The problem of universals, then, is the problem of deciding what universals are, or are supposed to be, and whether universals exist. Universals come in a number of kinds well-recognized by contemporary philosophers. Universals, it is said, are either properties, relations, or types, but not class. It is worth noting that all four items are generally considered abstract, nonphysical entities. They are at least so considered by realists; there are others who use the terminology of properties, relations, etc., but who do not wish to be realists. Part of the difficulty, indeed, of understanding this problem is understanding the complex and confusing relations between theory and language, and what the use of language does, or does not, imply. For more introductory information explaining the basic concept of universals, see universal.
In giving a more detailed exposition of the problem, we could do far worse than to begin by asking, "What are universals supposed to be, really?" What are they in general? Given the above gloss, we are asking: "What sort of beings are types, properties, and relations, or what are they supposed to be?"
One might well compare this question to the central question of what might be called problem of substance: what are objects, anyway? As far as ontology goes, we have no other way to describe objects than by their relations to their properties and relations. If we try to determine what is meant by the question "What are objects?", ultimately we interpret that question as asking, "What are objects in relation to their properties and relations?"
In the same way, when we ask what universals are, we ask: "What are universals--abstract properties, relations, and types--in relation to particular objects?" So one might well regard the problem of universals as complementary to the problem of substance. The problem of substance has one trying to explain what objects, or substances, are in relation to universals (properties and relations); the problem of universals has one trying to explain what universals (properties and relations) are in relation to objects.
Why is this a problem? Three facts about universals, or constraints on how we think about what universals are supposed to be, will help to see what the problem is. Philosophers should be able to agree (if these constraints have been correctly stated) that, no matter what our theory of universals is, if universals really are said to exist, then our theory about universals have at least to be consistent with, and even to explain, these facts. In other words, we can (if they are correctly stated) take these three facts as background assumptions. Definitely we have to have some background assumptions, or else we would not have any tools to evaluate any theory of universals.
So here are the three constraints.
First constraint: universals can be multiply instantiated. Universals (if they exist) are (or can be) multiply instantiated. In other words, universals are supposed to be able to have potentially many instances; if a universal has an instance, then we say it is instantiated. For example: the type horse is instantiated by all the horses in the world. (It is a matter of considerable dispute among realists, whether uninstantiated universals exist, e.g., there might be a dispute whether the universal, flying horse, exists in spite of the fact that there are no flying horses.) So universals, whatever else we think about them, have to be the sorts of beings that can be multiply instantiated. A theory of universals has to make sense of the assumption that universals are supposed to be multiply instantiatable.
Second constraint: universals are abstract. Universals are supposed to be abstract. So, if we can form concepts of universals, then when we do, we form a concept of something abstract. In other words, when we think of, to change our example, dryness, we are thinking of something abstract. Of course, when we conceive of dryness, we might imagine a particular dry thing, like the Sahara Desert. But even though we imagine it, we understand that the Sahara Desert is not dryness itself. It is just an instance of dryness. Whenever we have an example of a universal in mind, we know very well that the example is not the same thing as the universal itself; the Sahara is not dryness itself.
Third constraint: universals are the referents of general terms. This is perhaps a very important constraint, because a very important argument infers the existence of universals from the observation that general terms seem to refer to something multiply instantiated and abstract. The general term 'red' (or 'redness'), for example, does not refer just to a particular red apple. Rather, if abstract properties exist, then the word 'redness' refers to an abstract property, not just one instance, because after all there are other instances of redness besides this apple. So if, according to a theory about universals, general terms do not refer to universals, then that theory should also hold that universals do not exist. According to this third constraint, any theory that holds that universals really do exist had better have a way for general terms to refer to universals.
There might be other constraints we might want to put on theories of universals, but these three are very common and uncontroversial.
With these constraints in mind, we can present the problem of universals as follows, a different way that, hopefully, will make it more obvious how it is supposed to be a problem:
See Platonic realism. Some text from the latter article will probably have to be copied to back this page in order to ensure some flow to this article.
Aristotle also had a realist theory of universals, but it differed significantly in several points. See Aristotle's theory of universals.
Well, the people who oppose both Plato's theory and Aristotle's theory tend to be rather hard-headed, intellectually speaking. They don't like all this spooky talk of "forms," which exist in some never-never land apart from space and time. They don't even like this talk of qualities that can exist in many different things at once, as Aristotle has it. These people would prefer if we just talked about particular things, thank you very much, because that's all there are -- particular things.
This view has a name: nominalism. So nominalism is the view that universals don't exist. No abstract properties, relations, or types exist! That's what they say. Since nominalists deny that universals exist, they don't have to worry about explaining those facts about universals that I listed. But that doesn't mean that nominalists still have nothing to explain. Because, clearly, they have lots of explaining to do. Their position is really very strange! I mean, consider this little argument: We do say, correctly, that this apple, lots of roses, and many sportscars are all "red"; so there is a property they have in common, namely redness; therefore there is a property; properties are universals, so universals exist.
How do nominalists reply to that sort of argument? Whatever they say, they sure as heck do not want to admit that anything universal exists; everything that exists, they say, is located in space and time. So we'll just have to see if the nominalists have anything to say in reply to that argument. Now, the word "nominalism" comes from from nominalis, which means, in Latin, "pertaining to names." The first nominalists said that only general terms or names exist -- no general qualities exist for those terms to refer to. Just the names. So we can say the name "redness" exists, but there is no universal, redness, to which it refers. What does the term "redness" refer to, then? Perhaps any particular red thing, and perhaps the collection of all the red things. This is called extreme nominalism: the view that universals do not exist, and that general terms (such as "humanity" and "redness") stand for either particular objects or collections of particular objects (such as "all humans" and "all red things").
Now if you?re a very worldly sort of person, who wants to say that whatever exists, can only exist in space and time surrounding us here and now, then nominalism might appeal to you.
But nominalism definitely has some problems; I'll explain two of them. So here's the first problem. If a universal is just a name, then all that the three humans, John, Mary, and Sally have in common, is that they are called "humans." There is no property, humanity, that they have in common. That seems very hard to accept! After all, we need only ask: why are they all called humans? We don't just say that John, Mary, and Sally are all humans for no reason at all: we say so for some reason, don't we? But it is because each of them is an instance of the type, humanity, so you might say. Or maybe you would want to say: each of them is called "human" because each is a rational animal. But at any rate, they each appear to have some properties in common that make them all human! For example: they all have highly-developed minds; they walk on two legs; they talk; and so on. It certainly does look like there are some properties that John, Mary, and Sally have in common -- which are what we call universals. And their having these properties in common is explains why they are all called "humans."
The point is that any nominalist worth his salt is going to have to come up with some way of answering the following: why is it that things that are described by the same general term appear to have many properties in common, even though in fact (as the nominalist says), they don't have any properties in common? I'm not saying that extreme nominalists haven't tried to solve this problem, because indeed that have tried. I'm just saying it's a very hard problem for them to solve.
Let's move on to a second problem for extreme nominalism. According to extreme nominalism, general terms refer only to particular objects or collections of them, right? That's what I said anyway. But surely when we talk about, for example, the redness of the apple, we don't mean the apple itself, but instead a property of the apple, namely its redness. Suppose extreme nominalism denies that that exists. Then it seems to be denying that this apple has the particular shade of red that it obviously has! That just seems insane. It seems as clear as anything can be, that this apple has a certain color, which we call red; after all, we can see the color! Or to take another example: if I say that B is between A and C, but I deny that between-ness exists, then I seem to be saying that B's-being-between-A-and-C doesn't exist; because that would be an instance of between-ness. So it would seem we should reject extreme nominalism because it denies that instances of properties and relations can exist, when it is as obvious as anything that at least instances of properties and relations exist! Even if we can't see or otherwise experience abstract, or general properties, surely at least we can experience instances of them; and it's pretty hard to deny the existence of something that appears to be staring you in the face!
So now let's look at two less extreme examples of nominalism. We won't spend too much time on these two theories. Now these two theories both deny that universals exist, which is why they are versions of nominalism. But instead of saying that general terms refer to particulars, or collections of particulars, they say that general terms refer to something else -- namely, images, or concepts. So let's begin with imagism. Imagism is the view that universals are mental images, pictures in the mind; or that general terms refer to such images. So the general term "humanity" means an image of a human being in my mind. "Redness" means a mental picture I have of a patch of red. Now, notice that there is a distinction between mental images and concepts. I can have an image of a thing in mind, but that doesn't mean that I am conceiving of the type of thing it is: I can be imagining what a person looks like without thinking specifically of the concept of what a person is. The image is different from the concept. Images generally are different from concepts. So then here's the second version of nominalism, called conceptualism: this is the view that universals are concepts, or that general terms refer to concepts. So triangularity itself is a concept -- of a closed, three-sided figure. The universal, humanity, is the concept of a rational animal. To be human, then, is to be an instance of that concept that you have in your mind.
I think you may see that these are initially plausible views -- especially conceptualism. But there are various problems that can be raised for both imagism and conceptualism, and there is one objection which I think we can use to reject both views immediately. Namely: images and concepts are of something. So if I have an image of a triangle, or a concept of triangularity, it is an image or concept of that. So we cannot identify images or concepts with what they represent. What we want to know is the type, or the property, or the relation, that they represent. So if I have an image of a triangle in my head, or if I conceive of triangularity, and I ask what sort of thing is the universal, triangularity, then I want to know what sort of thing this image is an image of, or what the concept is a concept of. That image or concept in my mind can't be triangularity, because the image or concept is supposed to represent triangularity. So to sum up, we might have images, or concepts, of universals, but clearly the universals are different from any images or concepts we might have of them.
