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    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 map T on isomorphism types of well-founded extensional relations is not a set function.

    ?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.In NFU and related systems, the Burali-Forti paradox is blocked by stratification, allowing T to be defined as a legitimate set function.
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    • 2.Jensen's consistency proof of NFU demonstrates that type-lowering permits ordinal arithmetic without paradox, undermining the claim's generality.
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    • 3.The claim implicitly assumes a ZF-style cumulative hierarchy, but alternative foundations dissolve rather than inherit the Burali-Forti obstruction.
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    Reason for 2 of 2
    ?
    • 1.Scott's trick in ZFC assigns sets to isomorphism types by selecting rank-minimal representatives, making T a well-defined set function within standard set theory.
      ?

      Think about whether this reason is strong or weak

    • 2.If Scott's trick is applicable, the non-functionality of T is an artifact of naive type-ascent rather than a deep feature of well-founded extensional relations.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The map T sends the isomorphism type of a relation R to the isomorphism type of R^iota, which is one type higher in terms of TST.
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    • 2.There is no reason to believe that T is a function in the usual set-theoretic sense.
      ?

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    • 3.Considerations from the Burali-Forti paradox provide grounds for this conclusion.
      ?

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