Here is an argument purporting to show that the word “blue” is meaningless. There are many specific shades of blue that have their own names: aquamarine, navy blue, cobalt blue, azure, cerulean, indigo, etc. With respect to each of these we have a specific concept or idea, as well as a specific type of visual experience. But the word “blue” is more general than any of these words: it includes them all while not being as specific as any. What kind of idea corresponds to it? The natural and traditional answer is that the idea of blue is an abstract idea—it abstracts away from the peculiarities of each shade of blue. We form the idea by a process of abstraction whereby we eliminate what is concrete and specific to leave the pure abstract concept of blueness.  But what is this idea exactly? As Berkeley pointed out, it seems to be “all and none of these at once”, and hence inconsistent.  Certainly we can have no mental image of such an abstract quality, only of its more specific types. Nor do we ever see an object as simply blue but only as a specific shade of blue. The alleged abstract idea seems elusive and problematic, a will o’ the wisp with no substantial content. In the sense in which I have an idea of cobalt blue I don’t have an idea of blue simpliciter. The idea looks like an invention, a piece of mythology. What is this process of abstraction that deletes everything specific to a shade and leaves only what is common to all shades? It is certainly not like separating in thought the wings and beak of a bird. But if there is no such general abstract idea, then the word “blue” cannot express such an idea. If so, it must be meaningless, since meaning consists in the expression of (existent) ideas. Obviously the argument generalizes to other general terms such as “triangle” and “cat”; indeed, it would seem to apply to a vast range of words. So large tracts of language must be declared meaningless. Or else we have to rethink our general account of what meaning is, perhaps questioning the very idea that ideas constitute meanings. That theory has produced a monster in the shape of abstract ideas, so perhaps it needs to be demolished and replaced by something different and better.
This argument, which will be familiar, can be added to the family of arguments that purport to show that meaning is impossible (or must be radically rethought): Quine’s indeterminacy argument, Kripke’s skeptical paradox argument, rampant verificationism, and perhaps others. Thus: the extension of a predicate must be determinate if its meaning is to exist, but it is not; there has to be a right and wrong way to follow a rule if meaning is to be possible, but no fact can be found that constitutes following a rule correctly; sentences must be verifiably true if they are to be meaningful, but few sentences are verifiably true. The present argument contends that general terms must express abstract ideas if they are to be meaningful, but the notion of an abstract idea is incoherent. This is a serious argument: Berkeley clearly has a strong point against Locke. It is indeed difficult to make sense of abstract ideas: they are abstract to the point of non-existence. It is also difficult to make sense of abstract universals as mind-independent entities (as opposed to concrete universals): objects can exemplify shades of blue, and we can see these shades, but no object is simply blue and can be seen as such. This is an abstraction, not a perceptual given. Russell thought that we understand predicates by being acquainted with the universals they denote, but how does one become acquainted with the abstract universal blue? That alleged universal cannot come before the mind in its own right, but only as qualified by some specific shade of blue. We can’t have an idea of blueness as such because there is no such property as blueness as such—there is nothing to have an idea of. And yet we have the general term “blue”. Nor is it easy to confine the force of the argument to certain fragments of language: not only will it apply to a great many general terms; it will also generalize to singular terms. This is because singular reference is often or always mediated by general concepts, as in the description theory of names: predicates show up in the descriptions and they will be vulnerable to the same argument. Quine’s argument and Kripke’s argument are initially directed at a sub-class of expressions (“rabbit”, “plus”) and may or may not generalize to every expression of language, but they are enough to put the whole notion of meaning into question; similarly with the present argument—the argument seems to cut at the very essence of language, viz. generality. If “blue” is meaningless, something must be seriously wrong somewhere.
But this kind of theory is a radical repudiation of traditional ways of thinking. First, we have to give up the idea that understanding a word consists in associating a concept with it, i.e. a psychological state underlying the use of language. Second, the entire apparatus of reference and representation is called into question: for now we cannot say that meaning consists in intentionality, aboutness, reference. We used to say that understanding a word consists in having an idea of what it stands for or expresses—object or property—but we can no longer say that. To understand “blue” is not to know which universal (property, attribute) it stands for or expresses, but something else entirely—such as applying the word in a certain way. We lose the whole idea of language as a system of representation, replacing it with behavioral dispositions. So the problem with abstract ideas and general terms threatens to undermine fundamental assumptions about language and meaning. If we have no abstract idea (concept) of blue, then we cannot understand “blue” by invoking that idea; but then there is no psychological state that constitutes understanding—or none that involves the requisite intentionality. It must just be some sort of stimulus-response system that never reaches beyond language itself—a kind of syntactic machine without semantic interpretation (it’s not about anything, such as being blue). This is much more radical than a “skeptical solution” in terms of assertion conditions, because that at least retains much of the old apparatus. But this kind of solution will be vulnerable to the original argument from abstraction, since general terms will appear in the assertion conditions (“Assert ‘that is blue’ when something looks blue to you”). Once we abandon the idea of ideas (concepts, thoughts, mental representations) as the basis of understanding, we find ourselves in strange new territory. So it isn’t going to be easy to respond constructively to the skeptical argument from abstraction. As Locke recognized, his whole theory of language depends on the viability of the notion of abstract ideas; it was left to Berkeley to point out that this notion is riddled with difficulty. There is (as Kripke would say) no fact of having an abstract idea of blue; this is a fictitious notion. There isn’t even a fact of an object’s being blue: the facts consist of objects and specific shades of blue (as they consist of objects and specific types of triangle).  We have the word“blue”, but we don’t have the abstract attribute of being blue or the abstract idea of blue. Hence the attraction of construing meaning as merely the use of a word, without regard for any quality denoted or expressed. There are words and their use, but there is nothing else, semantically speaking.
It is worth noting that two standard ways of treating “blue” that try to preserve the basic form of the old apparatus don’t apply. The first is to switch from abstract ideas to dispositions to assent: instead of saying a speaker has an abstract idea of blue we say that she has a disposition to assent to “blue” in the presence of blue objects. But the trouble is that there is no such disposition, since perceptual objects are not blue simpliciter—they are navy blue or cobalt blue or some such. There is no stimulus of being abstractly blue; there are only stimuli corresponding to specific concrete qualities. A disposition to assent to “blue” in the presence of these variously hued objects would yield only a disjunctive concept not the unitary concept we think we possess. It is the same with the notion of a capacity: what is the capacity to recognize blue things but the capacity to recognize shades of blue (ditto for triangles)? Even Locke agreed that there is no objective property of being blue, only an abstract ideaof blue–so there can be no disposition to respond to the instantiation of such a property. A dispositional theory of abstract concepts thus does not evade the fundamental difficulty.
The second way is to stretch the concept of family resemblance and declare that blue is a family resemblance concept like game. Just as there are many kinds of game with no common connecting thread, so there are many kinds of blue with no common connecting thread (ditto triangles)—hence no concept of that thread. Whatever one might think of family resemblance as an account of the concept game, it surely looks singularly unapt for the concept blue. Isn’t this a paradigm of a non-family resemblance concept? There is something common to all blue things—their blueness. Similarly, all triangles have three sides, despite there being several types of triangle (scalene, isosceles, equilateral). To stretch the concept of family resemblance to cover these cases in an effort to solve the problem of abstraction smacks of desperation; you might as well say that every concept is a family resemblance concept. The problem is that “blue” has an unequivocal meaning, but there exists no idea corresponding to that meaning: all the ideas in the vicinity are too specific. It looks prima facie as if the meaning of general terms requires abstract ideas, but it turns out there are no abstract ideas, so meaning is in jeopardy. In order to save meaning we are compelled to contemplate radical departures—such as abandoning intentionality as constitutive of meaning. It isn’t just a minor hitch.
My aim in this essay is not to resolve this issue, but merely to add it to the list of other skeptical arguments concerning meaning. It is not the normative nature of meaning that is causing the problem, as with Kripke’s skeptical paradox, nor the extension-selecting nature of meaning, as with Quine’s indeterminacy thesis; it is the abstract nature of meaning that is causing trouble, its distance from concrete reality, both mental and non-mental. Meaning is too abstract to be possible, too far removed from actual human psychology (perhaps from any psychology), as well as from concrete physical reality. There is nothing in reality for it to be. It calls for feats of abstraction that are beyond the powers of man or nature. 
 The locus classicus is Locke’s An Essay Concerning Human Understanding, Book III, Chapter III: “Of General Terms”.
 Berkeley, Principles of Human Knowledge, section 13. He is discussing the case of “triangle”, arguing that the abstract idea of a triangle is impossible: it must comprehend all kinds of triangles, but it cannot be any specific one of them.
 We can of course say that different shades of blue or different types of triangle are similar to each other, but if we ask what the respect of similarity is we will fall back on such terms as “blue” and “triangle”—the very general terms that cause the problem. How do we understand such terms—in virtue of what fact? Is there any fact?
 Accordingly we find nominalist theories of meaning—theories that treat meanings as nothing over and above words, perhaps as used in certain ways (I would describe Wittgenstein’s later reflections on meaning as nominalist in this sense). Put in these terms, the problem of the abstractness of meaning is solved (or dissolved) by denying that there is any mental correlate of a word—no idea or concept or mental representation. For any such correlate would immediately face the challenge of matching the abstractness of the word: and nothing we find in the mind is capable of mirroring the abstractness of “blue” or “triangle”. There are no such abstract mental facts, so meaning either does not exist or it consists in something other than a mental correlate (maybe just a use—whatever exactly that may be). We end up with an anti-mentalist theory of meaning as the only way to avoid meaning nihilism.
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