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
    A type-theoretical formal property theory can be construc... — Carmelics
    Home/Philosophy of Language
    HistoryEditSee Inverse

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

    Philosophy of LanguageTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.If a predicate can be predicated of another predicate only when the former is of a higher type than the latter, then self-predication is banished
      ?

      Think about whether this reason is strong or weak

    • 2.Russell's paradox depends on the possibility of self-predication
      ?

      Think about whether this reason is strong or weak

    • 3.If self-predication is banished, Russell's paradox cannot even be formulated
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Type restrictions are stipulative and do not reflect the actual logical structure of predication as it occurs in natural language and thought.
      ?

      Think about whether this reason is strong or weak

    • 2.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.
      ?

      Think about whether this reason is strong or weak

    • 3.Ramsey and Wittgenstein showed that type distinctions, when applied to propositional functions, generate an infinite hierarchy that cannot itself be described within the system without violating its own constraints.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Grelling's paradox and other semantic paradoxes arise independently of Russell's paradox and are not dissolved by type-theoretic restrictions on property self-predication.
      ?

      Think about whether this reason is strong or weak

    • 2.A formal property theory that resolves Russell's paradox through typing while leaving semantic paradoxes intact has not achieved a principled solution but only a piecemeal one.
      ?

      Think about whether this reason is strong or weak

    • 3.Kripke's work on truth demonstrated that paradox-avoidance requires grounding conditions that type theory does not supply, making typing insufficient as a foundational remedy.
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.

    Topics

    Philosophy of LanguageTruth & Knowledge

    Related

    A formal property theory that resolves Russell's paradox through typing while le...Grelling's paradox and other semantic paradoxes arise independently of Russell's...If a formal system avoids paradox only by prohibiting grammatically well-formed ...If a predicate can be predicated of another predicate only when the former is of...
    +5 moreShow less
    If self-predication is banished, Russell's paradox cannot even be formulatedKripke's work on truth demonstrated that paradox-avoidance requires grounding co...Ramsey and Wittgenstein showed that type distinctions, when applied to propositi...Russell's paradox depends on the possibility of self-predicationType restrictions are stipulative and do not reflect the actual logical structur...

    Similar

    The simple theory of types can serve as a prototypical formal property...88%A formal theory of properties requires the ability to express basic fa...82%The full ramified theory of types is not needed to resolve mathematica...78%The simple theory of types, if the principle of extensionality is set ...78%

    Source

    AI-extracted1/3 agreementValid
    SEP: properties
    View source passageHide passage
    Standard second-order logic allows for predicate variables bound by quantifiers. Hence, to the extent that these variables are taken to range over properties, this system could be seen as a formal theory of properties. Its expressive power is however limited, since it does not allow for subject terms that stand for properties. Thus, for example, one cannot even say of a property \(F\) that \(F = F\). This is a serious limitation if one wants a formal tool for a realm of properties whose laws one
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit