I don't like to resurrect old threads, but I'll give this one a go since this might help clarify issues for others as well. The blogger is getting at what is come to be known as "Ramsey's Problem."
Ramsey's problem is a simple question. A universal is something that runs through many distinct particulars. One universal runs through many particulars. Redness is instantiated by the fire hydrant, my lollipop, and my flower. A particular is something that runs through many universals. My particular lollipop instantiates redness, sweetness, and sphericity (if geometrical shapes are universals at all). How then do we distinguish a universal from a particular? This problem is supposed to be insurmountable for someone who holds to a universal/particular distinction. If you cannot draw a proper distinction to distinguish particulars from universals, then why hold to such a distinction in the first place?
Bundle theorists say that there are no such things as particulars, only universals which are tied together by a relation of compresence. Compresence is a relation that holds between any two properties of the same thing. Bertrand Russell's complex of compresence is a class of universals, where each member has the compresence relation to each other members. A complete complex of compresence (CCC), as Russell defines it, is a complex of compresent universals where no further universal can be added because if there was another, it would fail to have the compresence relation with at least one of the members in the group. To the Bundle Theorist, particulars are complete complex of compresent (CCC) universals.
If we cannot trace back from a finite number of properties to a
particular that will bear properties
then why even bother with particulars at all?
True, if there is no ultimate possessor of the universals in question, then. . . why bother with particulars, whatsoever? So you can't hold to the particular/universal distinction.
Why not just say an object is a chain of properties? Perhaps this chain is finite in the number of properties that compose it. But if a philosopher wishes to maintain that “has” is a universal, then it seems based on the reasoning we considered in section IV.
If the particular is simply something which is a matter of a complex of compresence, then it's a universal. As I read section IV, this would lead to an infinity of properties. It is far more probable that there are not an infinity of properties (if someone thinks otherwise, I want to know what kind of truthmaker they are using for it). So, even the Bundle theory is plagued with massive problems.
Let me elaborate a bit more on infinite regresses, since a lot of people have a problem with understanding this.
There is a relation C, in which A and B stand; and it appears with both of them. . . . The relation C has been admitted different from A
and B, and no longer is predicated of them. Something, however, seems
to be said of this relation C, and said, again, of A and B. And this
something is not to be the ascription of one to the other. If so, it
would appear to be another relation, D, in which C, on one side, and,
on the other side, A and B, stand. But such a makeshift leads at once
to the infinite process. The new relation D can be predicated in no
way of C, or of A and B; and hence we must have recourse to a fresh
relation, E, which comes between D and whatever we had before. But
this must lead to another, F; and so on, indefinitely.
–––, 1893. Appearance and Reality, Oxford: Oxford University Press.
Bradley's Regress: The early Russell was a believer in transcendent Platonic universals. A relation is a universal and gets exemplified by two particulars when the relation relates two particulars. So, to give an example. The proposition, "The rose is red." has about 3 entities in play, (1) the rose, (2) the universal redness, (3) the relation of rose having redness. 1 & 2 are not enough. You cannot get a red rose by lumping redness and the rose together, you need something more. This 'something more' is what we call a 'relation,' which ties the redness to the rose, so that it is red. This 'having' is what is known to be essential to making the proposition < The rose is red. > true. You can think of this as the sort of metaphysical glue which ties two entities, A and B, together.
F. H. Bradley argued that if there are two entities, A and B, and are in a relation with each other, call it C, C is what is being exemplified by the two particulars (I'll come to this later). Since exemplification is yet another relation, it is an independent universal entity, call it D. Now if C is exemplified by A and B, by the exemplification relation D, then there must be another exemplification relation. . . and so on, ad infinitum. Thus, we won't have explained anything we set out to explain.
Few comments. Infinite regresses in causal chains is one thing, but this is a kind of infinite regresses in the sense of constitution, so whatever arguments that might work in appealing to an infinite regress in causation, fails here. If you posit an infinite set of entities, you are multiplying them to explain something, but you're never explaining what metaphysically grounds them. Your metaphysical pudding, gets pushed under the rug, and what do you do when you see the lump elsewhere? You keep pushing it, again, and again, and again. . . It's for this reason that philosophers see that becoming a realist is pointless, since its theories have too much complexity and make you posit entities ad infinitum, which in the end don't serve to explain anything but bloat your theory. Why not become a nominalist and avoid all this trouble? (That's not to say that nominalism doesn't have the same problems :)) This is one reason why one should 'drop' the theories. I've been charitable enough in my reading to allow for such a regress (most people simply reject this kind of talk, an infinity of posits don't seem to be able to explain anything), since should this infinite regress ensue, there would be an infinity of properties.
Faced with this, something's gotta give. Realists have since then argued that exemplification is a non-relational fundamental tie, however, how does this not seem ad-hoc? Can it be motivated independently to avoid Bradley's regress? Certain realists can definitely do that. Certain realists, in other words, think that the exemplification relation is not on par (not in the same category) with other relations. This reply would work and avoid Bradley's regress, should one be able to independently motivate this.
If both the theories in offer are faced with such massive problems, what then is to become of the picture?
Here are my points now. Metaphysicians are willing, although not happy, to admit brute facts into their ontology. It is still a negative for their theories. A brute fact is something that can't even in principle be explained, a primitive concept is something which cannot be further analyzed. Bundle theorists take the compresence relation to be a further unanalyzable affair, whereas, the ones who uphold a universal/particular distinction hold instantiation to be an unanalyzable affair.
The resemblance nominalist takes resemblance be primitive, some people take naturalness as a primitive, realists take instantiation to be a primitive, bundle theorists take the compresence relation to be primitive. How then, is the debate advanced? The endeavor is to keep primitives to a bare minimum and look for other reasons to accept or deny the theories available.
I won't be giving an answer as to who is right, but if you're interested and engage with me (provided you think I've explained enough), I will give you directions where you can look for them :).