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Identity And Universals: A Conceptualist Approach to Logical, Metaphysical, and Epistemological Problems of Contemporary Identity Theory
Chapter 3, Universals
by Carolyn Ray

Date: 11 Nov 98
Copyright: Carolyn Ray

Implicit commitments to nominalism or realism make their appearance in identity theory, but their advocates are not necessarily aware of them. Both an adequate theory of universals and a good understanding of the purpose of definition are essential for identity theory; yet the student emerges from school with a very unhealthy skepticism with regard to universals and definitions, which is encouraged in the professional community. The doctrine of logical possibilism, too, is part of the mainstream; nominalists find it compelling, while realists are confounded by it. Because these unstated commitments seem to be at the heart of many of the puzzles and the disputes, it is important to confront them and their implications, and to briefly describe a theory of universals that can resolve the genuine questions and block the puzzles at their source.


Extreme nominalism takes common terms to be conventions. W.V.O. Quine has argued, influentially, that it is inconsistent to take a midway position, such that some terms--such as relations--do not name real entities, while others--such as properties--do. He is so worried about unnecessary ontological posits that even the appearance of abstract singular terms in subject position is troublesome:

One might begin by explaining 'Humility is a virtue' and 'Redness is a sign of ripeness' away as perverse ways of saying of humble concrete persons and red concrete fruits that they are virtuous and ripe. But such a program cannot without difficulty be carried far. What of 'Humility is rare'? We may for the sake of argument construe 'Humility is a virtue' and Humility is rare' as 'Humble persons are virtuous' and 'Humble persons are rare'; but the similarity is misleading. For whereas 'Humble persons are virtuous' means in turn that each humble person is virtuous, 'Humble persons are rare' does not mean that each humble person is rare; it means something rather about the class of humble persons, viz., how small a part it is of the class of persons. But these classes are abstract objects in turn--not to be distinguished from attributes....Maybe this abstract reference can still be eliminated, but only in some pretty devious way (Quine, Word and Object, sec 25).

Words are meaningful in the context of other words, but general terms only refer to other words, not to real universals nor even to real concrete entities. The extreme nominalist position thus holds that the only thing common to a group of particulars is that they are all called by the same name--objects "are" men because we call them 'men'. This means that no account can be given as to why only certain things are indicated by that word but others are not; this fact gives rise to a special problem when the identity of a thing over time is in question, since sortal relativity is involved in identity claims.

The role of definitions in extreme nominalism is to keep straight which words are agreed upon to go with which other words; they are taken to be the whole of what the word means, and thus are frequently stated as necessary and sufficient conditions--as 'iff' statements. Nominalists approach identity questions by attempting to supply such definitions (see, e.g., Noonan, Personal Identity). Fusing the doctrine of logical possibility with the belief that there is no interesting connection between the real world, general terms, and definitions, extreme nominalists are quite willing to rearrange the conceptual scheme at any time. Implicit commitment to this theory of universals combined with skepticism and logical possibilism is perhaps what makes some identity theorists comfortable with ignoring science and making up their own science fiction examples: scientific discoveries are no better reason nor no worse reason to rearrange the conceptual scheme. Thus, identity theory presents a special problem for nominalism because identity statements must be relativized to a sortal--and the sortals of nominalism are infinitely plastic.


Responding to the ideas of logicians such as Quine and Bertrand Russell, E. J. Lowe has found occasion to claim that "there are no bare particulars" (as against Russell's, e.g., logical atomism (1905)). He understands this claim to be equivalent to saying that particular objects are only identifiable and individuable as particulars of a certain kind. And a corollary of this second claim is that "individuals and kinds are ontologically on an equal footing;" thus realism with regard to individuals implies realism with regard to kinds (Lowe, Kinds of Being, pp. 3-6). Realism is the theory of universals that takes the referents of common terms to be mind-independent existents over and above the objects themselves--whether the universals are in the things themselves or somewhere else.

Realism is a metaphysical doctrine about existents, not an epistemological one about how we know them. Its basic thrust is that there are real, mind-independent essences in virtue of which we call things by general terms--we call objects 'men' because they are Men, meaning that there is a metaphysical essence Man (or Rationality, etc.) which is common to some objects, and we call anything with that essence 'a man'. Realists attempt to approach questions about identity by making metaphysical claims about those essences; it is concerned to answer questions of the form, "why is a man a man rather than a dolphin?" or "what makes a man, a man?" or "is this the same man or a different one?"

Identity theory presents specific problems for realism. According to Lowe, "individuals are only recognizable as individuals of a sort, while sorts are only intelligible as sorts of individuals" (Lowe, Kinds, p. 11-12). As a realist responding to the claims of extreme nominalism, Lowe feels it is necessary to make this claim in order to avoid positing either bare particulars or Platonic Forms. The claim requires him to explain how we can experience unfamiliar objects for the first time, particularly objects of natural kinds and particularly in infancy, by positing at least some innate concepts. Unfortunately, this leaves us with a dilemma: with regard to unfamiliar artifacts, we must either have innate concepts for them, or else they are indistinguishable from their background. Neither choice seems very likely to be true.

Many questions about the identities of objects and persons are straightforwardly epistemological ones: "what are the criteria of identity for persons and how do we determine those?" and "how do we reidentify?"--and it is impossible to avoid the epistemological character of the inquiry by simply denying it, or with disclaimers that the epistemological questions are not interesting philosophically (e.g., Noonan, ibid, p. 2). But realism's metaphysical answers to these questions only create additional problems: (1) how we come to know those real universals, (2) what their ontological status is, (3) what the criteria of identity for real universals is, and (4) what to do with borderline cases and massive transformation. Nominalists, it seems, have a field day constructing thought experiments born of logical possibilism to thwart the realists' sorting projects; and, being thoroughly indoctrinated into the mainstream of logical possibilism--perhaps against their better judgment, since they seem to desire most of all that the referents of their terms be real--realists feel they have to deal with them.


In the effort to make universals known, realism makes them mysterious, since it is not at all clear how we come to know of them, and thus makes science, the propositions of which are general, mystical. In the effort to avoid unnecessary ontological posits, extreme nominalism denies that general words refer to anything extralinguistic, with the result that science's general propositions are not about anything at all. But there is an alternative.

Conceptualism is a theory of universals that takes the things named by general terms to be mind-dependent abstractions. These mental entities are based on similarities that the conscious subject notices between real objects. Higher level abstractions are based on similarities between the preselected objects that are the referents of two or more concepts. Although individuals are experienced as being some way--as "this-such"--they are not experienced as individuals of a sort until the conscious subject sorts them by abstraction and integration; in other words, concept formation is always an active, if sometimes automated, process of discriminating individuals from their background and grouping them on the basis of similarity. To put it another way, individuals are experienced as having an identity, of being some way rather than no way; but we do not "recognize" individuals on the basis of a real essence which they share or of a sort to which they belong, nor are our concepts innate--they are formed by us.

Conceptualism takes scientific inquiry to use general words but to be about particulars, by acknowledging that particulars are the source of the concepts that conscious subjects form by abstraction. Concepts are thus general or universal, in that they refer to many particulars, and comprehensible, in that they are simply mental entities or activities. Unlike extreme nominalism, which takes definition to be the content of the concept (word) defined, conceptualism takes definitions to be the means by which the conscious subject (1) connects concepts to the particulars that give rise to them and (2) organizes information about the referents of a concept and enables users of concepts to compare and check their understanding.

Historical Context of Conceptualism

Conceptualism is an old theory of universals, with many variations. The reader may find a brief excursion through the views which have had the most influence on this work to be helpful in integrating this conceptualist view with more familiar ones.


Aristotle was apparently a moderate realist. However, his method of objectivity--the method by which he analyzes concepts--is used throughout this work. The method consists of asking "To what in reality does this concept refer?" I also rely upon Aristotle's real definition by genus and differentia (without the realist posit).

William of Ockham

Ockham considered the universal an activity of the mind--an intention toward particulars--rather than an entity in itself:

But what is it in the soul that is such a sign? It must be said that with respect to this article [of the question], there are different opinions. Some say that it is nothing but a certain [something] contrived by the soul. Others [say] that it is a certain quality subjectively existing in the soul, [and] distinct from the act of understanding. Others [say] that it is the act of understanding. Reason is on the side of these last, because 'What can be done through fewer [things] is done in vain through more' (Ockham, Summa Logicae, I, 12, 29-36)

With Ockham, I adhere to both the principle of parsimony and the intentional view of concepts. While I think it is reasonable to say that concepts are what our minds do rather than things that they contain, for simplicity I refer to them as 'mental entities.'

