Language and information

Lecture 1. A formal theory of syntax

1.5. The reduction constraint

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Now, the third constraint. This constraint makes existing sentences more compact. It consists, for each language, of a few specifiable types of reduction, even to zero, in the phonemic shape of particular word occurrences.

Now, the main thing to say is what are the word occurrences that get—that is, the domain, therefore, of reduction. What is reducible is the high-likelihood material. We'll see that in a moment. Certain words which have exceptionally high likelihood in a given position are reducible. An example is what we just saw about the zeroing of the second Schnabel of words that are repeated, and there are other which I'm afraid I don't have time to give. The words with highest likelihood, that is [which] are expectable, in a given environment contribute little information when they enter at that point in the sentence-making. That is, in an information-theoretic sense, which will be noted next time. Their informational contribution, the amount of information that they contribute, is low if their expectancy is high, and in general if their likelihood or frequency is high in that situation, in that position.

In this connection, it is worth noting that there are not one but many, or at least quite a few, different situations of high likelihood which lead to zeroing, or to shortening. I'll only give one example, for considerations of time. The fact that there are many different kinds of high-likelihood situations, all of which lead to zeroing, suggests that what is the real factor is the low information, that that is common to all the high likelihood situations. This suggestion is supportive—the fact that we are dealing here not merely with frequency per se, just so, but with a certain property of frequency, namely, the fact that highly familiar things have low information—is supportive by an example I want to give of how low information—I mean, excuse me—low likelihood can block a reduction which otherwise is slated to take place. I want to give an example here.

We have seen in the Schnable case how high likelihood leads to a reduction, to zeroing. Here, I want to give an example of how low likelihood—rarity—blocks an reduction. To see an example, consider that one can say He has truly left, but one does not say He has falsely left. And you can say He has certainly, or undoubtedly, or possibly left, but you cannot say He has uncertainly, or doubtedly, or impossibly left. Now, the question is why. It is not that false or doubtful cannot be said of He has left, because one can say That he has left is false, or doubtful, just as one can say, for example, That he has left is true. But it can be shown that He has truly left is a reduction, roughly, of He has left; that he has left is true, that we actually have two sentences, with the second sentence having the intonation of a subsidiary sentence. This can be shown on other grounds. If so, He has falsely left would have to have been reduced from He has left; that he has left is false. Now, it is reasonably likely for a subsidiary sentence to modify or weaken the primary sentence, especially with something like at least, as in He has left, at least his having left is possible. One can say that. And this is reduced to He has possibly left.

Now, it would be rare for the subsidiary sentence to seem to contradict the primary, as in He has left; his having left is false, or He has left; his having left is uncertain. One really cannot say at least there, one cannot say He has left; at least, his having left is uncertain. Hence, such a rare sentence there, if ever said, would not be reduced. And that is the reason for not having it, that is the reason we do not get He has falsely left, because He has left; his having left is false is such a rare combination that one doesn't reduce it.

There are further examples of a situation in which exceptionally low likelihood blocks reduction.

Now, each reduction can be shown to take place as soon in the making of a sentence as the conditions for it are satisfied, before any further operator acts upon the affected words. This makes it much easier to discover what the reductions are. These reductions therefore are ordered in the partial order of sentence-making. They fit in in among the words that enter into the sentence; we know exactly where each reduction came in.

The reductions don't alter the presence of a word, only its shape and visibility. This is seen in various examples. I'll give one example. If you show that I expect John is reduced from I expect John to be here or to show up, and so forth—there's a way of showing that. If one says I expect John momentarily, that momentarily doesn't fit with expect—you're not 'expecting' momentarily—it doesn't fit with John, to say that he is 'momentary'; it is the being here, the showing up, that is momentary. But the showing up is not said. It is said if you say I expect John to be here momentarily, but if you say I expect John momentarily, you have zeroed the highly likely word—which we of course still consider this as a special status here—giving it its modifier, its adverb—the adverb makes sense with the word. You say I expect John momentarily, the momentarily makes sense. That means, so to speak, that you know that the to be here, or to show up, is there. It is not visible, but it is there.

A reduction does not change the partial order of the affected words, they are there; it does not change their likelihood. What this constraint does do is, it says that certain phoneme sequences which are expected do not occur, because if a word has been zeroed, or has been changed in its shape, reduced, it is not there. So it doesn't change the constraint on the phoneme sequences, their combinations that appear in the language.

To see that the reductions apply not to a word as such, but to a word occurrence in high likelihood—because it isn't the word, it isn't Schnabel in itself that is zeroed, it is the second occurrence of Schnabel under and or but that is zeroed. And in each case, it is a word-occurrence, and in particular a word-occurrence in high likelihood that is zeroed, not just a word.

I want to give an example in colloquial English. In colloquial English, going to can be reduced to gonna. As we say, I'm gonna make it, from I am going to make it. But you cannot say I'm gonna the next room for I'm going to the next room. There, you cannot make the reduction. Why do you reduce going to in I'm gonna make it, and you do not reduce going to in I'm going to the next room? You don't say I'm gonna the next room. The reason is that before nouns, going to is of selectional frequency only before certain ones. It can be New York, the next room, and so forth, but not before a word or time, not I'm going to a word or I'm going to time, so that going to has a certain ... has reasonable frequency before certain nouns, not before other nouns. But before operators, before verbs, going to has selectional frequency before all of them. You say I'm going to go, I'm going to make it, I'm going to speak up, anything of this sort. Every verb can have going to before it. Therefore, the total frequency of going to before verbs is very high. The total frequency of going to before all nouns is not so high. For that reason, the going to is ... reducible to gonna before verbs, and not reducible to gonna before nouns.