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 Va direction of Basic Law V is not problematic. — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Truth & Knowledge
    HistoryEditSee Inverse

    The Va direction of Basic Law V is not problematic.

    Proof of definition segmentsTruth & 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.Va only entails that distinct extensions are correlated with distinct concepts, which is a functional constraint on concept-to-extension mapping.
      ?

      Think about whether this reason is strong or weak

    • 2.Distinct concepts may still be correlated with the same extension under Va, leaving room for non-injective mappings without contradiction.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Va presupposes that every concept has a determinate extension, smuggling in an existential commitment that cannot be taken for granted.
      ?

      Think about whether this reason is strong or weak

    • 2.Frege's own system shows that unrestricted concept-to-extension mapping generates contradictions, so Va's 'functional constraint' inherits this instability.
      ?

      Think about whether this reason is strong or weak

    • 3.A direction principle that assumes the coherence of its domain objects cannot be deemed unproblematic when that coherence is precisely what is at issue.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Boolos argued that the Va direction still relies on the same impredicative comprehension principles that make Basic Law V as a whole inconsistent.
      ?

      Think about whether this reason is strong or weak

    • 2.Separating Va from Vb obscures that both directions jointly constitute a biconditional whose left-to-right reading cannot be evaluated without invoking the full problematic law.
      ?

      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

    Truth & KnowledgeProof of definition segments

    Connections

    2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    A direction principle that assumes the coherence of its domain objects cannot be...Boolos argued that the Va direction still relies on the same impredicative compr...Distinct concepts may still be correlated with the same extension under Va, leav...Frege's own system shows that unrestricted concept-to-extension mapping generate...
    +3 moreShow less
    Separating Va from Vb obscures that both directions jointly constitute a bicondi...Va only entails that distinct extensions are correlated with distinct concepts, ...Va presupposes that every concept has a determinate extension, smuggling in an e...

    Similar

    Ascribing a straight contradiction to Aristotle should be avoided if p...74%If there exists even one such case, the necessity direction of (MA) fa...74%Meaningful expressions have correctness conditions essentially, as cap...70%Peano Arithmetic (PA) is consistent.70%

    Source

    AI-extracted1/3 agreementValid
    SEP: frege-theorem
    View source passageHide passage
    So the contrapositive asserts that if \(\epsilon F \neq \epsilon G\), then \(\neg \forall x(Fx \equiv Gx)\). But in the case where the material equivalence of \(F\) and \(G\) is a necessary condition for \(F = G\), i.e., in the case where \(\neg \forall x(Fx \equiv Gx)\) implies \(F \neq G\), then Va implies that if \(\epsilon F \neq \epsilon G\), then \(F \neq G\), i.e., that whenever the extensions of \(F\) and \(G\) differ, the concepts with which they are correlated, namely \(F\) and \(G\),
    Extraction notes

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

    Details

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