The Solution to the Problem of Universals

Late in the week of April 16, 2000, I solved the problem of universals. I have delayed publication for a number of reasons. Before publishing, I wanted to develop the perfect formulations, to have ready answers to all probable objections, and to have acquired a detailed knowledge of the history of the problem. I have never quite been able to find the time. Until yesterday, I figured I would just keep waiting. But then I found myself searching for a fitting way to celebrate a recent victory. It came to me: why not publish? And so I am. I would still especially like to have had time to have developed that detailed knowledge of the history of the problem, but eight idle years is more than long enough. If I am right in my solution, then it is, after all, a matter of some urgency.

Readers of philosophy of a certain bent of mind may wonder why I have been so concerned with the history of the problem, especially if they find themselves agreeing with my solution. It has been my experience that the majority of those who concern themselves with philosophy and its problems are, in fact, concerned not with philosophy itself, but with its history. In the case of the problem of universals, for example, attempts at solutions apparently fallen into one of two mutually exclusive traditions: nominalism and realism. These traditions loom so large in the minds of, it seems, most philosophers, that they cannot conceive of a solution that does not belong to one or the other. But the history of philosophy is their cave, and nominalism and realism shadows on the wall. The real solution comes from outside. My interest in a deeper knowledge of the history of the problem of universals has its origins where philosophy and rescue spelunking meet.

Since I have not had time for a full survey of the history of the problem, I will make do with something more modest.Instead of placing my solution to the problem of universals in the full context of the history of Western philosophy, I will place it in the context of Objectivist philosophy. One reason this appeals to me is that, while I am not an Objectivist, if I can be said to belong to any tradition or school of philosophy, Objectivism is it.

Many Objectivists reading this will now wonder how I might propose to place my own original solution to the problem of universals within the context of Objectivism, given that Ayn Rand claimed to have solved the problem of universals herself.The answer lies in that the problem of universals, while a real philosophical problem, is also a historical artifact. I am not sure exactly how or why Ayn Rand misapprehended the nature of this historical artifact, but, to a significant degree, she did.

Certain critics of Objectivism have claimed that Ayn Rand totally misapprehended the problem of universals, and was therefore totally unjustified in her claim to have solved it. These critics are quite wrong on this point, but their criticisms have been very useful to me, because they have provided an avenue for placing Ayn Rand’s solution to the problem of universals into the larger context of Western philosophy. By borrowing from these critics of Objectivism, I will be able to show that the critics are right on one point: Ayn Rand did not solve the historical problem of universals — and wrong on another, far more important point. Borrowing from these critics will also allow me to compensate somewhat for my own limited knowledge of the history of the problem since Plato.

Ayn Rand’s Unfinished Solution & The Real Problem

Ayn Rand frames the problem of universals as a question: "To what precisely do concepts refer in reality?" [Introduction to Objectivist Epistemology, 2nd ed., p. 1] Her answer is that concepts refer to entities. The concept ‘white,’ for example, means and refers to all white entities (all white sheets of paper, all white shoes, all white chickens), past and present, as well as all white entities that will ever be. Ayn Rand was satisfied that, by showing how concepts are formed and what they refer to, she had solved the problem of universals.

Rand treated the problem of universals as a problem of epistemology, as is plain from the title of the book in which she gave her solution. But the problem of universals is not an epistemological problem at all; it is a problem of metaphysics. The crucial moment at which Rand leaves metaphysics behind comes in her discussion of commensurable characteristics and similarity.

The element of similarity is crucially involved in the formation of every concept; similarity, in this context, is the relationship between two or more existents which possess the same characteristic(s), but in different measure or degree.

… All conceptual differentiations are made in terms of commensurable characteristics (i.e., characteristics possessing a common unit of measurement). …

… When, in the process of concept-formation, man observes that shape is a commensurable characteristic of certain objects, he does not have to measure all the shapes involved nor even to know how to measure them; he merely has to observe the element of similarity.

Similarity is grasped perceptually; in observing it, man is not and does not have to be aware of the fact that it involves a matter of measurement. It is the task of philosophy and of science to identify that fact. [IOE2, pp. 13–14. Emphases are Rand’s.]

Any solution to the problem of universals must not merely account for how we form concepts from diverse similar objects, as Rand does, but must account for the phenomenon of similarity-as-such, must account for commensurability-as-such. In other words, when, as Rand says, we grasp the similarity of two commensurable objects through sense-perception, what is it in reality that we are perceiving? If two white entities appear similar to us, and therefore commensurable, what is it in the white entities that makes them appear similar? What is whiteness itself? How is it that this whiteness is in two places at once? Do the two white entities literally have something in common, like conjoined twins might have a common breastplate, or does each white entity have its-own-whiteness, a radically unique and particular whiteness that we, ultimately arbitrarily, treat as if it were commensurable with other conventionally "white" entities’ own radically unique and individual whitenesses?

