Of Minds and Language (7 page)

At this point we have to move on to more technical discussion than is possible here, but I think it is fair to say that there has been considerable progress in moving towards principled explanation in terms of third-factor considerations. The best guess about the nature of UG only a few years ago has been substantially improved by approaching the topic “from bottom up,” by asking how far we can press the strong minimalist thesis. It seems now that much of the architecture that has been postulated can be eliminated without loss, often with empirical gain. That includes the last residues of phrase structure grammar, including the notion of projection or later “labeling,” the latter perhaps eliminable in terms of minimal search. Also eliminable on principled grounds are underlying and surface structure, and also logical form, in its technical sense, leaving just the interface levels (and their existence too is not graven in stone, a separate topic). The several compositional cycles that have commonly been postulated can be reduced to one, with periodic transfer of generated structures to the interface at a few designated positions (“phases”), yielding further consequences. A very elementary form of transformational grammar essentially “comes free”: it would require stipulations to block it, so that there is a principled explanation, in these terms, for the curious but ubiquitous phenomenon of displacement in natural language, with interpretive options in positions that are phonetically silent. And by the same token, any other approach to the phenomenon carries an empirical burden. Some of the island conditions have principled explanations, as does the existence of categories for which there is no direct surface evidence, such as a functional category of inflection.

Without proceeding, it seems to me no longer absurd to speculate that there may be a single internal language, efficiently yielding the infinite array of
expressions that provide a language of thought. Variety and complexity of language would then be reduced to the lexicon, which is also the locus of parametric variation, and to the ancillary mappings involved in externalization, which might turn out to be best-possible solutions to relating organs with independent origins and properties. There are huge promissory notes left to pay, and alternatives that merit careful consideration, but plausible reduction of the previously assumed richness of UG has been substantial.

With each step towards the goals of principled explanation we gain a clearer grasp of the essential nature of language, and of what remains to be explained in other terms. It should be kept in mind, however, that any such progress still leaves unresolved problems that have been raised for hundreds of years. Among these is the question how properties “termed mental” relate to “the organical structure of the brain,” in the eighteenth-century formulation. And beyond that lies the mysterious problem of the creative and coherent ordinary use of language, a central problem of Cartesian science, still scarcely even at the horizons of inquiry.

P
IATTELLI
-P
ALMARINI
: I am concerned with the parallel between the numbering system and language, and the conceptual possibility of starting with one single lexical item only and then generating the rest with something like the successor function. Peano was adamant in stressing that there can only be one empty set. This is a truth of reason, an inescapable necessary truth, that there is only one empty set. So, you form the set that contains it, and then the set that contains the previous one, and so on. The successor function and the necessary uniqueness of the empty set give you the natural numbers system. It does not seem to me to be quite straightforward to do something similar in the case of language. The necessary uniqueness of the empty set would be missing.

C
HOMSKY
: That's one way of doing it. If you want to generate it from set theory, that's a rich way of doing it. If you want to do it without set theory, what you have is one element, and then you have an operation that forms a successor, and it's simply repeating it. Okay, that's the numbering system. Now this system you can get by taking one lexical item, and one way of doing it would be with a Merge system, which does use limited trivial set theory. The one item could be, for example, the set containing 0. And then if you use internal Merge, you'll get a set which consists of 0 and the set containing 0, and you can call that 1, if you like. And you can do that again, and you get 2, and if you throw in associativity, you can get addition, and that's basically the number system. You can get addition, subtraction, and multiplication in the familiar way. So it does need
just a trivial amount of set theory, just as Merge does, and in fact I don't know if you even need that; it might be possible to develop a Nelson Goodman-style nominalist alternative.
²⁵
So that's one way of getting numbers, and there are others you can think of for just getting a numbering system by restricting language to the very narrowest sense.

H
IGGINBOTHAM
: Just to help clarify this. You know that in the mathematics of these things one studies semi-groups? You have groups (with a reciprocal operation) and semigroups, which are merely associative. The “free” semigroups have certain special algebraic properties; and then, as they used to tell us at Columbia, the numbering system is just the free semigroup with one generator. That's it.

C
HOMSKY
: Yes, that's basically what I'm saying. That's correct, it means that the numbering system might just be a trivial case of language, which would solve Wallace's Paradox. Wallace was worried about how it could be that everybody has this number system but it's obviously never been selected; it's not very useful.

R
IZZI
: I have a question on the division of labor between UG and third-factor principles. In a number of cases that come to mind, it looks as if there is a highly general loose concept which applies across cognitive domains. Take locality, for instance, a concept that seems to be relevant and operative in different cognitive domains in various forms. And then if you look at language, it is very sharp, very precise. It gets implemented in an extremely sharp manner, only certain things count as interveners, only certain categories determine impenetrability, etc. So the question, related to your short comment on the fact that minimal search may be a third-factor entity, is how much of that is in UG and how much of that is derivable from external general principles.

