  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 something (and hence, in some way, like) and B is like something (and hence, in some way, like). But, by One-over-Many, A and B are both like by virtue of partaking of a form of likeness (say, L1). Now assume for reductio that something is like L1 or L1 is like something. Clearly if L1 is like something, then L1 is (in some way) like. And if something is like L1, then, by symmetry of likeness, L1 is like it, and hence again L1 is (in some way) like. So, whether something is like L1 or L1 is like something, L1 is like. Now, by One-over-Many, L1 is like by virtue of partaking of a form of likeness (say, L2), and hence L1 partakes of L2. By Non-Identity, L2 is numerically distinct from L1.  But also, by Paradigmatism, L1 is like L2, and hence, by symmetry of likeness, L2 is like L1. So L2 is (in some way) like. By One-over-Many, then, L1 and L2 are like by virtue of partaking of a form of likeness (say, L3), and hence L1 and L2 both partake of L3. By Non-Identity, L3 is numerically distinct from both L1 and L2. This gives us three distinct forms of likeness. Repetition of the same pattern of reasoning then establishes the existence of an infinite regress of forms of likeness. Taking for granted that the existence of such a regress is in some way absurd or problematic, Parmenides infers that the assumption for reductio is false, i.e., that nothing is like L1 and L1 is like nothing. But this result is itself unacceptable. For we already have it that A and B are like by virtue of partaking of L1, and hence that A and B partake of L1. By Paradigmatism, A and B are like L1, and hence something is like L1. Moreover, by symmetry of likeness, L1 is like A and B, and hence L1 is like something. Thus the assumption for reductio is true. Contradiction. Notice that, on the second view, the reasoning leading to the relevant regress is not homologous to the Third Man argument: instead of deriving the claim that each form of likeness is like from Self-Predication, Parmenides infers it from the conjunction of Paradigmatism and the symmetry of likeness.