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Problem of universals

The neutrality of this article is disputed.

There are many ways to explain what the problem of universals is briefly. Perhaps the most common way to introduce the problem identifies it with Plato's "problem of one over many." Plato's problem can be presented as follows. We observe this red rose, this red car, this red hair, and that red bird, and conclude that there is a thing that they all have in common, which for short we call "red" or "redness." But what is "redness"? There are two broad classes of view on that question, and the problem of universals is the problem of deciding which is right. The classic view of the dispute holds that there are realists (more precisely, Platonic realists) and nominalists. Realists hold that redness is a nonphysical being, called in general a universal, that stands in some relation to each red thing. Nominalists, to the contrary, hold that there is no such nonphysical being; nominalists have a variety of other explanations of why it is that we call all red things "red." The original nominalists were so-called because they held that there is nothing that all red things have in common other than the fact that they are all called (have the "name") red.

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.

Table of contents

1 The problem and constraints on its solution 2 Platonic realism 3 Aristotle's theory of universals 4 Nominalism

The problem and constraints on its solution

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 must at least be consistent with, and even 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:

Are there any seemingly curious beings that can be multiply instantiated, which are abstract (and which we conceive of when we conceive of abstract attributes of things), and to which general terms refer? If so, can we give any more general account of what these things are? In other words, can we give any sort of general account of what universals are, in their relation to objects, such that these three constraints about universals come out to be true?

Platonic realism

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's theory of universals

Aristotle also had a realist theory of universals, but it differed significantly in several points. See Aristotle's theory of universals.

Nominalism

Some people oppose the views of Plato and Aristotle and argue that only particular things exist. This view is called nominalism. Nominalism is the view that universals don't exist-- that is, no abstract properties, relations, or types exist.

The word "nominalism" comes from nominalis, which means, in Latin, "pertaining to names." The first nominalists said that only general terms or names exist -- no general qualities, but only their names, exist for those terms to refer to. The name "redness" certainly does exist, 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").

Universalists argue that there are two problems to nominalism:

• 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." They might have the property "humanity", or the property "animal" in common. But the properties the three share is that they all have highly-developed minds; they walk on two legs; they talk; and so on; and their having these properties in common is explains why they are all called "humans.". Nominalists find it difficult to deny that things have some properties in common.
• According to extreme nominalism, general terms refer only to particular objects or collections of them. But when one talks about, for example, the redness of the apple, it is not the apple itself, but instead a property of the apple, namely its redness, that is meant. Universalists argue that denying the redness of the apple means denying the apple its "obvious" red. So extreme nominalism denies that instances of properties and relations can exist, even when it is obvious.

[Rebuttals by nominalists here]

Looking at two other examples of nominalism:

• Some nominalists instead say that general terms refer to something else -- namely, images, or concepts. Imagism, to take an example, is the view that universals are mental images, pictures in the mind; or that general terms refer to such images; for example, "humanity" means a mental image of a human being, and "redness" means a mental picture of the color red. Now, notice that there is a distinction between mental images and concepts. [following should have personal tone removed and neutrality restored] 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.

[following should have personal tone removed and neutrality restored]

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 resemblancetheory, 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 inaddition 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.

But it isn't obvious why the resemblance theory doesn't simply devolve into realism upon our asking the following question: can two individual colors or other properties "resemble" each other so closely as to be identical? If they can -- and surely identity is the extreme case of resemblance -- then it seems to be possible for one property to be identically present in two places or contexts.

What keeps this sort of trope theory from turning into realism is the rejection of a disputed principle called the "Identity of Indiscernibles" (sometimes mistakenly called "Leibniz's Law" because Leibniz defended a similar but distinct principle). According to this principle, to put it roughly, "two" things that can't be distinguished are really only one thing. If that principle is applied to individual colors, then "two" colors that resemble each other to the point of identity are really just one color -- a conclusion the trope theorist has to reject. In order to reject it, the trope theorist also has to reject the Identity of Indiscernibles.

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 triesto avoid 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'.

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