C
HOMSKY
: This looks ahead to Luigi's talk in this conference,
²⁶
so he is going to elaborate on this, but he mentions two principles that seem to be involved in these kinds of questions. One is something that comes out of sequential computation, which has strong computational reasons for it, and that could take care of some kinds of extralinguistic effects – though as an aside, I think there is good reason to suppose that computation of syntactic-semantic objects involves parallel computation as well. But there is another one, which he mentioned now and which is intervention effects, a kind which, as he points out, cross over the units of sequential computation, so they don't seem to follow directly. That is
more or less the story. And he raises and will suggest answers to the question of how these two things could interact. But then one may be third factor, like minimal search, and the other somehow specific to language? Now technically, if I have understood the abstract of his talk here correctly, one possible way of getting an indication (which does require work as his examples show) is that it all has to do with minimal search. Now that does require reanalysis of things like the Nominative Island Constraint and Superiority Conditions and so on, and I think there is some reason to believe that that is possible. But as you know, I am very skeptical about the Superiority Condition. I really don't think it exists; I think it's been misinterpreted, along lines I discussed a bit in my book
The Minimalist Program
(1995). There is some work on things like the Negative Island Condition which suggest that it may have an explanation in other terms, like in Danny Fox's recent papers.
²⁷
It is possible, like some future goal, that it might all be reduced to minimal search. That is, minimal search
could
be – we have to prove this, you have got to show it – in principle it could be just a law of nature. It is just the best way of doing anything. And you
would
expect to find it in efficient patterns of foraging, all sorts of neural structures, and so on. If that can be worked out, then you would reduce it all to third-factor principles.

Of course you are exactly right. In the case of language, it is going to have very special properties, because language is apparently unique as a system of discrete infinity. So it is going to be totally different from foraging, let's say, which is a continuous system, unlike language which is a discrete system. But it would be nice to try to show that the differences that occur in the case of language, in spite of the specific things you mentioned, are just due to the fact that it is uniquely a system of discrete infinity, which is then of course going to have different effects. Probably the nearest analogue with human language in the natural world, in the non-human world, is bee communication, which is a rich communicative system. In fact many kinds of different species use different forms of it. Oddly – somebody here who knows more about this can correct me, but as far as I understand the bee literature – there are about 500 species, and some of them use the waggle dance, others use sound, and they all seem to get along about as well, from the point of view of biological success, which does raise the question of what it is all for. If you can get by without the waggle dance, then why have it? But that is a typical problem in evolutionary theory. When people produce evolutionary speculations from adaptiveness, it just doesn't mean much. If you look at the encyclopedic reviews of the evolution of communication, what you actually find is people saying how beautifully
something works in this ecological niche. Okay, maybe it does, but that leaves open the question – it doesn't say anything about evolution.

But whatever it is, bee communication is fundamentally continuous insofar as an organism's behavior can be continuous (I mean, there are minimal perceptual effects), so they are just going to have different properties. Even with the same minimal search principle, it would show up very differently in a discrete system like language, and in a continuous system like, say, the bee dance. And maybe that's the answer. A shot in the dark, but I think it might be a direction to look.

P
ARTICIPANT
: Could I ask you to deal a little bit with Peirce's theory of abduction, and the importance of an abductive instinct?

C
HOMSKY
: Peirce posed the problem of abduction in lectures which I think are from about a century ago, but as far as I know, nobody ever noticed them until about the 1960s. When I found them and wrote about them then, I couldn't find any earlier discussion of them. Those were pre-electronic days when you couldn't do a real database search, but I couldn't find any reference to Peirce's theory of abduction.
²⁸

Now the term abduction
is
used, Jerry Fodor has spoken about it and others, but it is a different sense;
²⁹
it is not Peirce's sense. Peirce's sense was very straightforward and, I think, basically correct. He says you want to account for the fact that science does develop, and that people do hit upon theories which sort of seem to be true. He was also struck by the fact, and this is correct, that at a certain stage of science, a certain stage of understanding, everybody tends to come to the same theory, and if one person happens to come to it first, everybody else says “Yes, that's right.” Why does that happen? You take any amount of data and innumerable theories can handle them, so how come you get this kind of convergence in a straight pattern through even what Thomas Kuhn called revolutions?
³⁰

Let's take, say, relativity theory, special relativity. When it came along in 1905, Einstein didn't have much empirical evidence. In fact, there was a great deal of experimentation done in the following years by all kinds of experimental scientists, who refuted it, and nobody paid any attention. They didn't pay any attention to the refutations, because it was obviously right. So even if it was refuted by a lot of experimentation, they disregarded the experiments. And that went on for many years. I remember years ago reading the Born–Einstein
correspondence, and somewhere in the late 1920s (someone who knows more about this can correct me if I don't have it right, but it is something like this) a very famous American experimental physicist redid the Michelson–Morley experiment, which had provided the main evidence, and it came out the wrong way. And Born wrote to Einstein and he said “Look, do you think I'd better go over to this guy's lab and find out what mistake he made?” And Einstein said “No, it is probably not worth it. Somebody will probably figure it out sooner or later.”
³¹
But the point is he didn't even pay any attention to the refutation of the Michelson–Morley experiment because it couldn't be right. And it couldn't be right for conceptual reasons.

That is pretty much the way science often seems to work. It is true even in our areas. You just see that some ideas simply look right, and then you sort of put aside the data that refute them and think, somebody else will take care of it. Well, Peirce was interested in that, and he asked how it happened, and I think he gave the right answer. He says we have an instinct. He says it is like a chicken pecking. We just have an instinct that says this is the way you do science. And if you look at the famous scientists reflecting, that is what they say. I remember once I was at the Institute for Advanced Studies and Dirac was giving a lecture, so I went out of curiosity. Of course I didn't know what he was talking about, but in the lecture some hotshot mathematician got up and said “You made a mathematical error in a particular point,” and Dirac said “Okay, you figure out what the mistake is, I'm going on with this, because this is the way it has to be.” Well, that is sort of the way things work.
³²
Peirce's answer is that there is some kind of instinct, the abductive instinct, which sets limits on permissible hypotheses and says these kinds are explanatory theories, but this other kind are not, even if they work.