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    Carmelics

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

    It is not the case that Certain paradoxes arise from attempting to form an illegitimate totality by collecting into a single totality a collection whose members presuppose the existence of that totality

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Russell's paradox is dissolved by type theory without invoking 'illegitimate totalities'—the restriction is syntactic, not metaphysical.
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    • 2.Zermelo-Fraenkel set theory blocks paradox via the axiom schema of separation without presupposing any notion of self-presupposing collections.
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    • 3.The 'illegitimate totality' diagnosis is one interpretive gloss among several, not a discovered metaphysical fact about why paradoxes arise.
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    Reason for 2 of 2
    ?
    • 1.Priest's dialetheism accepts that some contradictions—including the Liar—are true, rendering paradox-avoidance an optional rather than mandatory theoretical virtue.
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    • 2.If contradictions arising from totalities can be tolerated within paraconsistent logic, the claim that such totalities are 'illegitimate' loses its normative force.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The set of all non-self-membered sets is a member of itself if and only if it is not a member of itself
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    • 2.The sentence 'This sentence is false' is true if and only if it is false
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    • 3.These contradictions result from treating a self-presupposing collection as a completed whole
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    Strongest counterpoint
    Explore the most compelling reason on the other side.