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    If two things A and B both have the property of being F, ... — Carmelics
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    Challenges→There exists an infinite regress of distinct forms of likeness (L1, L2, L3, ...)

    If two things A and B both have the property of being F, then A is like B and B is like A (symmetry of likeness)

    Modality & PossibilityPhilosophy of Language
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    By Non-Identity, L2 is numerically distinct from L1By Non-Identity, L3 is numerically distinct from both L1 and L2By One-over-Many, L1 and L2 being like entails they partake of yet another form ...By One-over-Many, L1 being like entails L1 partakes of a further form of likenes...

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    By One-over-Many, if A and B are both like, then A and B are like by virtue of p...By Paradigmatism, L1 is like L2, and by symmetry, L2 is like L1, so L2 is likeBy Paradigmatism, if A and B partake of L1, then A and B are like L1, and hence ...By symmetry of likeness, if something is like L1, then L1 is like that thing, so...If L1 is like something or something is like L1, then by symmetry of likeness, L...The same pattern of reasoning repeats without terminusThere exists an infinite regress of distinct forms of likeness (L1, L2, L3, ...)

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    If L1 is like something or something is like L1, then by symmetry of l...93%By symmetry of likeness, if something is like L1, then L1 is like that...92%By symmetry of likeness, if something is like L1, then L1 is like that...92%By Paradigmatism, L1 is like L2, and by symmetry, L2 is like L1, so L2...86%

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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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