Thinking About Universals
In chapter IX of The Problems of Philosophy (1912) Russell makes a good case for the existence of universals in a roughly platonic sense. He ends with these stirring words: “The world of universals, therefore, may also be described as the world of being. The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life.” (100) Let me add other characteristics of universals as traditionally conceived: they are undivided, non-spatial, non-temporal, non-mental, real, knowable, independent of particulars, capable of instantiation, yet not intrinsically instantiated. I want to focus on that last characteristic: in the platonic world (the word is appropriate) universals exist in a uninstantiated form—they are not exemplified in any particular. Hence they are not distributed in space or divided in their being: they are free-floating entities existing in their own right. While particulars cannot exist without dependence on universals, universals can exist in complete indifference to particulars. So they are not essentially and intrinsically instantiated: their original mode of being is not instantiated being. But in the world of sense their mode of being is to be instantiated: there are no universals in the world of sense that are not attached to a particular. You don’t see universals floating around without being tied to particulars. So in these two spheres of reality universals take quite different forms—particular-free or particular-bound. Particulars, however, take only one form—universal-bound. We can thus say that universals enjoy a double life: in one world they are thus and so, in another they are such and such. The very same entity can appear in quite different guises, quite different incarnations—here unattached to any particular, there attached to particulars at the hip. It is as if the universal undergoes a transformation—a metamorphosis—when it makes the trip to the world of sense. It looks very different at the other end. It undergoes an ontological makeover.
Plato introduced us to the idea of the cave as an analogy for having no acquaintance with universals as they are in themselves, seeing only particulars (mere shadows of reality). When a cave dweller escapes and encounters the world outside the cave he experiences a brand new reality and has trouble conveying his newfound knowledge to the other cave dwellers. This tells us that knowledge of universals as they intrinsically are is not attainable simply by sense perception, even though particulars exemplify universals (perceptibly so); we need to use our reason, the divine part of the soul. But we can construct another parable that illustrates the transformation wrought upon universals by their exemplification in the world of sense. Suppose there are people that live only on the surface of the planet and know nothing of caves: they have never been inside the earth and imagine it to be a solid block containing no cavities. Imagine there is no night on the surface, just constant sunlight. These surface dwellers are the analogue of beings that know only universals and never particulars; the world of underground caves is unknown to them. They are blissfully ignorant of darkness and shadows. Then one among them discovers a cave and enters its gloomy interior, thereby discovering a new reality. She is amazed by this new world, so different from the one she is accustomed to, but she has trouble explaining to the other surface dwellers what a cave is and is generally pooh-poohed by them. This is the condition of someone who knows only the world of abstract universals by the use of reason and is suddenly given senses through which particulars can be perceived. She had no idea that universals could be hooked up to particulars in this way, assuming them to be essentially autonomous entities. In fact, she doesn’t recognize them at first, finding them to be pale imitations of the real thing; it takes a while before she realizes that these funny little nuggets of appearance are in fact the dear old universals she knows from her use of reason. Ah, she thinks, so universals can actually become attached to things existing in space! Like Alice, she finds life very peculiar in her new world, a kind of distorted simulacrum of normal life outside the cave. The universals have changed into reduced parodies of their usual radiant selves.
I am saying all this to dramatize the point that universals, as traditionally conceived, exist in two quite different forms, according as they are instantiated or not instantiated. This means that our knowledge of them is also of two types: sense-based and reason-based. They can be perceived and they can be thought about, but they are perceived as instantiated and thought about as uninstantiated. That is, they can enter thought in their pristine form, but they cannot be objects of sense in that form, but only in their instantiated form. There is thus a double epistemology corresponding to their double ontology. I think Russell fails to see this and thus fails to grasp that universals are epistemologically problematic. He writes in chapter X, “On Our Knowledge of Universals”, as follows: “It is obvious, to begin with, that we are acquainted with such universals as white, red, black, sweet, sour, loud, hard, etc., i.e. with qualities that are exemplified in sense-data. When we see a white patch, we are acquainted, in the first instance, with the particular patch; but by seeing many white patches, we easily learn to abstract the whiteness which they all have in common, and in learning to do this we are learning to be acquainted with whiteness.” (101) Here Russell uncritically subscribes to the empiricist’s abstractionist theory of general concepts, not realizing that the step from perceived whiteness to the concept of whiteness in general is not as small and smooth as he appears to think. For the latter concept is of whiteness as uninstantiated but the former experience is of whiteness as instantiated. How do we get from concrete perceived instances of whiteness in space and time, as exemplified by particulars, to a concept of whiteness as unchangeable, undivided, uninstantiated, non-spatial, non-temporal, and intrinsically independent of particulars? If universals in the platonic world are as different from particulars as Russell urges, how is it possible to move from the latter to the former, as the quoted passage suggests? The answer is that it is not possible—abstractionism is a broken theory.  That is why rationalist philosophers, beginning with Plato, have adopted a non-perceptual theory of our knowledge of universals: we have innate ideas of universals that represent them in their original pristine form (allegedly: see below). That is, they adopted a double epistemology of universals to go with their double ontology; they didn’t try to leverage our pure concepts of universals from our perception of the particulars that exemplify them. Nor did they attempt, like Russell, to combine a robust platonic ontology of universals with a simple empiricist theory of concepts of them (Plato would be horrified). No, if you accept the platonic ontology of universals you need to recognize that empiricist epistemology won’t work for them; another epistemic faculty is necessary in order to account for our knowledge of universals. This is particularly true for knowledge of propositions that concern only relations of universals—a priori knowledge, as Russell says.  If you want to stay empiricist in your epistemology, you can’t very well accept a platonic ontology—you need to go nominalist or conceptualist or Aristotelian or skeptical. Russell here lazily combines his mathematician’s fondness for platonic ontology with his British empiricist predilections regarding knowledge. The brief passage I quoted contains a gaping epistemological hole whose existence it is hard to believe he didn’t notice.