Nominalism, at least the way I have presented it to you, would appear to be generally a very dubious theory, after we consider the objections to it. Now I'm going to ease our way into the final theory, which is called the resemblance theory, and which in my opinion at least has the best chance of being true. I'm going to introduce some terminology and motivate the theory, before I present it.
Remember our second reason for rejecting extreme nominalism: we said that surely at least instances of properties and relations exist! So this redness, this particular redness of this particular apple, or this instance of humanity, Mary, exists. Why not then admit that much, that the instances exist: this instance of redness, this instance of between-ness, this instance of humanity. Specific instances of types, properties, and relations are called tropes. So tropes are particulars, because they aren't multiply instantiated. There just one instance of each trope. Now although they are particulars, it's hard to say that they are concrete. Take Mary's humanity: of course Mary is a concrete thing, located in a particular place in space and time, but Mary's humanity? It sounds strange to say that that is located at all; rather, it's the type of thing she is, and it's just strange to say that the type of thing she is is located somewhere. Or take maybe a better example: London is north of Paris; so London's-being-north-of-Paris is a trope. Right? It's a particular instance of "being-north-of." But where is that particular relation? Is it at London? At Paris? Somewhere in the English Channel? That's just a strange question. London's-being-north-of-Paris doesn't seem to be a concrete thing at all. So even though it is a particular, it is, we might say, an abstract particular. The redness of this apple is a particular, but it's not concrete in the way that the apple is; so we say either that this redness is a trope, or more descriptively, that it is an abstract particular. "Trope" and "abstract particular" are two different names for the same category of being.
So then the suggestion now is to say: tropes exist; but universals do not exist, if conceived of as something over and above tropes. So the redness of the apple, the ball, and the flower each exist; but there is not something in addition to each of those things, some ghostly redness in general, which is somehow the same in each object. Now in saying that tropes exist, we?re not quite done explaining the resemblance theory, but that's an important part of it. If the resemblance theory is a solution to the problem of universals, then we should still expect some answer to questions like this: What is redness itself? Surely we aren't saying that redness itself is any specific instance of redness. Well then, what is it?
Try out this answer: "If I am not allowed to say that redness is any specific instance of redness, then I can still say that redness is the collection of all the particular instances of redness. So the universal, redness, would be a collection, of all the particular rednesses in the world. And, by the same token, humanity would be the collection of all the instances of humanity in the world." Well, this answer might fly, but we still have a problem. It is the same problem that was visited upon extreme nominalism: Sure, we can go ahead and say that the collection of all the redness tropes is what we mean by "redness in general"; but why do we call apple, the ball, and the flower all "red"? We can say that each particular redness is a trope, and that those tropes exist; but why are they all tropes of redness as opposed to any other property?
Well, here's a way to answer that question: we say that these three tropes, the redness of the apple, of the ball, and of the flower, resemble each other. Moreover, we can simply look at the three side-by-side and see the individual colors, and see that the individual colors resemble each other. Similarly in the case of John, Mary, and Sally: the reason we call all of them "humans" is that their individual properties resemble each other. So in general here's our theory: types, properties, and relations are particular attributes, or tropes, or abstract particulars, of objects; tropes are capable of resembling each other, and when a large number of tropes do resemble each other, we each formulate concepts and names which we use to apply to all of the tropes on account of the resemblance each of us sees. But nothing genuinely universal exists; there are only (1) particulars including objects and their tropes, and (2) particular collections of tropes, and (3) particular resemblances between particular tropes, or between groups of tropes. These three existence claims together make up the resemblance theory, which could also be called the trope theory.
Notice how the resemblance theory is different from Aristotle's theory. Aristotle said that a universal is the same in each object; but on the resemblance theory, each trope is quite distinct from each other trope.
The reading goes on to discuss this theory, but we are going to have to leave the discussion there. A lot of philosophers these days do find something like the resemblance theory as presented here attractive. But trust me, a lot more can be said on all sides. In fact, it is not uncommon to find whole graduate-level courses just on the problem of universals. But onto the next problem.
One more thing about nominalism. There is a type of nominalism -- ostrich nominalism -- which has none of the problems of the others. When asked 'What does one human have in common with another that makes us called them human?', the ostrich nominalist says 'Well, they have no entity in common, but they are both human. That's why we call both of them human.' This answer does not commit him to universals. Someone may reply, 'ah, but in virtue of what are they both human?'. The ostrich says to this 'We cannot analyse any further -- they're both human and that's it'. This sounds right to me.