 If one draws a sharp distinction between integral parts and substantial parts, the next natural thought would be to distinguish between integral and substantial wholes. The trouble is that in many cases the same thing seems to be both an integral whole and a substantial whole. Socrates, for example, has a quantity, and he is surely divisible into smaller quantities. It seems to follow that Socrates is an integral whole. But Socrates is also composed of matter and substantial form. So, he is a substantial whole. One could reject the notion that Socrates is an integral whole. But, then, what is it that has Socrates’s size? Socrates’ size is supposed to be an accident of Socrates, not of a part of Socrates. It is perhaps for this reason that some medieval philosophers try a different approach. As we already noted, Walter Burley draws a distinction between material parts and parts secundum formam (which we called “functional” parts, above). Related to this, Burley also draws a distinction between the whole considered in relation to its matter (secundum materiam) and the whole considered in relation to its form (secundum formam) (De toto et parte, 301). Socrates considered formally—i.e. as a unity of this form with some matter—persists through time and change. Socrates considered materially is constantly in flux. That is, Socrates on Monday is not the same whole materially as Socrates on Friday, because the sum of material parts belonging to Socrates on Monday is not identical to the sum of material parts on Friday. The distinction between the whole considered formally and the whole considered materially will play a role in some medieval theories of persistence, and we will pursue this use of the distinction in short order (see  Section 4.2).  But, first, we must consider the parts of universals and the special problems that the parts of universals entail.