So what should be said about the epistemology of universals under a platonic conception? It seems to me that an admission of inadequacy is in order. First, we do not acquire an adequate conception of universals by perceiving their instances, since (among other things) perception only presents them in instantiated form, which is not their original intrinsic form; nor is this conception derivable from perception by some intelligible procedure. If this were our only access to universals, we would be cognitively closed off from what they really are. But second, our actual intellectual grasp of them leaves much to be desired: we have only the most hazy and sketchy conception of what they like in themselves. Any mental images we might have corresponding to whiteness, say, do little to further our knowledge of the universal; but in their absence only the word provides a solid handle onto what we are talking about—and it is just a word. Notice how negative the list of characteristics is that define universals for us; we are shooting in the dark at an elusive target.  I think it is even unclear whether our thought concerning universals represents them as instantiated or uninstantiated: we know that the platonic tradition says the latter, but earnest self-reflection leaves the question up in the air (I suspect many people would reject the tradition on this point). We really have very little idea what these entities are like—yet if they exist they must have a determinate nature. They can’t be as wispy and airy as they seem. Plato was right to teach that they are extremely hard to know, requiring diligent training and focus; but I see no evidence that any course of training has actually succeeded in bringing them limpidly into our ken. They remain as elusive—as tantalizing—as ever.  I don’t think this casts doubt on their robust reality, but it does suggest that our knowledge of them is shaky and possibly inaccurate. Perhaps they are natural mysteries. Perhaps our grasp of them is like our grasp of the quantum world—just not very penetrating. Perhaps they belong to a world that our epistemic faculties are not well designed to comprehend; we do better with basic cave epistemology. Plato discovered a part of reality that is only dimly glimpsed by us. For those with different epistemic faculties it might present itself very differently. Russell should have considered the possibility that our knowledge of universals is inherently limited and sorely lacking in clarity and distinctness.
 Many criticisms have been made of the theory, which I won’t rehearse, but let me just note a couple of points arising from Russell’s breezy discussion. First, does he really believe that young children consciously go through this process of reasoning in order to come up with the general concept of whiteness? Does he think parents and teachers instruct children to do this in order to acquire general concepts? Second, where do we get the idea of what is in common between things? Isn’t this a general concept that precedes all occasions of (alleged) abstraction? And don’t we see what is in common precisely by already having the universal concept we are supposed to be acquiring? When you judge that snow and milk are similar don’t you judge that both are white?
 All knowledge, whether a priori or a posteriori, involves universals, but a priori knowledge is concerned with relations between universals in their uninstantiated form, while a posteriori knowledge is concerned with universals in their instantiated form. Thus we can define the difference between the two types of knowledge by invoking the concept of instantiation.
 Here is a puzzle for you: if you could see the universal Whiteness, would it look white? Maybe it only looks white when it comes exemplified in a particular; in itself it has no color. Then how does it make things look white?
 The idea that we have acquaintance with universals in our cognitive encounters with them seems particularly strained: to suppose that they come before the mind in naked form, fully revealing their contours and texture, is surely wide of the mark. Rather, they remain maddeningly out of reach, especially when no image accompanies their appearance in thought. This is why they have always seemed so speculative and suspicious to the epistemology obsessed. We are acquaintance-deficient with respect to them.