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Identity And Universals: A Conceptualist Approach to Logical, Metaphysical, and Epistemological Problems of Contemporary Identity Theory
Chapter 8, Intentional Contexts
by Carolyn Ray

Date: 11 Nov 98
Copyright: Carolyn Ray

It would be hard to know, given the Naive View and conceptualism, what identity outside an intentional context would be. However, since this is the standard designation for a certain type of puzzles, I introduce them as such.

'A Is A' Versus 'A Is B'

In his "On Sense and Reference," Frege considers the meanings of two propositions both of which seem to indicate sameness but each of which seems to have a different import:

...Is Sameness a relation? A relation between objects? Or between names or signs of objects? I assumed the latter alternative in my Begriffsschrift. The reasons that speak in its favor are the following: "a=a" and "a=b" are sentences of obviously different cognitive significance: "a=a" is valid a priori and according to Kant is to be called analytic, whereas sentences of the form "a=b" often contain very valuable extensions of our knowledge and cannot always be justified in an a priori manner....If we wished to view identity as a relation between the objects designated by the names 'a' and 'b' then "a=b" and "a=a" would not seem different if "a=b" is true. This would express a relation of a thing to itself, namely, a relation such that it holds between every thing and itself but never between one thing and another. What one wishes to express with "a=b" seems to be that the signs or names 'a' and 'b' name the same thing; and in that case we would be dealing with those signs: a relation between them would be asserted. But this relation could hold only inasmuch as they name or designate something. The relation, as it were, is mediated through the connection of each sign with the same nominatum. This connection, however is arbitrary. You cannot forbid the use of an arbitrarily produced process or object as a sign for something else. Hence, a sentence like "a=b" would no longer refer to a matter of fact but rather to our manner of designation; no genuine knowledge would be expressed by it. But this is just what we do want to express in many cases....

....Now it is plausible to connect with a sign (name, word combination, expression) not only the designated object, which may be called the nominatum of the sign, but also the sense (connotation, meaning) of the sign in which is contained the manner and context of presentation.... (Frege, "Sense," pp. 85-86).

Frege is here struggling with the fact that we mean things by propositions and concepts, and that that meaning (what he calls the 'sense') can differ with context of use. What puzzles him, however, is how we can force that context into the propositions themselves, without reference to minds. He was interested in specifying a "perfect" language; he agrees with Kant that 'a = a' is an analytic a priori statement. According to the theory, some propositions can be understood without reference to reality; they are known a priori. When the predicate of a proposition is contained in the subject, the proposition is analytic. But the proposition 'a=b' is not like this; it seems to indicate a fact that we have to learn by experience.

For example, before it was known that Venus was a planet, not a star, and that its motion was retrograde with respect to the earth, resulting in its appearance in both the morning and the evening sky, people referred to it by two different names: 'evening star' and 'morning star.' According to Frege, if 'a=a' is a relation between the thing and itself, then neither 'morning star = morning star' nor 'morning star = evening star' is informative. So he says we should interpret identity as a relation between different names for the same thing. Such an interpretation will result in propositions of the form'a=a' remaining analytic and a priori, while those of the form 'a=b' are informative.

Conceptualism and the Naive View of identity provide a different interpretation. I hold that "is identical to" or "=" stands for an intentional relation between the conscious subject and an object of attention. It symbolizes the axiomatic concept IDENTITY, which refers to all entities. As we have been discussing, this concept expresses the fact that a thing is what it is and is some way. To what in reality does the concept RELATION correspond? The conscious subject can attend to two or more concretes and identify some fact that applies to all of them. In this sense, there is a relation between any two or more given entities; we say that there is "no" relationship between things when there is no relation that is significant to us in the context. To use the concept RELATION to refer to just one thing is to extend that concept beyond the distinction it was formed to mark. This is unproblematic, as long as we keep in mind that it is such an extension, and do not attempt to infer anything about the typical case from the special case. Incidentally, this is why undergraduate philosophy students have so much difficulty with the idea that identity is a relation; because they formed the concept RELATION the way everyone else does, it does not make sense to say that identity is a relation that holds between every thing and itself. It is an arbitrary rule they grudgingly memorize, and it comes to seem meaningful only in the context of symbolic logic--which is to say, in a context-free notation.

