There are situations in the world. And there are words—which are, to put it circularly, what we use to talk about them with. What makes it circular is that the existence of words, and their relationship to meanings, and the interrelationships among them all, are also situations. When we talk about how words do what they do, we are apt to get into trouble because we are maneuvering through a complex house of mirrors, and there is almost no way to avoid that trouble, short of resorting to pictures—which I am not above doing.
Many situations in the world have aspects that can be talked of as directed binary relationships. Some examples of talk about these situations which highlight the directed binary relationship are:
“Vivian loves the Taj Mahal.”
“Alicia built a house.”
“Chang threw the ball.”
“Sad means unhappy.”
“The hammer hit a nail.”
Let us take the last sentence, “The hammer hit a nail,” and consider it and the situation it might commonly be used in, and explore the modeling process that is occurring in some detail. First, we have a thing, the phrase the hammer, standing for a thing, c=^ . In that phrase, we have a thing, the word the, standing for an attitude toward •=4 , and we have another thing, the word hammer, standing for the object n^ itself. Next, we have a thing, the verb hit, standing for a relationship. After that, we have still another thing, the phrase a nail, standing for another thing, T . As in the first phrase, in the second we have a thing, the word a, standing for an attitude toward the object T different from the attitude modeled by the word the. And, as in the phrase the hammer, we have a thing, the word nail, which stands for the object T itself. Also, we have a relationship, composed of which thing (i.e., word) is put before the verb and which thing (i.e., word) is put after it, that stands for an aspect of the relationship c==A not completely subsumed by the verb hit alone, i.e., which object is the comparatively active one and which is the comparatively receptive one—or what can be talked of as “the direction of the binary relationship.” Now the direction of the relationship is, itself, a relationship; so here we have a relationship, between noun, verb, and noun, standing for an aspect of the relationship c^A .
Now there are other notable relationships in the sentence “The hammer hit a nail,” to attract our attention. In the phrase the hammer, for instance, which we have said consists of two things, the word the and the word hammer, it is necessary that the things appear in just that order. Likewise, the phrase a nail must preserve its order, if the sentence is to strike us as proper. What are these particular relationships necessary for? What would be wrong with the sentence “Hammer the hit nail a,” or “Hammer hit nail a the,” or “Hammer a the hit nail,” or “The a hammer hit nail”? In all of these, we still have the things in the sentence which stand for the things in the situation, and in all of them the relation between hammer, hit, and nail, which models the direction of the relation in the situation, is preserved. Is the relation between the and hammer, or a and nail, modeling anything in the situation which is suddenly lost or obscured if these relations are lost?
To the extent that our attitudes toward the objects in a relationship are not in that relationship, the simple answer is no. The relationship between the and hammer and between a and nail are necessary to preserve the integrity of the model itself; they are necessary if we are to recognize the model as a proper thing for modeling in the first place. But these relationships, between the and hammer and a and nail, do not model anything in the situation talked about by the sentence. To destroy them, however, may prevent other relationships (that may be modeling something in the situation, or may be preserving the integrity of the model) from standing forth clearly. This simple answer is, however, rather oversimplified.
What shows the situation to be more complicated than our discussion so far is that the same thing may be said about the relationship between, say, the three <z’s in the sentence. About their relationship we can accurately say: “In the sentence The hammer hits a nail there must be seven letters and two spaces between the first a and the second, and one letter and one space between the second and the third. Though there may well be a number of other sentences that also have this relationship between three a’s, if there is any other relationship between three a’s in a sentence, that sentence will not be the proper sentence The hammer hit a nail.” Using just letters, and the number of spaces and letters between them, it is interesting to try and work out a minimum number of such relations that will completely describe a given sentence. (One eventually has to resort to specifying distances between different letters.) Notice, however: If we consider the sentence The hammer hit a nail to be made up of its letters and the relationships between them, then only a single thing among its elements, the single letter a, is doing any modeling. The vast majority of the things, as well as the vast majority of the relationships, that make up and describe the sentence are nonmodular. Notice also: How I decide to divide the sentence up into things is going to determine what sort of relationships, whether modular or non-modular, I must list to describe it, whether particularly or completely. If, for instance, instead of dividing the sentence up into letters as a typewriter might type it, I were to divide it into the single strokes that make up the letters on a computer display flash-out, where each letter is made up of lines in a matrix X/\lA’/V/X?Ks is going to be very different from the list we talked about before.
But let us sum up what modeling is being done by the sentence The hammer hit a nail. We are modeling attitudes, objects, and various aspects of a relation between them; to do this job, we are using, among a large group of things and relations, various of those things and relations to stand for the objects, attitudes, and relations we wish to model.