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    Set theory cannot be about bunches of ordinary objects or... — Carmelics
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    Home/Philosophy of Language
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    Set theory cannot be about bunches of ordinary objects or piles of physical stuff

    Modality & Possibility
    ?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
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    • 1.Sets are individuated by their membership conditions, not spatiotemporal location, making physical coincidence metaphysically impossible for distinct sets.
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    • 2.Extensionality axioms entail that set identity is fully determined by members, yet physical stuff has no determinate membership facts without abstract structure.
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    • 3.Paul Benacerraf's multiple-reductions argument shows physical bases underdetermine set-theoretic identity, severing any coherent reduction to physical objects.
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    Reason for 2 of 2
    ?
    • 1.The empty set exists as a genuine mathematical object, yet no physical stuff or ordinary object corresponds to it, falsifying any purely nominalist reduction.
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    • 2.George Boolos's plural quantification cannot rescue physicalism because iterative hierarchy requires sets of sets, which no finite physical base can ground.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Corresponding to every physical object, there are infinitely many distinct sets (e.g., the set containing the ball, the set containing that set, and so on)
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    • 2.All of these infinitely many sets share the same physical base
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    • 3.A pile of physical stuff cannot be simultaneously identical to infinitely many distinct objects sharing the same physical base
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    Topics

    Philosophy of LanguageModality & Possibility

    Connections

    1 topic

    Truth & Knowledge3 linked

    Related

    A pile of physical stuff cannot be simultaneously identical to infinitely many d...All of these infinitely many sets share the same physical baseCorresponding to every physical object, there are infinitely many distinct sets ...Extensionality axioms entail that set identity is fully determined by members, y...
    +4 moreShow less
    George Boolos's plural quantification cannot rescue physicalism because iterativ...Paul Benacerraf's multiple-reductions argument shows physical bases underdetermi...Sets are individuated by their membership conditions, not spatiotemporal locatio...The empty set exists as a genuine mathematical object, yet no physical stuff or ...

    Similar

    Set theory cannot be about ordinary physical objects because it entail...88%Physical theory does not describe the categorical properties of physic...83%Physical theory only tells us about the dispositional properties of ph...83%Physical theory does not tell us about the categorical properties of p...82%

    Source

    AI-extracted1/3 agreementValid
    SEP: platonism
    View source passageHide passage
    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 (2 for, 1 against)
    Edits
    1 edit