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    Carmelics

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    Inverse View

    It is not the case that Not all infinite sets have the same cardinality.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Predicativist mathematicians like Poincaré and Weyl reject impredicative definitions, which underlie the construction of the real number continuum.
      ?

      Think about whether this reason is strong or weak

    • 2.Without a predicatively acceptable construction of the reals, the claim that ℝ constitutes a well-defined set of greater cardinality than ℕ cannot be established.
      ?

      Think about whether this reason is strong or weak

    • 3.If the supporting argument's first premise relies on an illegitimate mathematical object, the comparative cardinality claim loses its primary evidential basis.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Cantor's diagonal argument presupposes that completed infinite totalities are coherent mathematical objects, which strict finitists like Wittgenstein deny.
      ?

      Think about whether this reason is strong or weak

    • 2.If 'infinite set' does not refer to a well-formed object, cardinality comparisons between such sets are meaningless rather than false.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The positive real numbers have a greater cardinality than the positive integers.
      ?

      Think about whether this reason is strong or weak

    • 2.Both the positive real numbers and the positive integers are infinite sets.
      ?

      Think about whether this reason is strong or weak

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