Jerry waltzes. According to the Platonist, this means that Jerry instantiates the universal waltzing. So, where initially we thought we had Jerry alone, we now have Jerry, instantiation and waltzing. But we also, equally, have Jerry, instantiation and waltzing when Jerry is sitting instead of waltzing. After all, instantiation and waltzing are universals, and so they exist necessarily, even when Jerry isn't waltzing. So, what is different between the situation where Jerry instantiates waltzing and the one where he does not? It won't help to say that the ordered pair <Jerry, waltzing> instantiates instantiation. For the same problem reappears. Whether Jerry waltzes or not, Jerry, waltzing, the ordered pair <Jerry, waltzing>, and instantiation necessarily exist. Going to further levels of the regress will get us more entities, but it will not help resolve the problem. For we will simply get more beings that exist even when Jerry isn't waltzing, and those beings don't help to differentiate betweent he case of him waltzing and him not waltzing. (Nor does this depend on time; we can distinguish between the case of Jerry's instantiating waltzing at some time or other and the case of Jerry's not instantiating waltzing at some time or other.)
So what can the Platonist do? Well, she could just say that it's simply a fact, a fact not analyzed in terms of further Platonic entities, that Jerry in fact instantiates waltzing, or that <Jerry, waltzing> instantiate instantiation. But then she says exactly the same sort of thing that the ostrich nominalist does. And if she says it in this case, why bring in instantiation at all? Why not just say that Jerry in fact waltzes, and be done with it? Or maybe the Platonist will say that there is a state of affairs of Jerry's instantiating waltzing or <Jerry, waltzing> instantiating instantiation. Fine, but why do that? Why not just say that there is a state of affairs of Jerry's waltzing, and be done with it? Or perhaps the Platonist will posit a trope of instantiating present in <Jerry, waltzing> or a trope of instantiating-waltzing present in Jerry. But why not, then, just posit a trope of waltzing in Jerry?
I do not think this kills Platonism. It just shows that if Platonism is to do something useful for us, it is something other than helping us understand the nature of predication. For if Platonism is seen as helping with predication, it does this by reducing all predication to predications of the form "x instantiates P" or "<x,P> instantiates instantiation". Now in some cases, it is helpful to ground all instances of a class in terms of a distinguished subclass. Thus, in my dissertation, I argued that all modal claims should be grounded in claims about the powers of things. The latter claims are, of course, modal. However, if such a grounding is to have any usefulness, the distinguished subclass must be somehow preferable, maybe epistemologically, maybe in terms of comprehensibility, or in some other way. But why should, say, the state of affairs of Jerry's instantiating waltzing be preferred to the seemingly simpler state of affairs of Jerry's waltzing?
Now it may well be that Platonism has other uses than helping with problems of predication. It may indeed.