A Proof of Platonism

A Proof of Platonism

I am going to prove that the universal whiteness is not identical to the class of white things. The proof is similar to the well-known proof that pain is not identical to C-fiber firing.[1] Thus: I can think of whiteness apart from the class of actual white things; I can conceive of a possible world in which a different class of things is white. That class is not identical with the class of actual white things, but the same universal is being instantiated. Therefore, whiteness is not identical to the class of actual white things. QED. Compare: I can conceive of a possible world in which pain is not correlated with C-fiber firing, but instead is correlated with D-fiber firing. It is the same sensation but a different physical correlate. Therefore, pain is not identical to C-fiber firing. Pain is modally detachable from C-fiber firing, so it can’t be identical to that. Whiteness is modally detachable from actual white things, so it can’t be identical to them. It can’t be reducible to those things, as pain can’t be reducible to that brain state. What about the claim that pain can exist without being attached to any physical state? That too seems conceivable, at least at first sight (pending a clearer idea of the “physical”). Similarly, it seems conceivable that whiteness could exist in a possible world without any white things; if so, it is detachable from all possible white things. This intuition is reinforced by the following reflection: if I reduce the number of white things in a possible world, I don’t reduce the universal whiteness—it doesn’t get any smaller. Indeed, what would it mean to say that a universal had been reduced in size? Classes can be reduced in size, but not universals. The identity and existence conditions of universals are not the same as those of classes of particulars.

There is a more general point to be made: what explains the ability to think of universals in the absence of particulars instantiating them? The most obvious explanation is that the two are separate and distinct: when I think of whiteness I am not thinking of a class of particulars. The explanation is simply that they are not the same thing. Similarly, for pain and C-fiber firing: the concepts are different because their reference is different. Intuitively, that is very plausible, because a class is a plurality of things but a universal isn’t—it is one thing. Also, particulars have many other properties, but whiteness doesn’t have this kind of heterogeneity; it is whiteness pure and simple. Universals aren’t collections of anything; they are unities. Nor can we say that whiteness is just a mode of presentation of the class of white things, since the same could be said of the class, i.e., that it is just a mode of presentation of whiteness. In fact, it is more plausible to suppose that whiteness is ontologically basic, since it is what unifies its instances into a class. The class doesn’t generate the universal; the universal generates the class. The class would not exist without the universal; it cannot be detached from the universal that forms it. The particular presupposes the general, not vice versa.[2]

[1] See Kripke’s Naming and Necessity.

[2] Actually, I don’t much like the traditional labels “general” and “particular”:  the particular is also general in that it has many properties (it is multiple), and the general is also particular in that it is a specific thing not some sort of generalized nothing. The particular is many and the general is one. We could call the universal whiteness a “particular” because of its specificity, and the particular white thing general because it is host to a plurality of properties. Calling a universal “general” suggests some sort of distributed unspecific nature, but in reality, universals are as particular and specific as one might wish. One is not thinking “generally” if one thinks of the universal whiteness. Still less is one thinking vaguely or indiscriminately or plurally or imprecisely. One is thinking of one specific universal in particular. We must rid ourselves of the idea (prejudice) that universals are somehow cognitively and ontologically improper or badly behaved. Plato elevated them over particulars for a reason.