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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 Russell's paradox is dissolved by type theory without invoking 'illegitimate totalities'—the restriction is syntactic, not metaphysical.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Syntactic rules must ultimately reflect something about reality; distinguishing type levels presupposes a metaphysical structure among collections.
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    • 2.Calling restrictions 'merely syntactic' obscures why those particular rules work—they work because self-membership is genuinely problematic metaphysically.
      ?

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    • 3.Type theory still implicitly rejects certain totalities as illegitimate; relabeling this as 'syntactic' rather than 'metaphysical' is semantic theater.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Type theory's hierarchical syntax prevents self-reference by structural rules alone, avoiding metaphysical assumptions about set existence.
      ?

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    • 2.Syntactic restrictions are more parsimonious: they explain Russell's paradox without positing that some totalities are genuinely illegitimate.
      ?

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    • 3.Type theory successfully formalizes mathematics without metaphysical commitments, proving syntactic solutions suffice for foundational purposes.
      ?

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