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    Non-Identity entails that each new form is numerically di... — Carmelics
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    Supports→Repeated application of One-over-Many, Self-Predication, and Non-Identity generates an infinite regress of forms of largeness.

    Non-Identity entails that each new form is numerically distinct from all previously introduced forms.

    Modality & PossibilityPhilosophy of Language
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    Philosophy of LanguageModality & Possibility

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    At each stage, Self-Predication entails that the newly introduced form is itself...One-over-Many entails a new form over each such expanded plurality.Repeated application of One-over-Many, Self-Predication, and Non-Identity genera...

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    This reasoning can be repeated without limit, producing forms L1, L2, L3, … Ln f...

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    Non-Identity: if one form partakes of another, the two forms are numer...89%Non-Identity: L3 is numerically distinct from both L1 and L2.83%By Non-Identity, L2 is numerically distinct from L183%By Non-Identity, L3 is numerically distinct from both L1 and L282%

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    SEP: plato-parmenides
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    (Notice that Non-Identity follows directly from Separation.) From the fact that L1 partakes of L2, Non-Identity entails that L2 is numerically distinct from L1. Thus, there must be at least two forms of largeness, L1 and L2. But this is not all. By Self-Predication, L2 is large. So there is now a new plurality of large things, A, B, C, L1, and L2. Thus, by One-over-Many, there is a form of largeness (call it “L3”) by virtue of partaking of which A, B, C, L1, and L2 are large. Hence L1 and L2 bo

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