If a philosopher finally answers that she believes whiteness is real, that all white entities have something literally "in common," like conjoined twins have body parts in common, she is a realist. If she says that these characteristics-in-common do not depend on the existence of particulars (entities), then she is a Platonist or "transcendent realist." If she says that these characteristics-in-common do depend on the existence of particulars, she is an Aristotelian or "immanent realist" or "moderate realist." If a philosopher finally answers that she believes whiteness does not exist, that it is an artifact of some or other kind of naming convention, she is a nominalist.

It is not clear whether Rand is a realist or a nominalist, because she never addresses the metaphysical problem of universals, which is both the historical problem of universals and the real problem of universals. My own tentative view is that Rand was some kind of realist, but I contend that there simply is no justification in the texts of Objectivism for a definitive answer either way.

(If this account of the problem of universals has not been perfectly clear for you, I recommend reading Michael Huemer’s account. If you are an Objectivist, pay special attention to Huemer’s comments on "dimension itself.")

The failing of Objectivism is that it takes the metaphysical commensurability of diverse and discrete entities as a given, and does not provide any validation of this position. Coming from the Objectivist tradition, I have come to prefer one phrasing of the problem of universals above all others. This phrasing integrates with the framework Rand built in Introduction to Objectivist Epistemology (IOE hereafter), but it clearly puts the question in the territory of metaphysics, where it belongs. It is to this question that we shall now turn:

What is the ultimate metaphysical basis for commensurability-as-such?

The Solution

I suppose I began my quest to solve the problem of universals in the third grade. The teacher was explaining fractions, I think, and was using a metaphor to communicate the idea of the common denominator. You could not add thirds and halves, he said, because they are not alike. Only like things can be added. Apples can be added to apples, oranges to oranges, but apples cannot be added to oranges. (Somehow, it was permissible to multiply unlike things.)

I found this metaphor consternating. It was obvious to me that you could too add apples and oranges, or apples and desk chairs, or apples and monkeys. My teacher’s claims to the contrary seemed to me to be part of an elaborate and cruel practical joke. I eventually just learned whatever rote mathematical convention it was that the teacher wanted me to learn, and I forgot about my consternation.

When I began, many years later, to see the commensurability oversight Ayn Rand made in IOE, I also began to ask myself: what, if anything, do the referents of concepts have, most strictly speaking, in common? This turned out to be a surprisingly difficult question to answer.

I began asking myself what members of various random unit groups had in common with each other: horses, men, tables, squares, groups of 24, trios, pairs, and so on. Eventually, it came to me that I should try to find the simplest possible units to deal with. Horses and tables were far too complex, even geometric objects like squares and triangles proved consternating.

My dive for simplicity finally hit bottom with ones. What do all entities that can be mentally grouped together for counting have in common? In other words, what do all referents of the concept "one" have in common? This is certainly a strange question to ask, since, at first glance, it’s apples and oranges. That is, it seems obvious at first that the infinitely diverse entities that can be enumerated need not have anything in common at all. What could one rock have in common with one counterfactual imagination of what might have happened yesterday?

What indeed? I then asked myself: what is the common denominator if one is trying to add one rock and one counterfactual imagination of what might have happened yesterday? Apples and oranges can be added if they are considered as fruit, just as halves and thirds can be added together if they are considered as sixths. Rocks and counterfactual imaginations of what might have happened yesterday can be added if they are considered as existents.

(Anything can be added to anything else if both are considered as existents. Zero makes such a poor denominator, I suspect, because it is strictly impossible for any two entities to have nothing in common. It is impossible to have something-that-is-not in common with anything, and it is impossible that any two entities should not positively have something in common.)

So if rocks and counterfactual imaginations of what might have happened yesterday can be considered as existents, if they are all legitimately subsumed under the concept ‘existent,’ do all existents have something real in common? Yes and no. (This is where the historic nominalism-realism dichotomy begins to break down.) Every existent has existence in common. I do not mean that existence is an attribute common to all existing things; existence is not an attribute, characteristic, or property. I mean rather that every existent has the very same existence in common with every other existent, in the strictest sense possible: there is, and can be, only one existent; what we perceive as entities are, on the metaphysical perspective, themselves the attributes of this primary, singular entity, existence itself.

In case this is not clear: from the metaphysical perspective, there is only one entity, which is existence itself, therefore the problem of universals, which asks why discrete entities apparently have properties in common, is radically dependent upon a false premise. There are no metaphysically discrete entities.

