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 relational generalization of CL is second-order in na... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Philosophy of Language
    HistoryEditSee Inverse

    The relational generalization of CL is second-order in nature, unlike CL itself

    Philosophy of Language
    ?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.CL applies to functions and is a principle of first-order logic
      ?

      Think about whether this reason is strong or weak

    • 2.The generalization of CL to arbitrary relations requires quantification over relations, which is second-order
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Relational generalizations can be expressed via higher-order typed lambda calculi where relations are first-class objects at the base type level.
      ?

      Think about whether this reason is strong or weak

    • 2.Church's own type theory (STT) encodes relations as functions to truth values, collapsing the first/second-order distinction within a typed framework.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Quine argued that second-order logic is 'set theory in sheep's clothing,' meaning purportedly second-order quantification over relations reduces to first-order quantification over sets.
      ?

      Think about whether this reason is strong or weak

    • 2.If relational quantification is reinterpreted as first-order quantification over set-theoretic proxies, the generalization of CL need not be genuinely second-order in logical kind.
      ?

      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

    Connections

    1 topic

    Modality & Possibility1 linked

    Related

    CL applies to functions and is a principle of first-order logicChurch's own type theory (STT) encodes relations as functions to truth values, c...If relational quantification is reinterpreted as first-order quantification over...Quine argued that second-order logic is 'set theory in sheep's clothing,' meanin...
    +2 moreShow less
    Relational generalizations can be expressed via higher-order typed lambda calcul...The generalization of CL to arbitrary relations requires quantification over rel...

    Similar

    The generalization of CL to arbitrary relations requires quantificatio...82%Truth in second-order logic ('M ⊨_s φ') is not an absolute property re...76%For second-order logic, while 'φ is a second-order formula', 'M is an ...75%F directly corresponds to one relational concept and G directly corres...75%

    Source

    AI-extracted1/3 agreementValid
    SEP: church
    View source passageHide passage
    It’s worth mentioning, firstly, that this principle underlies diagonal argumentation in general (cf. Gaifman 2006). Even venerable examples such as Post’s informal argument that there is a recursively enumerable set of positive integers whose complement is not recursively enumerable, rely in essence on CL (Davis 1965: 312). A slight variant of CL is frequently found in the literature on undecidability (cf. Shoenfield 1967: 131). Secondly, the proof of CL does not rely essentially on any axiom
    Extraction notes

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

    Details

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