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    Each form in the infinite hierarchy of forms of largeness... — Carmelics
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    Home/Philosophy of Language
    HistoryEditSee Inverse

    Each form in the infinite hierarchy of forms of largeness is not one.

    Modality & Possibility
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Each form in the infinite hierarchy of forms of largeness is infinitely many.
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    • 2.The property of being one and the property of being many are contraries.
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    • 3.Purity-F holds: a form cannot have contrary properties.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.A form's being 'many' (having multiple instances or participations) does not preclude its being numerically one as a distinct entity.
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    • 2.Plato's Purity-F principle, as Vlastos reconstructs it, conflates predicational and numerical oneness, committing a use-mention error.
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    • 3.Therefore, the inference from 'infinitely many' to 'not one' equivocates on the sense of 'one', undermining P2's force.
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    Reason against 2 of 2
    ?
    • 1.Aristotle's 'Third Man' regress in Metaphysics 990b targets self-predication, not the claim that forms lack unity.
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    • 2.A form of Largeness can be both a universal (hence 'many' in extension) and a single universal (hence 'one' in intension), as Frege's concept-object distinction clarifies.
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    • 3.Purity-F, if it bars forms from having any contrary predicates, collapses into an implausibly strict monism that Plato himself never endorsed.
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    Topics

    Philosophy of LanguageModality & Possibility

    Related

    A form of Largeness can be both a universal (hence 'many' in extension) and a si...A form's being 'many' (having multiple instances or participations) does not pre...Aristotle's 'Third Man' regress in Metaphysics 990b targets self-predication, no...Each form in the infinite hierarchy of forms of largeness is infinitely many.
    +5 moreShow less
    Plato's Purity-F principle, as Vlastos reconstructs it, conflates predicational ...Purity-F holds: a form cannot have contrary properties.Purity-F, if it bars forms from having any contrary predicates, collapses into a...The property of being one and the property of being many are contraries.Therefore, the inference from 'infinitely many' to 'not one' equivocates on the ...

    Similar

    Each form in the infinite hierarchy of forms of largeness is infinitel...93%One-over-Many, Self-Predication, and Non-Identity together generate an...87%Therefore there is a form L3 by virtue of which A, B, C, L1, and L2 ar...85%There must be at least two forms of largeness (L1 and L2).85%

    Source

    AI-extracted1/3 agreementValid
    SEP: plato-parmenides
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    One way to make sense of this claim is by way of the following chain of reasoning. As we’ve seen, One-over-Many, Self-Predication, and Non-Identity together generate an infinite hierarchy of forms of largeness, each of which partakes of the forms above it in the hierarchy. Thus, L1 partakes of infinitely many forms, L2 partakes of infinitely many forms, L3 partakes of infinitely many forms, and so on. Now there are passages in which Plato appears to assume that forms are as many as the predicate
    Extraction notes

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

    Details

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