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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Set-talk can be systematically paraphrased as talk about concrete pluralities or mereological fusions, as Goodman and Quine demonstrated in 'Steps Toward a Constructive Nominalism'.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Mereological fusions lack the structural properties sets possess; fusion of x and y differs from {{x},{y}}, making paraphrasing incomplete.
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    • 2.The empty set and singleton sets have no mereological correlates, creating a systematic gap in nominalistic coverage of set-theoretic discourse.
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    • 3.Nominalistic paraphrases become unwieldy for higher-order mathematics; translating set theory's elegance into fusion-talk sacrifices clarity and tractability.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Nominalism avoids commitment to abstract objects, reducing ontological bloat and respecting empiricist principles about what exists.
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    • 2.Concrete pluralities and fusions are spatiotemporally located and causally efficacious, making them more scientifically tractable than sets.
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    • 3.Goodman-Quine nominalism preserves mathematical utility while eliminating problematic abstracta, achieving parsimony without loss of explanatory power.
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