Lukas Novak comments and I respond.
Bill, what follows is what I consider the most important objection against your theory. It seems to me that in order to keep the basic meaning of "universal" and "particular" the following definitions must be assumed:
1. A universal is that which is (truly) predicable of many particular instances. BV: I agree if 'many' means two or more. I would add that a universal is a repeatable entity. But I suspect Novak will not agree with my addition. I suspect his view is that there are no universals in extramental reality. Universals are concepts. Hence I would expect him to balk at 'entity.'
2. X is an instance of a given universal U iff U is predicated of X. BV: I would say 'predicable' instead of 'predicated.' Predication is something we do in thought and with words. A universal can have an instance whether or not any predication is taking place.
3. U1 is subordinate to U2 iff all instances of U1 are instances of U2. This is expressed in language in the form "Every U1 is an U2" - for example, "Every man is an animal". BV: OK.
4. Every universal has at least some possible instances, unless it is intrinsically inconsistent. Now whiteness and color are universals. By common sense, color is superordinate to whiteness. So, every whiteness is a color. Peter's whiteness, on the other hand, is a particular. We must assume that Peter's whiteness is an instance of whiteness, and also of color - since whiteness and color are not intrinsically inconsistent and there are no more plausible candidates to [be] their instances than Peter's whiteness, Bob's blackness etc. BV: So far, so good!
But here comes the problem. If Peter's whiteness contains whiteness, then Peter's color contains color as its constituent. BV: It is true that Peter is white, and it is true that if Peter is white, then he is colored. But it doesn't follow that there is the accident Peter's coloredness. Accidents are real (extramental) items. Peter really exists and his whiteness really exists. But there is not, in addition to Peter's whiteness, the accident Peter's coloredness.
Argument 1: It is accidental that Peter is white (or pale) due perhaps to a deficiency of sunlight. But it is not accidental that Peter is colored. Peter is a concrete material particular, and necessarily, every such particular has some color or other. Therefore, being colored is not an accident of Peter. Being colored is essential to Peter.
Argument 2: The truth-maker of 'Peter is white' is Peter's being white. But Peter's being white is also the truth-maker of 'Peter is colored.' Therefore, there is no need to posit in reality, besides Peter's being white, Peter's being colored.
I therefore say that there is no such accident as Peter's being colored. Consequently, the rest of Novak's reasoing is moot.
You may perhaps say that Peter's whiteness also contains color because whiteness contains color, but certainly color does not contain whiteness in that case (else they would coincide), and therefore Peter's color does not contain whiteness.
BV: We have to be careful not to equivocate on 'contain.' In one sense of 'contain,' whiteness contains color or coloredness. We could call this conceptual inclusion: whiteness includes coloredness as a part. In a second sense of 'contain, ' if x is an ontological constituent of y, then y contains x. Thus the accidental compound [Peter + whiteness] contains the substance Peter and the accident whiteness, but does not contain them in the way whiteness contains color.
Consequently, Peter's color is not an instance of whiteness. But this contradicts the fact that Peter's color just is Peter's whiteness, because Peter's whiteness is a color (by def. 3, assuming that whiteness is subordinate to color), and there is no other color in Peter than his whiteness (let us so stipulate).
Put very simply: if Peter's whiteness is just Peter+whiteness+NE+time, then Peter's color is just Peter+color+NE+time, but then Peter's whiteness is not Peter's color. But this is wrong since whiteness is subordinate to color and so any instance of whiteness must be identical to an instance of color.
BV: Novak's argument could be put as follows:
a. If Peter's whiteness is a complex having among its constituents the universal whiteness, then Peter's coloredness is a complex having among its constituents the universal coloredness.
b. These are numerically distinct complexes.
c. Peter's whiteness is not Peter's coloredness.
d. (c) is false.
e. Peter's whiteness is not a complex.
By my lights, the argument is unsound because (a) is false as I already explained: there is no such complex as Peter's coloredness.