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    Carmelics

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    Made withinDC&Austin
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    Perspectives
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    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The Axiom of Pairing is true for sets

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.P4 assumes a separation-style comprehension schema, but this presupposes a background domain of sets that is itself not justified by the argument.
      ?

      Think about whether this reason is strong or weak

    • 2.The Axiom of Pairing is not derivable from comprehension alone without prior commitment to the existence of a set-forming operation, making P4 question-begging.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Predicativist critics like Poincaré and Weyl hold that definitions quantifying over all sets are impredicative and cannot ground new set existence claims.
      ?

      Think about whether this reason is strong or weak

    • 2.The formula x = a ∨ x = b implicitly quantifies over the totality of sets to isolate {a,b}, making its use in P4 viciously circular on predicativist grounds.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The formula x = a ∨ x = b (where a and b are sets) does not mention sethood
      ?

      Think about whether this reason is strong or weak

    • 2.The formula has only the sets a and b as parameters
      ?

      Think about whether this reason is strong or weak

    • 3.The formula is true only of sets
      ?

      Think about whether this reason is strong or weak

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    Explore the most compelling reason on the other side.