If simply repeating a fact counts as creating an analytic proposition, then statements of the form'a=a' are analytic in this sense. But then, so is 'a=b' once the referent of the terms is known. A statement is not analytic by itself; analyticity having to do with meaning, a proposition can only be analytic for someone. Statements of the form 'a=a' had to be learned, even if it only took one example for some people to get it. Once learned, it seemed like propositions of that form were always analytic. Statements of the form 'a=b' do not at first seem analytic; in fact, if the two names are not known to a particular person, then such a proposition can even be suspected to be false. But if 'analytic' means that the meaning of the subject term is contained in the predicate term, then once it is understood that the terms name the same thing, then the statement is analytic with respect to the person so informed. What about the alleged a priori nature of the statement 'a=a'? Since the meaning of the concept IDENTITY must be learned by experience (we are not born knowing that things are what they are), 'a=a' is not a priori; indeed, we have a great deal of evidence now that brain damage and certain approaches to identity theory can obscure the fact to which the concept refers. Let me explain these assertions by filling out my interpretation of the example that Frege gives.

The discovery that Venus was what people referred to by both the name 'morning star' and the name 'evening star' was indeed an astronomical discovery--for someone. But not for me. I learned the two other names of Venus by being told, in a course on Frege (1986) that 'evening star' and 'morning star' were both names that people used for it, because they did not realize that there was just one planet which appeared in the morning sky and the evening sky, and they did not even realize that it was a planet. The way that this story extended my knowledge was not the same way that it extended the knowledge of the people who were enlightened by the astronomical discovery. The latter were enlightened because they had made a mistake. They thought that the thing they called the 'evening star' rose in the evening, and then went away, not to return to their sight until the next evening; and they thought that the morning star rose in the morning and then went away, not to return until the next morning. They were wrong. That is why 'evening star = morning star' was informative for them.

Since I never made this mistake, having only been aware of one name for Venus ('Venus'), it is not informative for me in the same way. I am informed about the mistake that these people made, and the two other names that they called Venus. Having been so informed, for me, the term 'evening star' just means Venus, as does 'morning star;' these never had any other meaning. In Frege's terms, for me, not only is the reference the same for all three terms, but so is the sense. I can certainly imagine being in the place of those for whom this was an astronomical discovery, and seeing the enormity of this new piece of information. But that is to understand their context, and in their context, they do not mean the same thing by the identity statement. So there is a problem with the claim that, without regard to context, 'a=a' is analytic, a priori, and uninformative, while 'a=b' is synthetic, a posteriori, and informative due to a difference in the senses of the terms. The sense of any given term belongs to the conscious subject, not to the term.

If A=A, Then A=B

Leibniz's Law in formal logic is the inference rule of substitution, 'x = x.' Since Leibniz's Law is transitive, any expression that is equivalent to 'x' can be substituted for 'x.' If that is so, then why does the following argument using this inference rule draw a false conclusion from two true premises?

George IV wished to know whether Scott was the author of Waverley.

The author of Waverley is Scott.


:. George IV wished to know whether Scott is Scott. (Russell, "Denoting," p. 108).

Unless we are willing to grant that George was wondering about the validity of Leibniz's Law, we seem to have to give up the idea that inference by Leibniz's Law always preserves truth. In order to solve this puzzle, Russell takes the denoting expression 'the author of Waverley' to be meaningful only in the context of a whole proposition. It appears in the above argument in its abbreviated form; the expanded form is: 'one and only one entity wrote Waverley, and Scott was identical with that one,' so that the premises become:

George IV wished to know whether one and only one man wrote Waverley and Scott was that man.

One and only one entity wrote Waverley, and Scott was identical with that one.

The denoting phrase 'the author of Waverley' has been broken up into component parts, and thus no substitution of 'Scott' is possible. This is Russell's analysis of the puzzle.

On the conceptualist view, there is no puzzle. Substitution by Leibniz's Law requires that the conscious subject whose inference it is knows that both terms refer to the same thing. This means that, even when a particular argument form is valid, any particular argument can only be regarded as valid if the conscious subject making the argument knows that the substitution is accurate. The real problem with this puzzle is that it vacillates between contexts, because the argument is also about a conscious subject.

Whose argument is this? It is clearly not George's; George knows nothing of it, or else it would not be a puzzle in the first place. Let us say it is ours, since we are privy to it. That settles much of the difficulty immediately. While it may be true that George himself was not wondering about the law of identity itself, in a sense--from our point of view--he did wonder whether Scott was Scott. He picked out one thing by name, Scott, whom he knew to be an author. He wondered whether one of the things that Scott wrote, was in fact one of the things Scott wrote. The fact that he does not know the truth of the second premise is what makes the conclusion true in our context.

