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    Made withinDC&Austin
    Claims about sets are claims about objects of a different... — Carmelics
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    Home/Philosophy of Language
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    Claims about sets are claims about objects of a different kind from ordinary physical objects

    Modality & PossibilityPhilosophy of Language
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.There are infinitely many sets corresponding to any single physical object, as entailed by the principles of set theory
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    • 2.All of these infinitely many sets share the same physical base
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    • 3.Ordinary physical objects or bundles thereof cannot account for infinitely many distinct entities sharing a single physical base
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.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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    • 2.If set-theoretic claims are fully translatable into claims about physical pluralities without ontological remainder, sets require no distinct object-kind beyond ordinary physical entities.
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    Reason against 2 of 2
    ?
    • 1.Hellman's modal structuralism shows set-theoretic truths express possibilities about structural relations, not truths about independently existing abstract objects.
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    • 2.If set claims are fundamentally modal rather than referential, the inference from 'infinitely many sets share one physical base' to 'sets are a distinct object-kind' conflates structural possibility with ontological category.
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    Topics

    Philosophy of LanguageModality & Possibility

    Connections

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    Truth & Knowledge3 linked

    Related

    All of these infinitely many sets share the same physical baseHellman's modal structuralism shows set-theoretic truths express possibilities a...If set claims are fundamentally modal rather than referential, the inference fro...If set-theoretic claims are fully translatable into claims about physical plural...
    +3 moreShow less
    Ordinary physical objects or bundles thereof cannot account for infinitely many ...Set-talk can be systematically paraphrased as talk about concrete pluralities or...There are infinitely many sets corresponding to any single physical object, as e...

    Similar

    A contemporary Millian must take set theory to be about ordinary physi...85%There are many distinct concepts of set, each determining its own univ...82%Maddy's view holds that sets exist in spacetime but are not physical o...81%It is not plausible to maintain that the claims of set theory are made...81%

    Source

    AI-extracted1/3 agreementValid
    SEP: platonism
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    Let us move on now to immanent-realist, or physicalist, views of mathematics, and let us concentrate first on views like Mill's (1843, book II, chapters 5 and 6), i.e., views that maintain that sentences about numbers are really just general claims about bunches of ordinary objects. On this view, the sentence ‘2 + 1 = 3’, for instance, isn't really about specific objects (the numbers 1, 2, and 3). Rather, it says that whenever we add one object to a pile of two objects, we will get a pile of thr
    Extraction notes

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

    Details

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