Nevertheless, at least some theoretical interests are served by undertaking this and related exercises. For one thing, it highlights the fact that there is a great deal of
variation in the application or use of language and that it is to all intents and purposes free, suggesting strongly that use or application of language is not a place to look for success in constructing theories. For another, it offers some data, data that the scientist of language and mind can and probably should take into account. It suggests, for example, that at least in the case of nominal expressions (not adjectives, adverbs, or verbs) and the commonsense concepts expressed in natural languages, one should take into account the fact that our minds tend to look for and expect answers to questions such as “What can it be made of,” “What is it for,” and “Is it an artifact or a
natural object?” Julius Moravcsik (
1975
, 1990, 1998) made very useful contributions in this
regard; James Pustejovsky (
1995
) incorporates some of his insights in a proposal for a theory of language processing. It might also be captured in terms of a view of concepts and their acquisition that ‘breaks them up’ into features – specifically, what Chomsky calls the “
semantic features” that go toward specifying the ‘meaning’ side of a person's lexical entry. These matters come up on comments below.
More generally, data from cases such as these and many others got from observing how people use language joined with data from instrumentation of various sorts, language and other system impairment (for example, some of
Elizabeth K. Warrington's works [e.g., Warrington & Crutch 2005]), plus neuropsychological and neurolinguistic data, and so on, provide evidence for and against various proposals concerning the architecture, operations, and inputs and outputs of the
language faculty and other faculties-modules in the head. Placed in theoretical structures that are making progress, one can begin to understand what is going on in language, vision, object configuration, and so on. I mention these three in particular because there has already been considerable progress with them.
In line with the above, pointing out that
there is no single function that language serves also helps undermine some efforts to construct what their proponents call “
theories of language” (in one prevalent form, a ‘theory’ of linguistic meaning), efforts based on the misguided assumption that natural languages have a single use. There are philosophers, linguists, psychologists, and others who hold that language serves the single primary purpose of communication and – even more restrictively – communication of “
information.” It is obvious why they want to do this. They conceive of languages not as natural systems, as I-
languages or biophysically based systems in the head, but of languages in use – language as it appears in human “practices” and in the linguistic acts and actions of human beings. Looking at language in that way while also trying to construct what aims
to be a systematic and unified theory of language, they have to hope that they can find a single canonical use of language. For if they can, they believe, it will display regularities in use and application. If so, perhaps these regularities in use can be made into the
rules of language – a particularly tempting prospect to philosophers who would like to use their study of formal logic and inference as the basis for a theory of language. Their preferred strategy makes them look for a functional
essence of language, one that they hope to capture by some uniform set of
rules (of inference) or conventions that people invent in order to (say) communicate information to each other. Some of their efforts – e.g., those of David Lewis – are discussed below.
There is nothing wrong with describing use, of course. The problem is, as
Wittgenstein pointed out long ago, you cannot find in these highly context-sensitive and variable descriptions of the ways in which people use language to serve all sorts of purposes the regularities that any serious form of theorizing requires.
Lewis and others needed and need to be disabused of the illusion of
uniformity in the use of natural languages and told that if they want to construct theories of language at all, they must look to language not in use, but to languages as natural objects that allow for use. Emphasizing multiple uses and functions helps undermine their (at best, social science – not natural science) approach to theorizing about language and its sounds and meanings. You could, of course, stipulate an ideal form for use; but if you hope to offer an empirical theory rather than a hope, you had better pay attention to the facts. And if you cannot find displayed in the ways people speak a genuine essence of language use, you cannot hope to construct a theory, even in the much less ambitious form of a social, not natural, science. A plausible theory even of that sort requires at the very least a determinate relationship between a word and its referent, assuming that there is such (for which there is no guarantee at all). That cannot be found, for people use language to all kinds of ends in all kinds of circumstance. Granted, the strategy of looking to uniformity in use or application might appear to work to a degree when one focuses on a community of those who are determined to avoid ambiguity and reject metaphor, plus devote their attention to doing at most one thing with their language. You find something like that uniformity in use in communities of mathematicians and natural scientists when they use their symbol systems to (for example) construct proofs or develop testable hypotheses. They avoid using their symbol systems creatively for a good reason. If they engaged in these or other forms of creativity, it would not allow them to prove or demonstrate to others. Nevertheless, even in those communities, reference is ‘determined’ only because people make themselves conform in their uses. People using natural languages would find this stultifying;
people use natural languages creatively because they can. And they get satisfaction from doing so.
