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 correlation that Basic Law V sets up between concepts... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Philosophy of Language
    HistoryEditSee Inverse

    The correlation that Basic Law V sets up between concepts and extensions must be one-to-one.

    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.Basic Law V (Vb) implies that if concepts F and G differ, then the extensions of F and G differ.
      ?

      Think about whether this reason is strong or weak

    • 2.A one-to-one correlation is one in which distinct inputs are mapped to distinct outputs.
      ?

      Think about whether this reason is strong or weak

    • 3.Vb correlates distinct concepts with distinct extensions.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Russell's Paradox shows Basic Law V is inconsistent: the concept 'is not a member of itself' yields a contradictory extension.
      ?

      Think about whether this reason is strong or weak

    • 2.An inconsistent principle cannot establish any well-defined correlation, let alone a one-to-one mapping.
      ?

      Think about whether this reason is strong or weak

    • 3.Therefore, Vb cannot ground a genuine injective function between concepts and extensions in any coherent domain.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Cantor's theorem proves no function from a set S to its powerset P(S) can be surjective, since |P(S)| > |S|.
      ?

      Think about whether this reason is strong or weak

    • 2.If concepts over a domain outnumber objects (extensions are objects for Frege), no injective map from concepts to extensions is globally possible.
      ?

      Think about whether this reason is strong or weak

    • 3.Basic Law V's presupposed one-to-one correlation thus violates a provable cardinality constraint, independently of Russell's Paradox.
      ?

      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 one-to-one correlation is one in which distinct inputs are mapped to distinct ...An inconsistent principle cannot establish any well-defined correlation, let alo...Basic Law V (Vb) implies that if concepts F and G differ, then the extensions of...Basic Law V's presupposed one-to-one correlation thus violates a provable cardin...
    +5 moreShow less
    Cantor's theorem proves no function from a set S to its powerset P(S) can be sur...If concepts over a domain outnumber objects (extensions are objects for Frege), ...Russell's Paradox shows Basic Law V is inconsistent: the concept 'is not a membe...Therefore, Vb cannot ground a genuine injective function between concepts and ex...Vb correlates distinct concepts with distinct extensions.

    Similar

    Basic Law V's requirement of a one-to-one correlation between concepts...95%The correlation between concepts and extensions is one-to-one (distinc...92%The correlation between concepts and extensions established by Basic L...92%Every concept is correlated with some extension (the correlation is to...89%

    Source

    AI-extracted1/3 agreementValid
    SEP: frege-theorem
    View source passageHide passage
    So the contrapositive asserts that if \(\neg \forall x(Fx \equiv Gx)\) then \(\epsilon F \neq \epsilon G\). But in the case where the material equivalence of \(F\) and \(G\) is a sufficient condition for \(F = G\), i.e., in the case where \(F \neq G\) implies \(\neg \forall x(Fx \equiv Gx)\), then Vb implies \(F \neq G \to \epsilon F \neq \epsilon G\), i.e., that if concepts \(F\) and \(G\) differ, the extensions of \(F\) and \(G\) differ. So, the correlation that Basic Law V sets up between co
    Extraction notes

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

    Details

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