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    Existence claims about entities visible only from outside... — Carmelics
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    Challenges→An infinitesimal hyperreal exists

    Existence claims about entities visible only from outside the standard model are epistemically inaccessible and thus philosophically idle for grounding mathematical practice.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Mathematical practice succeeds without positing entities beyond the standard model; Occam's razor favors theories not multiplying unnecessary ontologies.
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    • 2.If entities are epistemically inaccessible, we cannot empirically verify or falsify claims about them, making them vacuous for grounding any practice.
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    • 3.Working mathematicians develop and apply formal systems without needing metaphysical commitments to non-standard entities; practical utility suffices.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Epistemic inaccessibility from outside a framework doesn't entail philosophical idleness; dark matter grounds astronomical practice despite invisibility.
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    • 2.The standard model itself is a theoretical construct; entities outside it may be necessary for explaining the standard model's consistency or completeness.
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    • 3.Mathematical practice has historically been grounded by entities initially considered inaccessible (infinitesimals, imaginary numbers); accessibility expands with theory.
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    Connections

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    Proof of definition segments1 linkedModality & Possibility1 linked

    Related

    An infinitesimal hyperreal existsEpistemic inaccessibility from outside a framework doesn't entail philosophical ...If entities are epistemically inaccessible, we cannot empirically verify or fals...Mathematical practice has historically been grounded by entities initially consi...
    +3 moreShow less
    Mathematical practice succeeds without positing entities beyond the standard mod...The standard model itself is a theoretical construct; entities outside it may be...Working mathematicians develop and apply formal systems without needing metaphys...

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