Syntax for the uncertain

 Originally published on Language and Philosophy, June 11, 2007

(This entry is for the Chomsky skeptic: the type of long distance relationship prohibited among prepositional phrases provides strong evidence for a generativist view of grammar and a computational view of syntax in the brain.)

Anti-Chomskians have focused their attacks on productivity, claiming that novel syntactic structures are rare. Certainly formulaic utterances are rampant in speech and have justly received much attention recently. Diana Sidtis, who has published widely on formulaic utterances, adds to these schematic utterances — utterance patterns structurally fixed like formulae, but not fixed for content. The claim seems to be that if schemata and formulae dominate speech patterns, the generative element is marginal at best, a mere intuitive capacity largely unused.

Setting aside the question of why humans would have such an unused capacity, this argument ignores the essential duality of the Chomsky program. The goal is not just to generate all the sentences of natural language. It’s to generate all and only the sentences of natural language. It doesn’t just explain novelty and unbounded productivity. The really dramatic, interesting and compelling side of Chomsky’s work from the very outset was the other horn of the bull: discovering one mechanism that will both generate all the sentences yet won’t overgenerate. Generative syntax crucially explains why some extremely simple sentences are unprocessable, even when they contain the same structures as more complex and easy-to-process sentences.

Sometimes I think Chomsky and syntax have garnered so many vitriolic enemies because Chomsky’s original examples were not chosen for pedagogical perspicuousness and the computational origins of generative theory are not consistently taught. So here’s an attempt at pedagogical perspicuity which I hope will convert both agnostics and scoffers-in-good-faith.

Both long distance and local relations are possible for prepositional phrases

You walk into the lobby of the hotel. There are several people sitting at the bar and in the lounge, some in suits. You approach the front desk. The attendant tells you you received a call, using one of these sentences:

1. The guy at the end of the bar in the suit with the stripes on the chair with three legs called.
2. The guy at the end in the suit of the bar called.
3. The guy on the chair with three legs at the bar called.

Notice that sentence (1) is easy to understand even though it is long and complex. I’ve yet to encounter a class of undergrads who didn’t understand it instantly. Yet it contains no less than three pairs of prepositional phrases, each pair holding a local relation within the pair and a long distance relation with the subject of the sentence. So

the chair with three legs

is a noun phrase with a prepositional phrase [with three legs] related directly to [the chair]. It’s the chair that has three legs, not the guy.

On the other hand, the stripes are not on the chair, it’s the guy who is on the chair. So there is no relation in this sentence [the stripes on the chair] even though there is a relation [the chair with three legs].

So these prepositional phrases can relate over long distances to the subject, or they can hold a purely local relationship with the nearest noun phrase. Both long distance and local relations are possible for prepositional phrases.

Some long distance relationships are impossible

But now consider sentence (2). It is a simpler string of words: only three prepositional phrases — yet I have not met any English speaker who can process it to get [of the bar] to relate to [at the end] even though it’s semantically obvious and it’s the only semantic possibility. This sentence is not difficult to process; it is impossible! Even when you know what it’s intended to mean, you still can’t get it to mean that.

And yet, it contains the same prepositional phrases, some with local relationships and some with long distance relationships, in no way different from (1), except (2) is simpler and (1) is a great deal more complex. Why is the more complex sentence easy and the simple sentence strictly impossible?

Is it because a prepositional phrase cannot intervene between two related prepositional phrases? Sentence three shows this cannot be the reason.

Sentence (3) has the most complex relationships of all three sentences, and yet it too is relatively easy to process. Imagine there are two guys sitting on three-legged chairs, one chair at the bar and one in the lounge.

3. The guy on the chair with three legs at the bar left this for you.

means

The guy on [the chair [with three legs] [at the bar]]

where the chair is both at the bar and has three legs.

It’s not hard to understand, even though there is a prepositional phrase intervening between [the chair] and [with three legs].

So prepositional phrases may intervene sometimes but not always. What’s the explanation?

What determines which are possible and which are impossible?

Computational theory early on gave us the answer. A machine that processes language word by word cannot exclude sentences like (2) while including sentences like (1) and (3). But a machine that processes phrases as well as words, can. A finite automaton can produce any and all of the prepositional relationships above, including, unfortunately, (2), which is not possible for native English speakers. A push-down automaton, however, can produce (1) and (3) without any trouble, but is mechanically, physically, structurally, logically unable to produce (2).

The internal structure of a prepositional phrase can be processed by a machine, like a finite automaton, that reads one grammatical category at a time

prep + determiner + noun

in that order. Such a machine consists of a set of states including an initial state and at least one final state and a set of functions that take one state into another depending on input. The initial state here accepts a preposition which takes it into a new state accepting a determiner. Feeding the machine at this point a determiner will take the machine to a noun-accepting state. (When I have a chance, I’ll flesh this out a bit. Meanwhile, if you’re curious, any textbook on computer theory will have a good description of how finite automata work and the push-downs mentioned below.)

To accommodate (1), such a machine could have a structure corresponding to a regular expression like

[PDN[PDN]]*
(P=prep, D=deter, N=noun, *=any number of times including zero)

and to get (2) and (3), it needs simply

[PDN]*
where any relationships among the prepositional phrases are allowed.

Such a grammar will allow any number of pairs of locally related prepositional phrases along with unrelated intervening prepositional phrases. In other words, a machine that processes one word at a time can be constructed to process all three sentences: it overgenerates to produce (2) as well.

But a push-down automaton — the kind of machine the accepts context free grammars — can’t be designed to produce (2) and needs no special complexity to accommodate the long distance and local relations of (1) and (3).

The simplest context free grammar that can be constructed to process (1)is:
(S=sentence, NP=noun phrase, VP=verb phrase, PrP=prepositional phrase)
S=>NP, VP
NP=> D, NP
NP=> N
NP=> NP, PrP
PrP=> Pr, NP
VP=> VP, PrP
VP=> VP, NP
VP=> V

This simplest grammar, exactly as it is, will also generate (3), but no context free grammar can be constructed to generate (2). (This is all much easier to see with trees, but trees are tough to draw on a blog.)

This is very powerful evidence that the brain has a context free grammar represented in it — not necessarily in a specific place, possibly only in a process distributed through a variety of locations in the brain — but represented somehow.

I haven’t touched here on examples that show that a context free grammar cannot handle all the phenomena of language or on examples that suggest that elements can be moved around by the brain. English speakers have more powerful machinery between their ears capable of taking this fundamental push down structure and playing with it, within some limits. Figuring out the limits is the stuff of current linguistic theory. I am interested here only in presenting sentences that demonstrate that the brains of English speakers must have a pushdown structure that prevents the generation of sentences like (2) which are strictly impossible for native English speakers to process. This demonstration is just for the agnostics and scoffers: How else can you explain why (2) is impossible?