3
Emphasizing that
communication is far from being a central function of language also helps undermine the work of evolutionary psychologists such as
Pinker and Bloom (
1990
) who tie an increasing capacity to communicate with a tale about how language must have evolved. That matter is discussed further in this appendix and
elsewhere in the text.
Enough of function-for-us and the temptations, problems, and opportunities it brings to the sciences of language and mind. Let us turn to the very different mathematical-scientific notion of a function. In mathematics and natural science, a function is assumed to be an operation that maps specific, stated domains of values (of a variable) into specific, stated ranges of values. The function
addition
applied to natural numbers, for example, maps pairs of natural numbers into a natural number: “N + M = X” takes arbitrarily chosen natural numbers N and M and returns the value X, which is their sum.
Algorithms (mathematized or formalized rules, principles, or laws) in other fields accomplish the same. In Chomsky's recent linguistic work, the ‘external’ version of the operation Merge (“external Merge”) takes one lexical item (which is perhaps nothing but a cluster of “features” made into what
Hagit Borer (
2005
) calls a “package”) and another and returns a new lexical item: X merged with Y yields {X, Y}. And Merge operates with more complex syntactic objects too. Assume Y has X inside it: Y = [. . . X . . .]. Internal Merge with this object yields {X, Y} = {X, [. . . X . . .]}; it amounts to what Chomsky used to call “Move” or “Displacement.”
In the relevant sorts of cases,
function
is usually well defined, so for a specific formal characterization provided by a theory, where there is a
specification of what the theory takes to be its domains and ranges, one gets unambiguous, unique solutions to functions. Sometimes what is called an “
extensional definition” of a function is available. Consider addition applied to a finite domain and range. For the natural numbers {1, 2, 3} and no others, the function addition yields three ordered pairs with the first set of values the domain and the second, the range: <{1, 1}, 2 >, <{1,1,1}, 3}>, <{1, 2}, 3 >. There are no others.
Recursive functions, such as those found in mathematics’ successor function and in linguistics’ Merge yield infinite ranges, given finite domains. In such cases, speaking of extensional definition is moot; no one can produce a list of the relevant items in the function's domain. One's ‘access’ to the range can be fixed only by the function itself, thought of here as an explicit statement of domain, and algorithm(s) that link elements in the domain to possible elements in the range. Often, a function-statement in mathematics or a science is called an “intensional”
specification of a function. This is an important convention for our purposes, because Chomsky's specification of an I-language, consisting of a grammar for the I-language, is an intensional one in this sense. That is why he speaks of I-languages as those that are
i
ndividual,
i
nternal, and
i
ntensional (see
Appendix I
). Speaking of an I-language as an intensional specification is necessary because it is impossible to specify an individual's language at a time (a specific state of his or her language faculty) by listing the sentences in its (infinite) range. It can be done only by appeal to the theory that allows one to articulate the domain (the finite set of lexical items he or she has in his or her mental dictionary) and relevant functions/principles, with any (parametric) variability provided for the combinatory principles, or provided in some other way (“
third factor” considerations) explicitly specified. These I-language grammars yield an intensional specification of the range (the infinite set of expressions/sentences that the relevant algorithms yield). And in doing so, they – if successful – adequately describe and explain the actual current state of an individual's mental grammar, a biophysical ‘entity’ that is otherwise inaccessible, having the status of what philosophers of science sometimes label as an “unobservable.” Generally, that is what
scientific theories look like: they are statements of functions aimed at describing and explaining what there ‘is,’ where it is assumed that there ‘is’ something ‘there’ that can be captured by a theory, and is captured by the correct theory. Call these and other mathematized or formally specified function statements “formal” functions. Formalization allows for precision and explicit statement – features of the sciences that are apparently not available in the use of the commonsense concepts embodied in our languages.
