  Aristotle's principal concern in discussing ontological issues in mathematics is to avoid various versions of platonism. Aristotle shares with Plato the view that there are objects of understanding, that these must be universal and not particular and that they have to satisfy certain “Parmenidean” conditions, such as being unchanging and eternal. However, Aristotle rejects the view of Plato that objects of understanding are separate from particulars. This is a general problem in Aristotle's metaphysics. However, in the case of mathematical objects, there are three important difficulties. First, if physical objects are the objects of mathematical understanding and satisfy the standard definitions of line, circle, etc., then it is arguable that they manifestly fail in two ways (cf. Met. iii 2 997b25-8a19): 