In addition, Ockham took in stride the objection that, if by 'man' no one man is understood more than any other, then universals enable one to understand every man whether one had ever thought about them or not:

In that respect, it seems it has to be said as a consequence that an infinity [of things] can be cognized by such a confused cognition. This seems no more unthinkable than the fact that by the same love or desire an infinity [of things] can be loved or desired. But the latter does not seem unthinkable. For someone can love all the parts of some continuum, which are infinite. Or he can long for all the parts of the continuum to endure in being. Yet by such a longing, nothing is longed for except some part of the continuum - and not one any more than any other. They all have to be longed for, and yet they are infinite [in number]. Likewise, one can long for there to be all the men who can be, and yet they are infinite, because an infinite [number of men] can be generated.

So, therefore, it could be said that the same cognition can be [a cognition] of an infinite [number of things]. But it will not be a cognition proper to any of them. (Ockham, Commentary, sec. 6).

Similarly, I hold that the concepts denote not only the concretes on the basis of which they are formed by an individual, but rather that part of their purpose is to enable the extension of a mind which can retain only a finite amount of information, to all concretes that will fall within its range (see Kelley, "A Theory of Abstraction," pp. 21-22).

John Locke

For he has the perfectest idea of any of the particular sorts of substances, who has gathered, and put together, most of those simple ideas which do exist in it; among which are to be reckoned its active powers, and passive capacities, which, though not simple ideas, yet in this respect, for brevity's sake, may conveniently enough be reckoned amongst them. Thus, the power of drawing iron is one of the ideas of the complex one of that substance we call a loadstone; and a power to be so drawn is a part of the complex one we call iron: which powers pass for inherent qualities in those subjects (Locke, An Essay Concerning Human Understanding, II, xxiii, 7).

Locke claims that we do not perceive things that correspond to more abstract concepts, such as iron, but rather we perceive things that are hard, shiny, gray or transparent, malleable or not. It is from these perceived qualities that keep appearing together that we then form the abstraction IRON. Moreover,

He that will examine his complex idea of gold will find several of the ideas that make it up to be only powers: as the power of being melted, but not of spending itself in the fire, of being dissolved in aqua regia, are ideas as necessary to make up our complex idea of gold as its colour and weight.... (Locke, Essay, II, xxiii, 10).

Locke includes the causal efficacy of an object to be part of the source of the concept that is formed (by abstraction) from those similarities. I follow Locke in taking the "causal powers" of things to interact with their environment to be part of the concepts formed by comparing those things.

David Kelley

Kelley is a contemporary conceptualist whose development of theories of perception and abstraction are relied upon heavily in this work.  He argues that the capacity to group objects by similarity requires, in addition, the capacity to notice differences: I can perceive two objects as similar in some respect only after I distinguish them as standing out from the rest of their environment. This theory of abstraction fits seamlessly with the Aristotelian form of definition by genus (the group of existents similar to each other in some respect) and differentia (the respect in which certain items in that group can be distinguished from the rest). Kelley's chief dispute with Locke (aside from disdaining his apparent representationalism) is with Locke's characterization of abstraction; this characterization is evident in the quotes above: (1) He points out that Locke's account assumes the ability to grasp abstract features perceptually, which leaves that ability unexplained; Kelley argues for a dimensional theory whereby determinate features, rather than abstract ones, are perceived, thus in turn enabling the comparison of those features along certain dimensions. (2) He notes that Locke assumes that objects are perceived as individuated properties and then put together by the subject, yet we know that it is more common for people to not distinguish properties from objects as they distinguish objects from their backgrounds; Kelley argues that we must take this fact into account when explaining abstraction (Kelley, "A Theory of Abstraction," pp. 8-14).

