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    Carmelics

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

    It is not the case that An infinite (nonstandard) hyperreal exists

    ?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.The saturation principle is only valid within a specific non-standard model constructed via ultrafilter; it is not a general logical truth.
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      Think about whether this reason is strong or weak

    • 2.The existence of a non-principal ultrafilter—required to construct hyperreals—cannot be proven in ZF alone and requires the Boolean Prime Ideal Theorem.
      ?

      Think about whether this reason is strong or weak

    • 3.Mathematical existence claims that depend on axioms independent of ZF do not establish existence in any robust ontological sense.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Wittgenstein's finitist critique holds that infinitary mathematical objects are not discovered but are artifacts of notational extension without determinate reference.
      ?

      Think about whether this reason is strong or weak

    • 2.If 'a > n for every natural number n' can only be verified schema-theoretically and never instancewise, the quantifier range presupposes what it purports to prove.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The saturation principle applies to the hyperreal line
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      Think about whether this reason is strong or weak

    • 2.The saturation principle implies the existence of a hyperreal a such that a > n for every natural number n
      ?

      Think about whether this reason is strong or weak

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    Strongest counterpoint
    Explore the most compelling reason on the other side.