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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
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    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Russell's paradox can be derived without appealing to the principle of Excluded Middle

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The paradox can be reformulated using the Law of Non-contradiction instead of Excluded Middle
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    • 2.From the definition of R, it follows that R ∈ R ≡ ~(R ∈ R)
      ?

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    • 3.From R ∈ R ≡ ~(R ∈ R), we can derive R ∈ R ⊃ ~(R ∈ R)
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Brouwer's intuitionism accepts the derivation of contradiction from R ∈ R ≡ ~(R ∈ R) without invoking Excluded Middle.
      ?

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    • 2.Intuitionistic logic validates ex contradictione sequitur quodlibet, so the paradox's explosive force survives without LEM.
      ?

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    • 3.Dummett's proof-theoretic semantics confirms that Russell's contradiction is constructively derivable from Comprehension alone.
      ?

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    Reason against 2 of 2
    ?
    • 1.Thierry Coquand showed in constructive type theory that the Burali-Forti and Russell paradoxes arise without classical logic.
      ?

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    • 2.The biconditional R ∈ R ≡ ~(R ∈ R) entails absurdity in minimal logic, which is strictly weaker than intuitionistic logic.
      ?

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