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 extensionality of classes is a derived result, not a ... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Philosophy of Language
    HistoryEditSee Inverse

    The extensionality of classes is a derived result, not a postulate.

    Modality & Possibility
    ?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.To say something G of the class of Fs is to say there exists a predicative property H coextensive with F such that H is G.
      ?

      Think about whether this reason is strong or weak

    • 2.If F and H are coextensive, then anything true of {x: Fx} will be true of {x: Hx}.
      ?

      Think about whether this reason is strong or weak

    • 3.Extensionality follows from this contextual definition via the logic of properties.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Quine argues in 'Set Theory and Its Logic' that contextual definitions of classes presuppose extensionality to individuate the propositional functions they quantify over.
      ?

      Think about whether this reason is strong or weak

    • 2.If the logic of properties used in P3 already treats coextensive properties as identical, extensionality is a hidden postulate smuggled into the definiens, not derived from it.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Russell's substitutional theory shows that eliminating classes via propositional functions requires intensional distinctions that extensionality actively destroys, making derivation circular.
      ?

      Think about whether this reason is strong or weak

    • 2.A definition that yields extensionality only by collapsing intensional differences between properties does not derive extensionality but stipulates it under a redescription.
      ?

      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 LanguageModality & Possibility

    Related

    A definition that yields extensionality only by collapsing intensional differenc...Extensionality follows from this contextual definition via the logic of properti...If F and H are coextensive, then anything true of {x: Fx} will be true of {x: Hx...If the logic of properties used in P3 already treats coextensive properties as i...
    +3 moreShow less
    Quine argues in 'Set Theory and Its Logic' that contextual definitions of classe...Russell's substitutional theory shows that eliminating classes via propositional...To say something G of the class of Fs is to say there exists a predicative prope...

    Similar

    The simple theory of types, if the principle of extensionality is set ...78%The actual source of the problem in NF is extensionality, not comprehe...75%The Recursion Theorem does not guarantee an extensional fixed point (a...74%Therefore, F ≠ G implies the extension of F ≠ the extension of G.74%

    Source

    AI-extracted1/3 agreementValid
    SEP: logical-construction
    View source passageHide passage
    Russell’s “No-Class” theory of classes from *20 of Principia Mathematica provides a contextual definition like that of the theory of definite descriptions. One of Russell’s early diagnoses of the paradox of the class of all classes that are not members of themselves was that it showed that classes could not be individuals. Indeed Russell seems to have come across his paradox by applying Cantor’s famous diagonal argument to show that there are more classes of individuals than individuals. Hence,
    Extraction notes

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

    Details

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