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
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The formula (p → q) ∨ p is classically valid because if p is false, conditionals with false antecedents are vacuously true

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Vacuous truth is a formal artifact of material implication, not a feature of genuine conditional reasoning (Anderson & Belnap, Entailment, 1975).
      ?

      Think about whether this reason is strong or weak

    • 2.Relevant logic requires that antecedent and consequent share propositional variables for a conditional to be valid, which p→q need not satisfy.
      ?

      Think about whether this reason is strong or weak

    • 3.Under relevant logic, (p→q)∨p fails when p and q are relevantly independent, undermining the claim's universality.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Intuitionistic logic rejects classical truth-value bivalence, so 'p is false' cannot be assumed whenever 'p fails' (Dummett, Elements of Intuitionism).
      ?

      Think about whether this reason is strong or weak

    • 2.Without bivalence, a false antecedent cannot be established merely from the absence of proof of p, blocking the vacuous truth inference in constructive settings.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.If p fails, p is false
      ?

      Think about whether this reason is strong or weak

    • 2.In classical logic, a conditional with a false antecedent is true
      ?

      Think about whether this reason is strong or weak

    • 3.Therefore (p → q) holds whenever p is false, making (p → q) ∨ p a tautology
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.