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    In the Third Man argument, the claim that each form is F ... — Carmelics
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    Supports→Paradigmatism combined with the symmetry of likeness generates the regress of forms of likeness, not Self-Predication as in the Third Man argument

    In the Third Man argument, the claim that each form is F is derived from Self-Predication

    Modality & PossibilityTruth & Knowledge
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    Related propositions within the same area of thought.
    In the likeness regress, the claim that each form of likeness is itself like is ...Paradigmatism combined with the symmetry of likeness generates the regress of fo...The two arguments therefore rely on structurally distinct principles to establis...

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    Hume's argument for the Copy Principle is inductive in form79%Non-Identity holds: a form is not identical to the things that partici...79%Self-Predication holds: each form predicates itself.78%The two arguments therefore rely on structurally distinct principles t...78%

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    SEP: plato-parmenides
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    On the second view, the regress arises differently. In particular, the reasoning relies explicitly on Paradigmatism and on an assumption that Parmenides emphasizes as he is setting up his criticism, namely that the relation of likeness is symmetrical: if X is like Y, then Y is like X (Parmenides 132d5–7). Consider two things, A and B, that both have the property of being F. Given that there is a property that A and B both share, it follows that A is like B and that B is like A. Thus, A is like s

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