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    Platonism is false — Carmelics
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    Platonism is false

    Truth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Benacerraf's epistemic challenge shows we lack any causal mechanism to reliably form true beliefs about causally inert abstract objects.
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    • 2.A truth-apt theory requiring entities we cannot in principle have epistemic access to violates the supervenience of knowledge on reliable belief-forming processes.
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    • 3.Therefore, Platonism's posited abstract objects are not merely metaphysically extravagant but epistemically self-undermining, making the thesis empirically bankrupt.
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    Reason for 2 of 2
    ?
    • 1.Nominalist programs like Hartry Field's fictionalism demonstrate that mathematical theories can be applied in science without quantifying over abstract objects.
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    • 2.If the theoretical work attributed to abstract objects can be done by concrete structures or fiction-relative truth, Occam's Razor eliminates the ontological surplus.
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    • 3.The indispensability argument, Platonism's strongest support, fails once Field shows Newtonian mechanics is nominalizable without remainder.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.If there are any sequences of abstract objects that satisfy our arithmetical theories, then there are infinitely many such sequences, and there is nothing metaphysically special about any of these sequences that makes it stand out as the sequence of natural numbers
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    • 2.Platonism is committed to the thesis that there is a unique sequence of abstract objects that is the natural numbers
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    Connections

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    Modality & Possibility2 linked

    Related

    A truth-apt theory requiring entities we cannot in principle have epistemic acce...Benacerraf's epistemic challenge shows we lack any causal mechanism to reliably ...If the theoretical work attributed to abstract objects can be done by concrete s...If there are any sequences of abstract objects that satisfy our arithmetical the...
    +4 moreShow less
    Nominalist programs like Hartry Field's fictionalism demonstrate that mathematic...Platonism is committed to the thesis that there is a unique sequence of abstract...The indispensability argument, Platonism's strongest support, fails once Field s...Therefore, Platonism's posited abstract objects are not merely metaphysically ex...

    Similar

    Uniqueness is false.98%[P1] is false97%Purity-F is false.96%The Relational Analysis is false.95%

    Source

    AI-extracted1/3 agreementValid
    SEP: fictionalism-mathematics
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    Given that the epistemological argument does not succeed in refuting platonism, fictionalists might attempt to provide some other argument against platonism. One such argument that has received considerable attention is the multiple-reductions argument. The classical statement of this argument is given, once again, by Benacerraf (1965). The argument can be run in connection with any of our mathematical theories, but the point is usually made in connection with arithmetic. Moreover, even when we
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    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit