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
    The metatheoretic variation Cohen's forcing reveals is a ... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→The semantics of second-order logic depend on the metatheory with respect to the Axiom of Choice.

    The metatheoretic variation Cohen's forcing reveals is a pathology of first-order set-theoretic surrogates for second-order semantics, not evidence that second-order semantic content is itself indeterminate.

    ?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

    Cohen(as a reference to mathematical results about axioms)
    Paul Cohen was a mathematician who proved in the 1960s that certain basic assumptions about infinity and sets cannot be proven true or false from the other standard rules of mathematics.
    First-order logic/First-order set theory(as a limited substitute for second-order logic)
    A mathematical logic system that can only talk about individual objects and their properties, not about all possible properties at once.
    Indeterminate(Reichenbach's three-valued quantum logic)
    The value of propositions that quantum theory implies cannot be assessed to be either true or false
    Pathology(describing what the variation Cohen's forcing reveals actually is)
    In this context, a disease or defect in a system—a problem or failure rather than a feature.

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    Second-order semantics/Second-order logic(as the fuller, more complete system that first-order logic is being compared to)
    A more powerful logic system that can quantify over properties and sets themselves, not just individual objects—it's more expressive but also more complicated.
    forcing(set theory)
    A technique in set theory for constructing new models in which certain statements hold or fail, used to prove independence results
    metatheoretic(Used to characterize the role of logical semantics)
    Providing a framework for theorizing about the relationship between symbols (used externally in language and internally in thought) and the world, rather than positing cognitive entities for computational manipulation
    semantic content(Cappelen and Lepore's literalist/minimalist framework)
    Propositions determined solely by conventions of meaning, precisification, disambiguation, and reference fixing — not by pragmatic inference.

    Connections

    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    The semantics of second-order logic depend on the metatheory with respect to the...

    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