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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
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    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Nonstandard hyperreals must exist

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Mathematical existence requires only formal consistency within an axiomatic system, not ontological necessity.
      ?

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    • 2.The saturation principle is a stipulated axiom of NSA, not a discovered truth about mathematical reality.
      ?

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    • 3.What can be consistently postulated need not thereby be said to 'must exist' in any robust sense.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Benacerraf's challenge shows that mathematical Platonism requires an unexplained epistemic access to abstract objects.
      ?

      Think about whether this reason is strong or weak

    • 2.If hyperreals 'must exist,' their necessity presupposes a Platonist ontology that remains philosophically contested.
      ?

      Think about whether this reason is strong or weak

    • 3.Robinson himself characterized NSA as a formal tool, not a metaphysical revelation about necessary mathematical entities.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The set of real numbers is infinite
      ?

      Think about whether this reason is strong or weak

    • 2.The hyperreals include all standard reals plus additional elements entailed by the saturation principle
      ?

      Think about whether this reason is strong or weak

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