  Some scholars, e.g., John Malcolm (1981), while accepting this characterizing reading of the ‘is’, deny that the property predicated of the Form and the particular are exactly the same. According to the Approximationist, the Form is the perfect instance of the property it stands for. A particular that participates in the Form is an imperfect or deficient instance in that it has a property that approximates the perfect nature of the Form. For instance, the Circle Itself is perfectly circular. A drawn circle, or a round ball, is deficient in that it is not perfectly circular, not exactly 360 degrees in circumference. It follows that the very properties particulars possess will differ from the property ‘of the same name’ possessed by the Form. If Beauty Itself is characterized by perfect beauty, then Helen has imperfect beauty and she does not have perfect beauty. Since nothing rules out that there are numerous kinds of imperfect beauty, perhaps as many as there are beautiful participants, it seems either that there is no one kind of beauty that particulars have in common, or that there are one or more (commonly shared) imperfect kinds of beauty. In the former case, there will be no need to posit a ‘one’ over the many beauties. In the latter case, there is every reason to posit a Form(s) of Imperfect Beauty in which the commonly qualified imperfect particulars participate. Neither alternative is a happy one. While the appeal to the perfection of the mathematical properties is great, even in these cases it is doubtful that Plato adopts an approximationist strategy (see Nehamas 1999b; 1999c).