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    If hyperreals 'must exist,' their necessity presupposes a... — Carmelics
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    Challenges→Nonstandard hyperreals must exist

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

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Hyperreals are indispensable to nonstandard analysis; mathematical indispensability arguments suggest ontological commitment to abstract objects.
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    • 2.Without Platonism, the applicability and truth-conditions of hyperreal statements lack adequate grounding in physical or constructivist frameworks.
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    • 3.Nominalist alternatives to hyperreals face technical difficulties explaining their formal properties without implicit abstract object commitments.
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    Reasons Against

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    Reason against
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    • 1.Mathematical entities may be tools or formal structures rather than existing things; usefulness doesn't entail ontological necessity or Platonism.
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    • 2.Structuralist accounts explain hyperreals via abstract relationships without committing to transcendent Platonic objects or contested realist ontologies.
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    • 3.The claim conflates logical/mathematical necessity with metaphysical necessity; hyperreals need not 'exist' to be mathematically valid constructs.
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    Connections

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    Proof of definition segments1 linkedModality & Possibility1 linked

    Related

    Hyperreals are indispensable to nonstandard analysis; mathematical indispensabil...Mathematical entities may be tools or formal structures rather than existing thi...Nominalist alternatives to hyperreals face technical difficulties explaining the...Nonstandard hyperreals must exist
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    Structuralist accounts explain hyperreals via abstract relationships without com...The claim conflates logical/mathematical necessity with metaphysical necessity; ...Without Platonism, the applicability and truth-conditions of hyperreal statement...

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    claim
    Perspectives
    2 (1 for, 1 against)
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