I emphasize that an
intensional or theoretical specification of an I-language may be a construct in the mind of a linguist, but for Chomsky, it is also a description of a ‘real’ state of an ‘organ’ in a human mind. That state is a developed state of
UG, developed in accord with biophysical constraints on
a possible language. An I-language so described is assumed to be ‘the real thing,’ the proper object of linguistics thought of as a natural science. The sentences produced by a person, necessarily with the aid of whatever ‘performance’ systems the language faculty cooperates with, is an epiphenomenon, and only that (Chomsky
1980
: 82–93). The theory of language is a theory of a ‘real’ internal system. UG instantiated as a developmental procedure in the human genome, plus any other non-biological constraints on development, is a theoretical specification of the ‘initial state’ of the language faculty, what it has available to it to develop a steady state, given lexical items.
In line with a remark above, formal functions themselves thought of as sets of symbols and their theory-specified forms and specified allowed combinations are invented ‘objects,’ not natural ones. They amount to the ‘syntax’ of a formal symbol system, and those who are adept in the relevant formal ‘language’ apply the system's symbols in a regimented way. These symbols do not appear in any naturalistic science's object language of which I am aware. They do appear in the object languages of some formal accounts of formal functions: mathematics includes studies of the natures of functions. But these are not naturalistic theories, theories of the natural objects found in nature. They are rather accounts of some of the formal tools that we can and do construct, formal tools that humans employ in constructing natural sciences. If it should turn out that there are natural constraints on these and other functions – constraints revealed by some naturalistic theory of mind, presumably – perhaps we could begin speaking of a naturalistic science of functions, presumably an internalist science of the mind like Chomsky's theory of language. Perhaps such a science would help make sense of – among other things – how it is that humans seem to be able to construct formal systems and sciences at all and in the case of a science, manage to construct and entertain a very limited but plausible set of hypotheses for a set of phenomena, far fewer hypotheses than are logically possible. If there were such a theory, it would be illuminating. Perhaps we would have taken a step toward an account of what Charles Saunders Pierce used to call “
abduction,” our capacity to construct hypotheses that turn out to be fruitful, unlike the potential infinity of the others. Perhaps then functions in the formal sense, at least those employed in the natural sciences, would turn out to be special sorts of natural things. It is an interesting idea, but one that we can ignore, at least at this point. As it stands, explicit and clear mathematical-formal production and specification of functions in this sense – either extensional or intensional – seem to be achievements of individuals, and so are artifacts.
Employing the tools of formal functions as they do, the natural sciences are capable of dealing with randomness and with objects that have what appear to be relatively stable, fixed natures and – in the case of biological
entities – ‘channeled’ forms of growth. If so, we are lucky that nature seems to be populated with such objects and systems. They must be so populated, we believe; they must because the sciences we construct turn out to make progress, making improvements rather than circling aimlessly. It is no accident that the natural objects and systems we can understand are conceived of as having fixed natures, natures that allow for interactions and changes that the formal principles (laws) of the natural sciences can capture. These – and entirely random systems – are the ones our sciences can understand.
Of course, many formal objects such as numbers and operations such as calculations also seem to have fixed natures. When I speak of aleph-null, you know just what I have in mind, assuming you have the relevant kind of mathematical knowledge. One might be tempted, then, to think of aleph-null (or the number 3,447,209,531, for that matter) as having a kind of
objective existence in the way we presume hadrons or chromosomes do. Philosophers have often thought along these lines, populating a world of abstract objects, and conceiving of mathematics and the like as ways of exploring that world, a world that some believe is more perfect than the one we deal with in ordinary life, at least. It is, I think, a good idea to resist the temptation. Taking into account what was said above, aleph-null has what appears to be a fixed nature because we – or rather those who have the relevant knowledge of mathematics – define the nature of the ‘object’ and in some sense agree to use the term “aleph-null” in the same way. The entities of the natural sciences such as electrons and mu-mesons, organisms, and chemical substances that are described and explained by our formal natural theories have fixed natures, we presume, not merely because we agree to use the terms in the same way and construct proofs according to agreed-upon procedures. We do not invent the objects and systems that the natural sciences describe and explain, unlike – it seems – those of advanced mathematics. That – and the success of the theory – is why we think it is reasonable to say of a theory of an I-language that it describes a ‘real’ instantiated system in an ‘organ’ in the human
mind.