So there is an interpretation on which the original argument, without rewriting, is valid. To make the puzzle run, an equivocation must be committed, because an argument presumes an arguer. The arguer is obviously Russell here. Because he talks about George's states of mind, we implicitly fall into looking at the argument from George's point of view, as though he is the arguer. As we struggle with the puzzle, we weave freely between these two arguers, and this is what gives rise to the puzzle.

This solution highlights an interesting fact about puzzles regarding the truth preservation capacity of Leibniz's Law in belief contexts. This one, for example, can only arise if we (1) take into account (a) the usual meaning of the word 'wonder,' which implies 'does not know,' (b) the context of the assertion, to wit, that George really does not know that Scott wrote Waverley, and so would have no way of knowing how to do the substitution himself, (c ) how Leibniz's Law of substitution works, which is by substituting one term for another when we know that both refer to the same entity; and then (2) forget what we know about all of the foregoing. By attempting to find meaning in propositions from which reference to minds has been removed, it is easy to generate intractable puzzles.

Do Concepts Have Identity?

Existents have identity. Actions do not. An action is some way, but it is only some way in virtue of the entities engaged in it. As a mental activity, a concept therefore cannot be said to have its own identity. It is a mind-dependent "entity."

So what is the nature of my concept COLOR in 'These objects are exactly the same color'? The objects of my attention are not identical. Color results from the reflection of light, and each object reflects its own bit of light, so there is no identity among the colors either. But I am thinking about the objects (so of course we have my identity). When I judge that two objects are the same color, I am describing my interaction with the world: namely, that I perceive a similarity among the objects, and that I happen to have a word for that particular type of similarity. That is the whole story. It does not matter if I view the objects all at once, or over a period of time. Each time I categorize an object by color, I am engaging in the integration of this object of perception with other previous acts of perception. Concepts do not persist; I persist. My concepts recur.

An analogy may serve to clarify the relationship. I run every day. I was born with the capacity to run in the sense that the activity requires limbs and energy, but I had to learn to run. It took me a long time to get good at it. The fact that I am now so ready to run and that I do it pretty much the same way each time does not mean that there is a persistent running in me or that is a part of me. Similarly, by virtue of having a healthy mind, I abstract automatically, but I had to learn to do it properly. Now I am good at it, and can do it well almost "without thinking" in the easy cases. I do not have to

laboriously reconstruct my concepts every time I am met with similarities in perception, just as I do not have to relearn how to run every day. There is no persistent concept in me; rather, the concept itself is that act of integration.

Fictional "Objects" And Intentional Women

The concept IDENTITY is formed on the basis of a primary fact of reality--on the basis of entities that are some way. I hold that fictional "objects" (hereinafter 'figments') fall outside the class of entities, and that when we use a name for a figment, we fail to refer. Any application of the concept IDENTITY (or the concept REFER) to figments is a metaphorical extension. No identity without an entity.

How can discussions of literature proceed, then? When I speak of Elizabeth Bennet, the well-defined principle figment in Pride and Prejudice, other people who read the book seem to know what I mean. We can argue about what Elizabeth's actual moral code was, and at what moment she really began to fall in love with Mr. Darcy. This coincidence is sometimes referred to as 'intentional identity:' our intentions, like the arrows of several archers, seem to all aim toward one point, whether or not there is anything at that point (Geach, "Intentional," p. 627). But this is simply too strong; it is one thing to metaphorically extend the concept IDENTITY to figments; it is quite another to extend it to the intentional places where intentional objects would be if there were something to which we were all referring.

This problem is sometimes solved in terms of possible worlds--a method to which I am opposed. There is an alternative in any event. It is the very nature of our concepts as integrations of an unlimited number of concretes that allows us to understand stories about people we have not met, create ethical principles, make mistakes, believe lies, and understand fiction. The fact that our statements about Elizabeth fail to refer does not make them meaningless. Referential failure simply means that there is no real object that corresponds to the name 'Elizabeth Bennet.' Because you and I both understand all of the concepts used in the book, we can talk meaningfully about Elizabeth without having to impute identity to a figment.

To see how this works, we have to alter our standard question slightly, and ask, "To what in reality is the name 'Elizabeth Bennet' supposed to refer?" And I think the answer is clear: the name is supposed to refer to a person--specifically, a woman. We have experience of women, and we have many concepts formed on the basis of those experiences. Thus it is not hard for us to begin to grasp what Austen is talking about. Note that it is harder to understand what an author like David Brin is talking about, since his figments are so often not supposed to be the referents of any of our current concepts (see, e.g., Startide Rising).

Austen gives the figment a name. We know how names work: they are always attached to entities. And she uses concepts with which we are familiar to describe the entity. This is all that is needed to make Elizabeth something we can talk to each other about. There need be no entity in any possible world to be the subject of our discussion. To put it another way, she is a hypothetical woman, elaborately described. In addition, when we argue about what her actual moral sensibilities are, there is someone else who is implicitly included: Jane Austen herself. What we are really trying to understand is what Austen intended her figment to represent.

What are we doing, then, in a case that is not so clear? Almost the same thing. For example, suppose that we are arguing about Elizabeth's moral character, and someone who has not read the book overhears us and thinks that we are analyzing one of our friends. Our audience also knows the concepts we are using, and she thinks that they refer to something in reality. She is deceived, because she extends her concepts to include an unknown as a real thing. The difference between our discussion and what is overheard is that we know that Elizabeth is Austen's creation, that it is really her intentions that we must analyze through her words; while our hapless eavesdropper thinks we are gossiping.

But we are all making mistakes. You and I are making the mistake of talking about this figment as though it is a woman, while the eavesdropper is making the mistake of thinking that it is a woman. Our mistake has our complicity; hers is involuntary.

It is possible for me to make claims about Elizabeth that you think are not correct. If Elizabeth has no identity, then how can we describe what happens? When we talk about Elizabeth, we are not stating propositions that are literally true or false of her. Rather, we are making statements that are either consistent with Austen's presentation of her, or we are making statements inconsistent with that presentation. In many cases, these points are fairly easy to verify, Austen being a consistent writer.


Is the proposition '5+7=12' an identity claim? If so, then what is the nature of the entity whose identity is being asserted? To answer this question, or course, we must ask, "What in reality gives rise to the concept NUMBER?"

The concept NUMBER results from a high-level abstraction from abstraction. The concepts it subsumes are the concept ONE, the concept TWO, the concept THREE, and etc. To what in reality do concepts such as these refer?

The concept THREE refers to the fact that the conscious subject may attend to a group of concretes for some purpose. The concept UNITY refers to an existent with boundaries. The conscious subject may attend to any particular unity by itself, and such acts of attention gives rise to the concept ONE. The subject may also attend to any given unity and another given unity together. Such acts of attention give rise to the concept TWO. Attending to this group of two and another unity together gives rise to the concept THREE. And so on for the natural numbers. Similarity with regard to one-to-one correspondence between groups is the only dimension along which groups are compared to get the counting number concepts. I will not plague the reader with the derivation of the integers and the real numbers, since it is actually another concept in which we are interested.

If numbers are concepts, and identity just means that something is some way, then when we use the symbol '=' in the proposition '5+7=12,' to what does it refer? One might suppose that an identity is asserted because '5+7' and '12' are two different names, or ways of expressing, the same concept. But following Ockham's principle of parsimony with regard to the nature of concepts, one can only mean this in a metaphorical sense.

One's concepts are not objects; they are mental activities. As such, they have no identity on their own. So one cannot coherently interpret the '=' as indicating an assertion of identity between concepts. Let me turn to the analysis of the proposition itself.

The concepts FIVE, SEVEN, and TWELVE refer to the conscious subject's capacity to attend to 5 units, seven units, and 12 units, respectively. The units themselves need not be present to the subject's awareness; like any concept, number concepts are the means whereby we think about concretes, but they need not be any particular concretes. And the concepts are formed by each conscious subject as a result of attention to concretes, but once abstracted, the acts of attention need no longer be part of the present cognition. The concept PLUS refers to the act of attending to two groups as a single group. The concept named by '=,' then, refers to the subject's recognition of the fact that '5+7' and '12' refer to groups that have the same number of units in them. Does '=' stand for the concept IDENTITY in such a proposition, or the concept EQUAL?

I contend that it stands for the concept EQUAL. There is no single object that is the referent of two names or phrases here. The symbol '12' does not name a thing at all, the way 'Venus' names a thing. Venus is an object. TWELVE is a concept, and it refers to the grouping of concretes by an act of attention.

Concluding Remarks

The human tendency to name has led to the realist tendency to find real objects to correspond to all words, and to the nominalist tendency to think that all words are arbitrary. We name our concepts because it is the easiest way to keep a grip on the vast amount of data we amass when engaging in integration. But the search for things to go with those names will only turn up (1) the conscious subject who uses the concepts, and (2) the objects of experience the conscious subject intends by means of those concepts. Thus, the concept IDENTITY has a metaphorical use in intentional contexts such as those discussed in this chapter, which, though understandable, will confuse philosophers who attempt to analyze propositions without reference to the conscious subject.

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