  Parmenides’ first argument appears to have the following structure. First, all thoughts have intentional objects: every thought is of something rather than nothing. Second, the object of any thought T is something that T thinks to be one over all the instances. But anything that is thought to be one over all the instances is a form. Parmenides concludes that the intentional object of every thought is a form, and hence if every form is a thought then every form is a thought of a form. Although Parmenides does not make this explicit, it is plain that if every form is numerically distinct from the form of which it is the intentional object, then (thanks to Self-Predication and Non-Identity) an infinite regress of forms beckons (see Rickless (2007, 75–79), and also Gill (1996, 40) and Sayre (1996, 84)). Again, there is nothing to suggest that Plato finds the existence of an infinite regress problematic in itself. Rather, the existence of a regress threatens Uniqueness, and, when combined in the appropriate way with Purity-F, threatens Oneness. The reasoning that leads to conflict with Oneness is parallel to the relevantly similar portion of the Third Man argument (see section 4.3 above, and Rickless (2007, 79–80) for details).