  What should we think about forms of negations, such as the not-large and the not-beautiful? Aristotle criticized Plato for commitment to such forms (Metaphysics A.9, 990b), but notoriously Aristotle was not always fair in his criticisms. The Sophist explicitly speaks of the form of not-being (Sophist 258d: to eidos…tou mê ontos), and a number of scholars regard the not-large and the not-beautiful as forms (e.g., Moravcsik 1962, Frede 1967, 92–94, Szaif 1996, 439–45, Crivelli 2012, 204–14). The Stranger’s lecture on parts and kinds in the Statesman, rejecting forms of barbarian and numbers other than 10,000, poses a well-known problem for that view, yet as we saw (§ 7.1 above) the lecture and second stage of the dichotomous division are themselves puzzling. Not only that: the Stranger warns Young Socrates not to think he has heard anything clear from him about the difference between a kind and a part (Statesman 263b). This warning could strengthen the hand of those who attribute to Plato a commitment to forms of negations. One question we should be asking, though: what function(s) do Platonic forms perform? Does Plato need a form whenever people call several things by the same name (as stated perhaps at Republic 10.596a)? Or does he invoke only those forms needed to explain the features of things? In the latter case, perhaps he can do without a form of the not-large, because he can explain that range of sizes by appeal to the form of largeness and the form of not-being. Perhaps he needs no form of mud/clay (rejected by Socrates as a separate form at Parmenides 130c–e), since he can explain the mixture by appeal to forms of its ingredients, earth and water, and the ratio of their combination (Parmenides 130c, with Theaetetus 147a–c). Questions about the scope of forms in Plato remain far from settled.