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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Nominalist programs (Goodman, Field) demonstrate that linguistic and mathematical practice can be reconstructed without positing abstract universals.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Nominalist reconstructions (Field, Goodman) require artificial apparatus—proxy objects, inscriptions—that seem as ontologically costly as universals.
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    • 2.The success of nominalist programs remains limited to fragments of mathematics; higher set theory resists nominalist recasting without severe distortion.
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    • 3.Linguistic competence requires grasping abstract properties; nominalism struggles to explain how concrete tokens ground infinite productivity of language.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Nominalist reconstructions successfully formalize mathematics using only concrete objects and logical operations, avoiding ontological bloat.
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    • 2.If abstract universals aren't required to explain linguistic/mathematical behavior, parsimony favors their elimination per Occam's Razor.
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    • 3.Nominalist schemes show mathematics works instrumentally without commitment to Platonic existence, making realism metaphysically optional.
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