by Noam Chomsky
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.
II.2 Mathematics and natural science: formal functions
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 individual, internal, and intensional (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 n
aturalistic 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.
II.3 Biology: function-for-an-organism
Interest-dependent functions of the sort we began with are not good objects for scientific investigation. However, there are other notions of function that seem to involve interests in a way that makes them more reasonable candidates for scientific study. They are found in the biological sciences. Evolutionary scientists speak of adaptations, where an adaptation is a feature of a group of organisms – a feature such as an organ like the vertebrate eye – that is claimed to have the shape and complex structure that it does as the result of evolutionary processes, and that has its current transmissible form in the species, it is claimed, because it enhances the reproductive capacity of the creatures that have it.4 Typically, one finds the assumption that reproductive success comes from some transmissible mutation serving some specific role in an organism's operations that is assumed to aid the viability of a species – in that sense, the species’ interests. At the least, it performs a function for an organism that enhances its ability to procreate. Pinker and Bloom (1990), for example, read in this way what they suppose is increasing communicative success of adaptations they claim appear in the evolution of language, and they believe that they can explain the ‘shape’ of natural language in this way. It is not at all obvious what evidence they have for their suppositions, or for those advanced by Pinker and Jackendoff (2005) in their critique of Hauser, Chomsky, and Fitch (2002). All these appear on the face of it to be ‘just-so’ stories of the sort that Richard Lewontin sharply criticized in his (1998). However, it is not too difficult to find plausible examples with other organs – the eyes and the visual system, the ears and the auditory system, for example – cases that appear to be plausible because there is accumulated evidence (comparative, whether involving analogies or homologies) of improved viability of a species – although where such evidence is found, it is entangled with other factors, including contributions best understood only by appealing to non-biological sciences such as physics. In those cases where there is clear evidence of adaptation for survival, evidence gathered by investigating the evolutionary path of a species compared to others, one can speak of specific subsystems of an organism that serve a function in something a bit like the interest-dependent-function sense, although generalized to amount to something like “survivability for species x.” For it is assumed that the shape and structure one encounters in a species’ ‘adaptive’ system are what they are because they serve the reproductive interests (in some broad sense) that they are claimed to for the creatures that have them – that the selectional advantages of having such a structure explain (in the relevant sense) its evolution and current state. Vrba and Gould, for example, once suggested that use of the term “function” (in the evolutionary biological sense) be restricted to cases where there is some evidence of evolutionary ‘shaping.’ There is some danger in speaking of interest in this domain, for the evolutionary biologist does not – or should not – allow the notion of an agent's interests to play a role in science, and it can be difficult to disentangle that notion from one that is part of the explanatory toolbox of a field of scientific research. If the notion of interest enters at all, it should be a carefully defined notion, isolated from commonsense notions of agents and their projects and intentions in carrying out actions.
There are very significant challenges to the scope and validity of at least some adaptationist claims within biology itself. Darwin himself expressed doubts about the explanatory reach of selectional adaptation; the last sentence of the introduction of the third edition of The Origin of Species reads, “I am convinced that Natural Selection has been the main but not exclusive means of modification” (emphasis added). He was right to be cautious, as current understanding of ‘channeling’ of growth in ‘evo-devo’ (evolution-development) has abundantly shown. Wallace at Darwin's time pointed out that it is very unlikely that selection could explain the introduction of the capacity we humans alone have to do mathematics. That natural selection does not deal with everything in the way of explaining ‘shape’ and biological form – and perhaps deals with very little – was emphasized by D'Arcy Thompson in the early 1900s and Alan Turing in the mid-1900s. They pointed to a significant role for physiochemical explanation in dealing with structure and modification and emphasized that formal fun
ctions could explain form and its permissible variations in a way that brought into question the value of adaptationist and selectional explanations. Further, Waddington and more recent proponents of the developing field of evo-devo have pointed out that not all organic structure can be scientifically explained in this way, and perhaps very little. For one thing, there is the fact that modification requires mutation, and mutation can only proceed within the constraints set by physics and chemistry, among other sciences: possible structures and modifications of structure are limited by the laws of nature. Various structural features of organisms, for example, cannot be explained by genetic instruction sets alone, nor can the way phenotypical development takes place; ‘epigenetic’ factors play a crucial role in the latter. Scaling of skeletal structure (the genome cannot be thought to provide a complete specification of the sizes of each bone in a specific organism) and symmetry (the fact that each rib on the right has a homologue on the left, each wing of a butterfly the same pattern as the other . . .) are two examples. And there are issues that bear on structure and form that selectional adaptation does not speak to in any significant way: the fact, for example, that what have been called “control” or “master” genes are found in the same form in a large number of different species that cross biological clades. Walter Gehring has long pointed out that vision in all species in different clades must be linked to the fact that all species have homologous control genes – PAX-6, in the case of vision. This suggests that vision did not evolve separately in (say) fish, insects, and vertebrates, but that it is available to all creatures with PAX-6 (and other genes involved in introducing rhodopsin and putting its sensitivity to photons to use through various mechanisms), with variation depending on the rest of the structure of the organism, plus background conditions. Similar points can be made for other ‘organs’ and their distributions in species of organism.