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 sound calculus is necessary for any useful deductive sy... — Carmelics
    Home/Truth & Knowledge
    HistoryEditSee Inverse

    A sound calculus is necessary for any useful deductive system

    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.A calculus must never allow erroneous reasonings
      ?

      Think about whether this reason is strong or weak

    • 2.A calculus must not drive us from true hypotheses to false conclusions
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Paraconsistent logics (Priest, da Costa) derive useful conclusions from inconsistent premises without trivializing, yet are technically unsound by classical standards.
      ?

      Think about whether this reason is strong or weak

    • 2.Usefulness in deductive systems is measured by inferential productivity and domain applicability, not solely by preservation of truth across all models.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Gödel's incompleteness theorems demonstrate that any sufficiently powerful sound calculus must be incomplete, sacrificing derivability of true statements.
      ?

      Think about whether this reason is strong or weak

    • 2.A system that cannot prove all truths of its domain fails a core criterion of usefulness, making soundness and usefulness stand in irreducible tension.
      ?

      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

    Related

    A calculus must never allow erroneous reasoningsA calculus must not drive us from true hypotheses to false conclusionsA system that cannot prove all truths of its domain fails a core criterion of us...Gödel's incompleteness theorems demonstrate that any sufficiently powerful sound...
    +2 moreShow less
    Paraconsistent logics (Priest, da Costa) derive useful conclusions from inconsis...Usefulness in deductive systems is measured by inferential productivity and doma...

    Similar

    A deductive calculus must be sound to be useful.93%Lambda-calculus is a formal system with rich interconnections with pro...80%PDL's calculus is sound and complete only in the weak sense.79%Without soundness, a calculus may derive false conclusions from true h...79%

    Source

    AI-extracted1/3 agreementValid
    SEP: logic-many-sorted
    View source passageHide passage
    , determining validity, or equivalently, testing for satisfiability of given formulas) for many-sorted logic is undecidable. So, we are in the same situation encountered in one-sorted first-order logic. Of course, if a calculus is to be helpful it would never allow erroneous reasonings: it is not going to drive us from true hypotheses to false conclusions. It must be a sound calculus. Further, it is highly desirable that all the consequences of a set \(\Gamma\) of hypotheses could be derived fr
    Extraction notes

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

    Details

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