Universals and Identity

I asserted earlier that identity theory is impossible without an adequate theory of universals, and that nominalism and realism create more problems than they solve. From a conceptualist point of view, what do theories of universals have to do with theories of identity? To answer this question, it may be helpful to answer a second question: When we use the word 'same,' to what do we refer? Sometimes we refer to a thing, a unity, as in "I'm still driving the same car after all these years." Sometimes, however, we say, "Your car is the same color as mine." What is it that we are saying is the same?

When I use this locution, 'same color,' it indicates that I have formed the concept RED by perceiving a difference between some things and their background, and similarity among these things taken together. I find that your car and my car are similar in such a way that I would classify them both under the concept RED. But to what in reality do the concepts SIMILARITY, DIFFERENCE, and SAME refer?


What facts in reality give rise to the concept DIFFERENCE? Our perceptual apparatus detect edges--metaphysically real edges--along which an object stands out from its background and from other objects. Differences in color, for example, between an object and its background enable us to find the edge. The edge of a ball stands out as a visible difference between the ball and its background, even for infants only hours old, as is indicated by the fact that their eyes will track a ball that is moved in front of them. We are able to perceive objects as different because our perceptual apparatus are set up to measure various features of the world. For example, our eyes can measure the wavelength of light within a certain range of values, and color is the form in which we perceive light. Along the dimension of color our eyes might measure two balls to reflect light of two different wavelengths, and the difference in wavelength is perceived as a difference in color. We can also measure the extension of edges, and the form in which we perceive such extension is length. Thus, things are some way, but difference is not in them; rather, difference is an aspect of the conscious subject's intention toward two or more things the dimensions of which it measures.


What are the referents in reality of the concept SIMILARITY? The difference between one thing A and another thing B may be less (as measurable by our perceptual apparatus) than the difference between A and a third thing C, along some dimension. For example, two oranges stand out for us as different in a box of apples. When the wavelengths of the light reflected by two oranges are closer to each other than the wavelength of light reflected by an apple as compared to that reflected by an orange, we say that the oranges are more similar to each other than either is to the apple along the dimension of color. This is the fact that gives rise to the concept SIMILAR.

Since our ability to measure wavelength in this way is often considered mysterious and indicative of real universals, consider the fact that all measurement is done by comparison, either of one non-standard object to another, or of any given object to a standard. I can tell when there is more sugar in one container than another, to some degree of fineness. I also have the approximate dimensions of the "one cup" standard memorized; so even when I do not have the physical standard handy, it is in virtue of the fact that I have used that standard so often that I no longer need it. I compare the sugar in the bowl to the size of my hands, the bowl, the counter, my body, the kitchen itself, the cookbook, taking into account the distances of all these things from my eyes. (This characterization of measurement is explained particularly well by Albert Einstein: see Relativity, Chpt. II.) Just as I do not need the measuring cup to see that there is more sugar in the bag than there is in the bowl, I do not need a spectrometer to measure wavelength unless I have some scientific purpose requiring finer distinctions. I have a measuring device built into my body. I need not know anything about the wave nature of light, nor even about the spectrum, to make these comparisons.

The concept SIMILAR is chiefly epistemological, and it is metaphysical only by extension. When our concepts are valid, there is some basis in external reality for the classification. Similarity is not in things, but the word refers to something: namely, the intention of the conscious subject with respect to the objects compared.


To what does the concept SAME refer when I say, "Our books are the same color red"? 'Sameness,' in this sense, refers to the fact that I can compare the wavelengths of light reflected by the books, but cannot distinguish them from each other along the spectrum.

This is also the sense that the word 'same' has in the phrase 'same kind.' "I grow the same kind of plant in my outdoor garden in La Jolla as I grew indoors in Bloomington." Realists would have it that this is an identity claim, and that the claim of sameness is possible because there is a real universal in my plants (or elsewhere). On the conceptualist view with the theory of abstraction we have been considering, I measure the genetic endowment of plants via the wavelengths, shapes, and vertical or horizontal attitudes and lengths. Botanists have taken great pains to categorize plants with respect to much finer gradations than I can measure perceptually (for example, they find similarities between the poinsettia and the crown of thorns and call both 'Euphorbia'), but I do use scientific concepts for some of them. Sameness is not in things either; the concept refers to the fact that, with respect to some dimension, no distinction can be made using some given measuring instrument.

