Language and information
Lecture 3: Information
3.4. Added structure adds information capacity
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I want to give a slightly brief, or hurried example of how the information capacity of a system—of language—is increased. Just to give an example of how little it takes, but what it takes, aside from the things that I already mentioned—from the ordering of the words in a dependence relation and from having different likelihoods—to increase the information capacity. And this is the following:
If we think for a moment of how a meaning of a word is indicated—if it were indicated, let's say, by pointing, then that would suffice to give you the meanings of words. It could not be used to create any new type of meaning in addition, that is to say, you cannot point to each pointing and get something out of that.
Now, in language the meanings are given by words, so the words determine the meanings, they are associated with some things in the real world. However, there is nothing that can prevent a word from meaning not only something outside, but from meaning another word. Just as words can refer to 'chair' by saying chair, there is nothing to prevent a word from referring to a word, or to a word-occurrence. It cannot refer to itself, interestingly enough, and that's something else again which may come up. But it can refer to other words, or it can refer to their occurrence. This fact, that a word is able to refer also to words, brings to language three major extensions of ability. They are the following three: One is, it makes possible a metalanguage of language as a subset of a language. This is based on the sentences in which the words refer to words. This we have touched upon last time. There are two other structures in language which are created by this ability of words to refer to words. One of them is a metasentential operator, that is to say an operator which operates on sentences as such, on the saying of sentences. It is indeed the word say and certain words that are added to it, which include things like to gainsay, to deny, and several other words; and to ask as a matter of fact, to say as question, and so on. So there is the word say as a metasentential operator, operating on sentences. And there is the ability of reference, referentials, of pronouning, which is also based on the ability of words to refer to words. I will say something briefly about each one of them.
For a person to say I say yes, or Yes is hereby said, means the same thing as yes in quotation marks, or yes which has undergone the activity of saying. Whereas, if a person says I said yes or He says yes, this does not mean that yes has hereby been said, it merely means that the speaker claims its having been said. But if he says I say yes, this is not only a claim, he has said it. Now, on these conditions, the I say contributes no information to the saying of yes, of the sentence; and it is therefore zeroable by the conditions that we have referred to in the first lecture.
There is much evidence, of varied kinds, that this I say can be assumed to have existed on every said sentence. For instance, in every sentence one can make an assertion such as to tell the truth or not to repeat myself. Now a phrase of that kind has to have been reduced from for somebody to tell the truth and for somebody not to repeat himself. In fact, we know that it is I, because if it's for not to repeat myself it has to be for me not to repeat myself. Well, where did this I which must have occurred on the sentence disappear, how come it disappeared? Where is the verb that it has? Because I cannot appear by itself, it must have been some verb, I do something. For reasons I cannot go into now, there is strong consideration for saying that there was an I say that was missing, and that it was zeroable, again, for standard reasons. If there was such an I say zeroable, there are very many grammatical constructions that can be explained by means of it, by reconstructing the I say.
One for instance is that the the three set-theoretic operators, not, and, and or, which exist in language but differ grammatically from all other operators in language, a difference that is very hard to explain. These three, it can be shown for good reason, can be derived from modifiers on I say, which would explain the peculiarities in their behavior in grammar.
Another thing is that tense does not act like an operator in language, it doesn't do the normal things that operators have to do. Some languages of course don't have tense, but for languages that have tense. According to the theory that is being presented here, we would want tense to be an operator, because everything has to be an operator or an argument. It can be shown, again on varying grounds, that tense, in languages like English in any case, can be reduced from before and after as a relation between the sentence and the I say on the sentence. I won't go into that.
There are also a number of smaller things that one can show. To take a very childish example, the word hardly has a connection to hard which is not readily explained. If a person says He is hardly the one to ask, it isn't clear what hard is doing there. However, one can derive this from I would hardly say he is the one to ask, meaning I would only with difficulty say that he is the one to ask. The connection of hardly to hard is understandable if hardly arose as a modifier of say, not of the sentence under say. And there are other things I won't go into.
So much for this construction which results from words being able to refer to words. There is one other construction, and that is referentials. We have seen last week that words can be pronouned, or zeroed, if they refer to the same thing as another word-occurrence at an easily-located point in the sentence. We had the example of the zeroing of Schnabel, of the reducing of John I have long distrusted to whom I have long distrusted when it was right after John, and so on. For pronouning and zeroing to take place—it obviously is an event that happens, and of course everybody knows that this happens—how does it take place? If we had an external metalanguage to language (of course we use English, and say it freely, but how did we get the pronouns into the metalanguage of English?) if we had a metalanguage, then we can explain what I have just now said. We can say that certain words, if they are repetitions of a word in a stated location, are reduced to a pronoun or to zero. If we don't have an external metalanguage, if any metalanguage that we had would already be using pronouns, or would already have the capacity for pronouns, and therefore wouldn't explain it, how could we do it? The answer is that we have to have an adjoined sentence to the given sentence saying what I just now said. Saying that this word before is a repetition of the other word. What reduces that sentence? What zeroes that sentence? Why has that sentence disappeared? It was replaced by the act of carrying out the pronouning. In other words, whereas a metalanguage cannot give an instruction to language, because it is outside, and would have to be defined, here, we have, without a metalanguage, merely by the capacity of words to refer to other words in the same sentence, we can add an adjoining statement—we require no outside metalanguage, nothing new, except the ability of words to refer to words—and the saying of this has a reduction. The reduction is, you do what it says, and then you don't need it any longer, and the adjoining sentence drops. This is of course a gimmick, but this is to show what is the status of the information.