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    Each form in the infinite hierarchy of forms of largeness... — Carmelics
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    Home/Philosophy of Language
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    Supports→Each form in the infinite hierarchy of forms of largeness is not one.

    Each form in the infinite hierarchy of forms of largeness is infinitely many.

    Modality & PossibilityPhilosophy of Language
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    Reasons For

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    Reason for
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    • 1.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.
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    • 2.Forms are as many as the predicates that can be truly applied to them.
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    • 3.Under the Piece-of-Pie model of partaking, if a form partakes of infinitely many forms, then it has infinitely many parts.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.The Piece-of-Pie model of partaking is not the only coherent account; Plato's own 'Presence' model treats partaking as non-mereological participation.
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    • 2.If a form's participation in another form does not require the form to contain parts corresponding to each participated form, then infinite partaking does not entail infinite parts.
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    • 3.Without the mereological entailment, a form may stand in infinitely many participation relations while remaining a unified, non-composite entity.
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    Reason against 2 of 2
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    • 1.Frege's distinction between a concept's extension and the concept itself shows that predicates applying to an object do not decompose that object into as many parts as predicates.
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    • 2.If forms are analogous to Fregean concepts rather than to extensional sets, then the number of predicates truly applicable to a form does not determine the form's internal multiplicity.
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    • 3.Premise P2—that forms are as many as the predicates truly applied to them—thus conflates intensional predication with mereological composition, invalidating the inference to infinite many-ness.
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    Topics

    Philosophy of LanguageModality & Possibility

    Related

    Each form in the infinite hierarchy of forms of largeness is not one.Forms are as many as the predicates that can be truly applied to them.Frege's distinction between a concept's extension and the concept itself shows t...If a form has infinitely many parts, then the form is itself infinitely many.
    +9 moreShow less
    If a form's participation in another form does not require the form to contain p...If forms are analogous to Fregean concepts rather than to extensional sets, then...One-over-Many, Self-Predication, and Non-Identity together generate an infinite ...Premise P2—that forms are as many as the predicates truly applied to them—thus c...Purity-F holds: a form cannot have contrary properties.The Piece-of-Pie model of partaking is not the only coherent account; Plato's ow...The property of being one and the property of being many are contraries.Under the Piece-of-Pie model of partaking, if a form partakes of infinitely many...

    Similar

    Each form in the infinite hierarchy of forms of largeness is not one.93%One-over-Many, Self-Predication, and Non-Identity together generate an...89%The regress leads to the claim that each form in the infinite hierarch...86%If a form has infinitely many parts, then the form is itself infinitel...84%

    Source

    AI-extracted
    SEP: plato-parmenides
    View source passageHide passage
    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

    Details

    Type
    premise
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit
    Without the mereological entailment, a form may stand in infinitely many partici...