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    Platonism cannot adequately account for mathematical know... — Carmelics
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    Platonism cannot adequately account for mathematical knowledge

    SkepticismTruth & Knowledge
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    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Benacerraf's dilemma shows any adequate epistemology must connect truth conditions to belief acquisition, which Platonism structurally cannot do.
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    • 2.Platonist appeals to rational intuition (à la Gödel) lack any principled account of why intuition reliably tracks mind-independent abstract reality.
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    • 3.Field's fictionalism demonstrates mathematics can be nominalistically reformulated, removing explanatory necessity for abstract objects entirely.
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    Reason for 2 of 2
    ?
    • 1.Indispensability arguments (Quine-Putnam) that support Platonism equally support epistemic access to physical entities, but abstract objects lack analogous confirmation pathways.
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    • 2.The reliability challenge (Hartry Field, 1989) stands independent of causal theories: any epistemology must explain why mathematicians' beliefs systematically correlate with abstract truths.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Our best theory of knowledge is the causal theory of knowledge
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    • 2.The causal theory of knowledge requires that knowledge of entities results from causal interaction with those entities
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    • 3.According to platonism, abstract mathematical objects are not spatially or temporally localized
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    Topics

    SkepticismTruth & Knowledge

    Key Terms

    knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
    Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.

    Connections

    2 topics

    Causation2 linkedModality & Possibility1 linked

    Related

    According to platonism, abstract mathematical objects are not spatially or tempo...Benacerraf's dilemma shows any adequate epistemology must connect truth conditio...Causal interaction requires some form of spatial or temporal connection between ...Field's fictionalism demonstrates mathematics can be nominalistically reformulat...
    +6 moreShow less
    Flesh and blood mathematicians are spatially and temporally localizedIndispensability arguments (Quine-Putnam) that support Platonism equally support...

    Similar

    Psychologism cannot adequately account for the huge infinities in math...80%Fictionalism cannot adequately account for the objectivity of mathemat...80%A contemporary Millian account of mathematics is untenable80%Intuitionism, restricted to intuitively cognizable truths, is insuffic...79%

    Source

    AI-extracted1/3 agreementValid
    SEP: philosophy-mathematics
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    Benacerraf formulated an epistemological problem for a variety of platonistic positions in the philosophy of science (Benacerraf 1973). The argument is specifically directed against accounts of mathematical intuition such as that of Gödel. Benacerraf’s argument starts from the premise that our best theory of knowledge is the causal theory of knowledge. It is then noted that according to platonism, abstract objects are not spatially or temporally localized, whereas flesh and blood mathematicians
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Our best theory of knowledge is the causal theory of knowledge
    Platonist appeals to rational intuition (à la Gödel) lack any principled account...
    The causal theory of knowledge requires that knowledge of entities results from ...
    The reliability challenge (Hartry Field, 1989) stands independent of causal theo...
    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit