The Concept of Language
What is language? What does the word “language” mean? What does it refer to? We can distinguish two sorts of answer: performance-centered and competence-centered. Alternatively, utterance-centered and cognition-centered: answers that stress the actual use of language in speech and answers that focus on the internal mechanisms and structures that underlie such use. The later Wittgenstein provides an example of the former type; Chomsky provides an example of the latter type (as does the early Wittgenstein). Here is Chomsky: “The Basic Property [of language] is generation of an unbounded array of hierarchically structured expressions mapping to the conceptual-intentional interface, providing a kind of ‘language of thought’”.  For Chomsky actual speech is merely the externalization of this internal structure not part of its essence (for him language is primarily a tool for thought and much of it is entirely in the head). Chomsky distinguishes sharply between language as a cognitive system—a property of the brain—and language as overt speech involving the sensorimotor systems. Wittgenstein never makes any such distinction, and the same is true of many other philosophers of language. The OED clearly sides with these philosophers: for “language” we read “the method of human communication, either spoken or written, consisting of the use of words in a structured and conventional way”. We could read this as referring to an internal “method” for performing external acts that strictly go beyond the method, and so as not incompatible with Chomsky’s characterization, but the intent of the definition is clearly to identify language with a set of behaviors, specifically communicative acts. For Chomsky this is confusing language itself—a cognitive structure–with its various expressions in acts of performance. We might compare the question with the question, “What is memory?” Does the word “memory” refer to a cognitive system realized in the brain or does it refer to acts of remembering—competence or performance? Are we speaking of mental faculties or sensorimotor manifestations of such faculties (if faculties are admitted at all)? This is a question about the semantics of the word “language” (or “memory”), or equivalently the concept language. Is the word perhaps ambiguous between these two interpretations, or is it that we should replace one definition with another, or is the meaning a mish-mash of both? Is one definition a folk definition and the other a scientific one, both perhaps useful but serving different purposes? We certainly seem tugged in two directions with much scope for irresoluble disagreement.
I want to suggest that the answer is to be found in recent discussions of natural kind terms, though with a twist. I will put this roughly by saying that Chomsky gives us the real essence of language while Wittgenstein gives us the nominal essence. Consider the dictionary definition of “water”: “the liquid which forms the seas, lakes, rivers, and rain and is the basis of the fluids of living organisms”. Perhaps this gives (some of) the nominal essence of water, but it is a far cry from the real essence: it is neither necessary nor sufficient to be water that a liquid forms the seas, lakes, etc. Water might never have done that and some other liquid might have. It is an entirely contingent property of water. Similarly, Chomsky would urge that the externalization of the language faculty in vocal speech is entirely contingent: we could have spoken in gestural signs instead, or not spoken at all except in inner speech, or used the cognitive mechanism Chomsky describes only in thought. And overt communicative vocalization could arise from a different kind of internal competence, as is presumably the case for animal signaling systems. We might well associate the word “language” with these contingent manifestations, forming the nominal essence corresponding to the term, but they are not what language intrinsically and essentially is—its real essence. For that we must look to the scientific analysis of the underlying cognitive faculty, which turns out to be a tightly structured computational system obeying specific rules. Thus UG is the analogue of H2O. Syntactic structure is the analogue of chemical structure. We can talk about the superficial features associated with the words “language” and “water” but their real-world referents are captured in real essence descriptions of an underlying reality. The words contain a kind of hidden indexical that picks out this underlying essence, bypassing the nominal essence.
So should we say that “language” is a kind of directly referential term that rigidly designates the Basic Property? Is it a name of a natural kind with this essence? Is it semantically just like “water” on the standard model? I think that would be going too far—or perhaps I should say not far enough. The term has both sorts of meaning, real and nominal: connotation as well as denotation. In other words, the concept of language contains a dual polarity: it both designates a hidden real essence and it expresses a nominal essence—just like “water”. Both ideas enter into our understanding of the word: the Basic Property and the contingent superficial appearances. Which idea is uppermost in our mind depends on context, scientific or everyday. The dictionary isn’t wrong, but it highlights only the superficial aspects; we need to supplement it with a specification of the actual structure of language as a cognitive system. Thus there could be a scientific dictionary that gives a Chomsky-style definition of language, as well as a chemist’s definition of “water”. Both dictionaries are correct and not in competition with each other; together they comprise the full meaning of the terms “language” and “water”. Like other natural kind terms, “language” has a kind of double meaning, and this is the source of the disagreement over the nature of language. Linguistics can occupy itself with both subject matters and claim to be talking about language, though strictly speaking the study of performance is the study of the externalization of the brain-based language faculty. But a follower of Chomsky might allow his colleagues to speak loosely of performance as “language”—after all, it is the internal language system in action. The word “memory” is similar: strictly speaking it refers to a mental storehouse (or some such), but we can allow ourselves to call acts of remembering “memories”. This is pleasantly irenic because now we don’t have to declare much of philosophy of language not about language at all, but only about its sensorimotor manifestation. We just need to be clear about how the semantics of “language” works: inclusively not exclusively (compare Kaplan’s content and character). The word “language” has dual component semantics, being partly indexical and partly descriptive: “language” means, “that underlying cognitive structure, which is typically expressed in acts of communication of speech and writing (and in other ways)”. Compare: “water” means, “thatliquid, which is found in seas, lakes, etc.”. We might then say that Wittgenstein was doing descriptive anthropology of language use, while Chomsky does scientific investigation of the language faculty itself. Wittgenstein makes sketches (his metaphor) of language use, as it presents itself, in an effort to capture nominal essence, while Chomsky puts language under a microscope in order to discover its real essence. Both ventures can claim support from the meaning of “language”, according to the dual component semantic model; and it would be wrong for the nominal essence theorist to exclude the real essence theorist from being a student of language as such. Likewise we don’t want to detach the concept of language too sharply from its actual expression, on pain of losing the concept altogether. If the mutation that led to the abstract computational system Chomsky describes had never resulted in the linguistic phenomena that it did, we would not describe that system as language. Suppose that the Merge operation constitutes the real nature of the language faculty as we actually have it, but in another possible world it never led to anything like inner and outer speech: would we then say that language exists in this possible world? I think not. We can’t divorce the concept of language completely from its normal expression, just as we can’t divorce the concept of water completely from its normal manifest properties. Both concepts incorporate the superficial as well as the deep.
Could there be fool’s language as there can be fool’s gold? Suppose we come across a species that speaks a mile a minute and behaves a lot like us when they do so: do they necessarily share our underlying grammar? No, because they might have a grammar obeying different principles from ours but which doesn’t reveal itself under casual inspection. They might look like they speak a human language but in fact their grammar diverges substantially from ours—just like iron pyrites resembles gold superficially but has a different atomic structure. We can say that these speakers have a language, appealing to the nominal essence notion of language captured in the dictionary definition, but we should follow that up with the admission that their language isn’t really of the same natural kind as ours; we might choose to put the word “language” in scare quotes when speaking of the noises they emit. In any case, there are two questions here and they can receive different answers. The meaning of “language” points in two directions. 
 There has been a lot of dispute in linguistics and philosophy about what language is, but I don’t recall ever seeing a discussion about what “language” means, i.e. about its semantic analysis. It turns out to have a rather complex meaning.