Language and information
Lecture 3: Information
3.5. Form and content
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Now, at this point, we can summarize some things about the relation of form to content in language. It is hard to specify in traditional grammar. Obviously, there is some connection, and so forth, but it is very hard to say. In respect to the basic constraints which we have just now surveyed, it is clear that there are two constraints, which are also basic to the language completely, and which are combinatory constraints, they determine very clearly the possibilities of word combination, and there, the relation of form—namely of the constraint—to the information is intrinsic, to the content is intrinsic. We see exactly what each does, and every occurrence of one of those constraints has to carry that information.
Now, this is not to say that across language everything that we want in information and content is available in form. There are languages which specify in their grammar tense or aspect, or such a thing as whether the verb is being stated by report or by direct observations—there are such languages—and there are languages that don't do it, of course. There are also things that are only with the greatest difficulty sayable in language at all. There are meanings which are just barely, if at all, expressible, like the fact that a speaker may know perfectly well, when he says he, who he is referring to—meaning not who, outside in the world, but in the sentence, who he is referring to. He has virtually no way of telling the hearer this piece of information. Language does not have an addressing system, not one, even though in principle it could have it, but not one, it's too much trouble, and it does not have the provision. And if you tried to say it in the general case—I mean, obviously, if the word is very close you might be able to indicate it—in the general case for anything that could possibly be the antecedent of a he, it would be incommunicable, it would be beyond what anybody could follow.
Another thing that is virtually unsayable is for a word to refer to itself or to its own location, or for a sentence to refer to itself. One can show that in grammar, whatever is used in the slightly artificial sentences of logic, the sentence this sentence is false is not grammatical. The this applies to a prior sentence, not to the given sentence. Now, there are ways of getting around it, of course, famously. One can say The first sentence in this book is false, and and it turns out that you've written the first sentence in that book, and we'll say that the this is OK because you're holding it in your hand, or something of that sort. But the language didn't express this. This came via something else, via the fact that you were actually holding a book in your hand, and so forth. This was not a direct expression of the language. The language has virtually no way of doing this.
Now, I want to give one other example, because it shows something of how adding a constraint can add information capacity, slightly differently from what I did with the metalanguage. And that is, in language asd a whole, the grammar is partially ordered—is a partial ordering of words. The meanings are defined by the likelihood—or at least if not defined, they are exhibited, or something, demonstrated—by the likelihood relations of words within the partial ordering; it's a substatement, a subdescription, under the partial ordering. The result is that we cannot make ungrammatical sentences that we don't like because of their likelihoods. In other words, we cannot exclude nonsense from language, let alone falsehood, and lying, and everything else. But we cannot exclude nonsense from language. Nonsense results from using words not in their standard frequencies, in respect to the operators above them. But the partial ordering, which is the main determiner of grammaticality, is before that, and is not affected. However, in science languages, not because of any fiat by the scientists, but because of the nature of the material that they are working with, likelihood differences have been replaced by subsets of words, such that inside the argument sets of words there are certain subsets of arguments and they mean certain things: they may have synonyms, they may have subtypes under them, and so forth, but not a gradation of likelihood. The result is that the possibility of words to appear is grammatically controlled by these subsets, and there is no nonsense in science languages. You can say false things in science languages but you cannot say irrelevancies. The irrelevancies don't fit the grammar of the science languages.