Suppose the Big Bang theory is true. Suppose further that our universe is the only one that exists. At some point in the ultimate past, then, everything that existed existed as a single infinitesimal entity of "infinite" density and temperature. The attributes, properties, and characteristics of existence-as-such were just the attributes, properties, and characteristics of this single entity. At this point in natural history, the problem of universals vanishes. Since there was only one entity, it is impossible to frame for this era the questions of the problem of universals, which all depend upon there being more than one entity through which a property can make its mysterious repeat appearances.

Eventually, this single entity expanded, so the theory goes, blooming into our whole universe and everything in it. At what point, then, did one entity become two? At what point did it become reasonable for us to ask of our world: how can one property be present in two discrete entities?


Existence is a metaphysical plenum. There are no gaps, no voids, no rifts of non-being dividing one entity from the next. Yet metaphysical gaps, voids, and rifts are just what the problem of universals presupposes. The submerged premises of the problem assume that entities are metaphysically isolated, that this rock and that one have nothing in common except perhaps mysterious universal properties such as "rockness." In fact, this rock and that one have not merely their "rockness" in common, but everything in common. This rock and that rock are, on the metaphysical perspective, precisely the same thing: existence itself.

Camouflage ordinarily makes it more difficult for observers to differentiate an object from its immediate background. But entities qua existents are given to us disguised with an inverse sort of camouflage. From our everyday perspective, the entities we perceive are indeed distinct from their backgrounds, and from each other. This perspective becomes deceptive when we concern ourselves with certain questions of metaphysics.

Imagine a furnished room made of a single, continuous flow of injection-molded plastic. The walls, the floor, the ceiling, the tables and chairs — all of these are of a piece. To an observer standing in this room, it might not be immediately obvious that it had been constructed in this unusual and counterintuitive way. In this room, a table is both a table and the room itself.

This observer would be equally correct if he were to point to a chair and say, from the quotidian, anthropocentric perspective, "that is a chair," or if he were to point to the same chair and say, from the "room perspective," "that is the room." Existence is, in fact, very like this unusual room, and the metaphysical perspective is the "room perspective" unbounded by the limits of metaphor.

The anthropocentric perspective is so problematic when investigating questions of metaphysics because it is so persistent and resilient. Because of this persistence, it might occur to us, for example, to ask what all visible entities have in common, but we would tend to answer by looking outward to the entities. We should instead look ourselves in the eye. What do all visible, olfactible, palpable, audible, gustable, and intelligible entities have in common? Against the instincts of realists, what these all have in common is neither something in the entities themselves, nor even something "out there," in any usual way we would understand this. What all these infinitely diverse entities have in common is — man.

Man is the measure of all things. Perceptual entities are abstractions from and measures of existence, measures measured out by our senses, and measured out from a metaphysical plenum. Attributes, characteristics, and properties are conceptual abstractions from these perceptually given measures, and as such are already abstractions from abstractions, double derivatives twice removed from the primeval, unitary entity.

Perception gives us discrete entities, and so it is natural that our attempts to understand the world begin with these. If we follow abstraction to its ultimate limits, however, these discrete entities given by perception dissolve, as existents, into existence. We find ourselves returning, through abstraction, to the level of pre-perceptual raw sensation. Every attribute, every property, every characteristic is of the primeval entity presented in its undifferentiated totality by sensation. Ultimate abstraction and no abstraction whatsoever turn out to be two sides of the same Moebius coin.

How are we then justified in treating the properties of one entity as commensurable with the properties of another? What is the ultimate metaphysical basis for commensurability-as-such? It is this: everything is perfectly commensurable with itself.

8 thoughts on “The Solution to the Problem of Universals”

  1. Fascinating.

    Can you write more on this? Can you provide more detail and flesh out the understanding some more?

  2. @Pete: Yes, I can write more on this, and I intend to, but presently my attention is elsewhere.

  3. I don’t think this solution works.

    Suppose we accept the premise that nothing is truly metaphysically discrete because everything shares existence in common. Ok, so a red shirt and a red car share existence in common; that tells me nothing of the “red” they share in common.
    If you say “Well, they have red in common because they are both really part of the same single entity; existence,” then a reasonable response would be “Then why isn’t everything red?”

    Seems like we’re back to square one.

  4. @XOmniverse:

    If there is only one entity, then that entity is everything, and, if anything is red, shirt or car, the answer to “Why isn’t everything red?” is: “Everything is red,” bananas notwithstanding.

    The essential error within the problem of universals is context-dropping. The problem is posed in the context of metaphysics. In that context, there are no discrete entities. But, though it is posed in the context of metaphysics, its genesis is in the more quotidian world of ordinary sense-perception and ordinary language. In this context, there are a plurality of entities.

    If, as I have done, one refuses to answer a question posed in one context by reference to another, the problem dissolves.

    Put another way: “we” are not back to square one, because you and I are, in the context of this discussion, discrete entities, even though we are, each of us, aspects of the unitary metaphysical plenum.

    tl;dr: Everything is red.

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