How Identity Is A Universal

The concept IDENTITY has as its referents all existents. Each thing that exists, is some way, or is characterized in various ways, and all these ways, including its dimensions, the ways it interacts with its environment, etc., are part of its identity. This is what I take Henry Veatch to mean by characterizing all concepts as "relations of identity": concepts are the intentional relations through which the mind intends things as they are in reality (Veatch, 'Realism,' p. 19).

On one hand, we use the word 'identity' when talking about just one thing. On the other hand, since the thing under discussion might be any thing, it is one of the broadest concepts. Thus, in the respect of having an identity, any particular thing is similar to every other thing. Why do we need such a concept at all? The fact that identity is so obvious explains why we form the concept, regardless of whether we feel inspired to reflect upon it or use it deliberately. Furthermore, philosophically, it is useful to have facility with the concept and be able to focus on the facts that give rise to it, as a means of directing attention to problems. We can see what happens when the conscious subject does not integrate that feature of reality denoted by the concept IDENTITY with a given endeavor; for example, the science fiction philosophers fail to take the nature of their objects of study into account, and the consequence is the unrestrained generation of spurious puzzle cases. At any stage in any investigation, one may ask oneself whether one is properly applying the concept, or whether instead one is making statements that contradict known facts about the nature of a given inanimate object or organism.

Finally, we have experiences which are fundamentally different from our experiences of real external reality. For example, we sometimes have dreams in which the "natures" of the "entities" change radically: a dream-dog has an intelligent verbal dream-exchange with a dream-person, or in an instant a dream-brick becomes a dream-bird and flies away. These are cases that are properly understood as being in violation of the "law of identity"--which is to say that they fall outside the concept IDENTITY. Nonetheless, these cases are reason enough for our need for the concept IDENTITY, just as they are reason enough for the concept REALITY: we need to distinguish conceptually between the real and the unreal.

Axiomatic Concepts

The above concern--why we would bother to have a concept that was so obvious and that included all things--brings us to axiomatic concepts. These concepts are not formed by means of differentiating some things from others, as other concepts are; rather, they are formed by means of attending to one aspect of all of reality, abstracting away from all distinctive measurements, and attending to what is common to all.

An axiomatic concept identifies a self-evident, undeniable fact, present in every act of awareness, upon which all further knowledge depends. For example, existence is such a primary fact. Without awareness of the fact of existence, no knowledge would be possible. I need not show you existence; you already know it. To "prove" that I am right about this fact of existence would be to assume the fact: even if I point, I assume that there is something to point to, that there is someone to see me, and that you know what I mean. To deny the fact of existence again requires affirming it: the one who denies, exists. Hence, EXISTENCE is an axiomatic concept.

Consciousness is a self-evident, primary fact in this sense as well: you are aware of being aware. Consciousness is present in all knowledge--and in all acts of denial. Thus CONSCIOUSNESS is an axiomatic concept. For obvious reasons, establishing the character of this concept will be important in the discussion of personal identity. Bear in mind, however, that if identity statements are always properly relativized to a concept, and concepts are simply mind-dependent entities that sum up information about the concretes to which they refer, then we must be on our guard about identity claims that appear to deny the reality of consciousness and its involvement in the categorization of those concretes. This point will be stressed throughout the remaining chapters.

Identity is another primary fact. I cannot observe that there are existents, without observing that they exist in some manner, that they are what they are, and are never other than they are. All proofs ultimately rest on this fact of identity, so it is not possible to prove it or deny it. So we see that IDENTITY is an axiomatic concept as well. These points are sometimes considered trivially true; but this is to miss the full meaning of those points. We will see that the "law of identity" is frequently violated in identity theory when specifying necessary and sufficient conditions, and when specifying epistemological criteria for the reidentification of existents. Consequently and most importantly it is violated at the level of definition: theorists attempt to "specify the boundaries of the concept" by violating the law of identity with regard to the existents which gave rise to those concepts in the first place. Nowhere is this habit more evident than in personal identity theory.

Ultimately, the reason that we "bother" to form axiomatic concepts implicitly is that we cannot help but notice the facts to which they refer. We bother to make these concepts explicit because we are capable of conceptual error; axiomatic concepts help us to formulate exactly what the problem is.

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