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What is "Trope Theory" Supposed to Explain?

I'm taking a graduate seminar in metaphysics this semester and, for the first part of the course, we are focusing on the metaphysics of properties. One account of properties is known as "trope theory". Tropes are often spoken of, rather sloppily (it doesn't seem to be possible to speak of tropes without being sloppy - a point I take to be significant to the epistemological problem we are about to discuss), as "property instances." The reason this is sloppy is that the point of trope theory is to get rid of universals (Platonic forms or their equivalents in other small-p platonist accounts), so tropes are not actually instantiations of anything. Now, there are various forms of trope theory, and we haven't really studied them yet, so I'm going to talk on a very general level, and give some first reactions to a general problem in trope theory that occurs to me, while acknowledgeing that it is possible, even likely, that someone has discussed this in the literature and attempted a solution with which I am not familiar.

Trope theory, it seems, is, like other theories of properties going all the way back to Plato, supposed to explain homonymy. That is, it is supposed to explain why we call the whiteness of my cup and the whiteness of my plate by the same name "whiteness." It reacts against the (large-P) Platonist account that says we do this in virtue of their both having the one Form of whiteness as their paradigm in which they participate, and the (small-p) platonist account that says that each whiteness is an instance or token of the same one universal. Rather, it seems in most forms to posit a form of nominalism, according to which the two whiteness tropes are totally unrelated entities which we call by the same name due to some perceived similarity. Thus it seems that it is supposed to explain why objects have properties/qualities/characteristics, and why we call these by the same name, without recourse to any weird abstract entities like universals.

But why do we say that objects have properties? It seems that we do so because we can "separate in thought" certain characteristics from the actual objects and consider them separately. Now let me bring in my Berkeleian epistemology: try considering the whiteness of a cup without considering the cup or any word or symbol that could be applied to any other whiteness. You might do this by inventing a new word, say, "whup," to apply to the whiteness trope belonging to this particular cup and then you could say various things about "whup" (for instance, that its physical cause is the reflection of all or nearly all visible wavelengths of light), but could you define or think of "whup" without the antecedent concept whiteness? Could you come up with it if the cup was the only object you had ever perceived? I think not. Certainly you could imagine the white cup taking up your whole field of vision so that you only saw the white, but why would you think this was a trope or anything like that? It is even more difficult with properties like "cupness" (which may not actually be a "real" property, but leave that aside) or "virtue."

I imagine that the only reason we think of properties as separable from the objects in which they inhere is because we see the "same" (whether properties are literally repeatable or merely similar tropes in one object and another) property in more than one object. The trope theorist might escape this if he could explain how two tropes can be similar and then say that we don't notice a trope until we see two similar ones, but this is a far from simple task, and now we are saying that epistemologically awareness of a universal (even if such things are only nominal - that is, if they are convenient intellectual fictions) precedes (or at least is simultaneous with) awareness of (some of) its instances. This seems to be bad news for trope theorists, since they now must explain how this epistemic fact could be true if tropes are fundamental and universals supervene on them. Of course, there are plenty of problems with universals as well...

On a side note, I find it amusing that the discussion of trope theory in the introduction to Mellor and Oliver's Properties outlines a problem that is basically identical to Plato's "Likeness Regress" in Parmenides 132c-133a. Basically, the metaphysics of properties doesn't seem to have progressed much in the last 2300 years. Well, such is the difficulty of metaphysics...