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    The supporting argument's use of de Morgan's Laws implici... — Carmelics
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    Challenges→∀x[P(x) → D(x)] is equivalent to ¬∃x[P(x) ∧ ¬D(x)]

    The supporting argument's use of de Morgan's Laws implicitly invokes double negation elimination, which is intuitionistically inadmissible and thus smuggles in a non-neutral logical commitment.

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    Reasons For

    1 perspective
    Reason for
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    • 1.De Morgan's Laws require that ¬(A ∧ B) equals (¬A ∨ ¬B), which demands double negation elimination to derive constructive content from negations.
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    • 2.Intuitionionism rejects double negation elimination because it treats ¬¬P as epistemically weaker than P, making classical logical equivalences unjustified.
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    • 3.Using classical logic rules without acknowledging their non-neutral commitments misrepresents arguments as logically neutral when they embed specific metaphysical assumptions.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.De Morgan's Laws hold in intuitionistic logic without invoking double negation: ¬(A ∧ B) → (¬A ∨ ¬B) is intuitionistically valid regardless of eliminability concerns.
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    • 2.Applying classical logical forms is not inherently 'smuggling' commitments—it's transparent methodology; the real issue is whether intuitionistic constraints are justified as neutral.
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    • 3.Calling classical logic 'non-neutral' assumes intuitionionism is the neutral baseline, but constructivity is itself a substantive philosophical commitment, not a default.
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    Key Terms

    Double negation elimination(as an implicit assumption in the argument)
    The logical principle that saying 'it is not the case that it's not raining' is the same as saying 'it is raining'—removing two negatives to get a positive.
    Intuitionistically inadmissible(describing a logical move that intuitionism rejects)
    Not allowed or acceptable according to intuitionism, a school of logic that is stricter about what counts as valid reasoning than standard logic.
    Non-neutral logical commitment(the hidden bias the critic is accusing the argument of having)
    An assumption about which logical rules are valid that secretly favors one side of a debate rather than staying impartial.
    de Morgan's Laws
    Laws concerning the relations between negation, disjunction, and conjunction
    intuitionism(Mill's characterisation of a target he rejected; linked to conservative deference to inherited belief)
    The view that anything a person believes deeply enough must be true, such that conviction itself is taken as justification.

    Connections

    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Applying classical logical forms is not inherently 'smuggling' commitments—it's ...Calling classical logic 'non-neutral' assumes intuitionionism is the neutral bas...De Morgan's Laws hold in intuitionistic logic without invoking double negation: ...De Morgan's Laws require that ¬(A ∧ B) equals (¬A ∨ ¬B), which demands double ne...
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    Intuitionionism rejects double negation elimination because it treats ¬¬P as epi...Using classical logic rules without acknowledging their non-neutral commitments ...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    ∀x[P(x) → D(x)] is equivalent to ¬∃x[P(x) ∧ ¬D(x)]