot simply be compared in terms of t...The languages in which PM and ZF are expressed differ in logical powerThe sentences of PM are expressed in the theory of types, whereas ZF is expresse...

    Similar

    These two hypotheses are logically distinct and neither trivially enta...80%Dynamical theories determine their own logic of possible propositions,...80%If theories are sets of sentences in a particular language, then stati...79%Interpretability is a good criterion for fixing a comparison between t...77%

    Source

    AI-extracted
    SEP: principia-mathematica
    View source passageHide passage
    Strictly as presented in PM, however, the no-classes theory differs significantly from ZF. The sentences of the PM theory are expressed in the theory of types, as opposed to the first order theory of ZF. ZF and PM cannot simply be compared in terms of their theorems. Not only are there different axioms in the two theories, but the very languages in which they are expressed differ in logical power. If we follow Gödel and Boolos, however, the two are seen to be based on the same intuitive basis, a

    Details

    Type
    premise
    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