Anatomy of a Proposition

Anatomy of a Proposition

In his Notebooks 1914-1916 Wittgenstein writes as follows: “My whole task consists in explaining the nature of the proposition” (39) and “All this would get solved of itself if we understood the nature of the proposition” (33). He clearly thinks we don’t understand the nature of the proposition and that there is something here that needs explaining. To that end I will sketch a diagram of the proposition that incorporates some thoughts of Wittgenstein and adds some of my own. I think of this as an anatomy of the proposition. However, I will proceed by describing the sketch not actually drawing it; it should be easy to make the sketch once it has been described. First, write down the letter “p” in the middle of the page; gaze at it for a moment—that is going to be the proposition. Now draw two arrows pointing upwards from it with “true” and “false” written by them. This signifies what Wittgenstein called the “bipolarity” of the proposition. Now draw two arrows pointing down; write “subject” and “predicate” by each arrow head (this is to be an elementary proposition). Now join the two with a line indicating the operation of predication (this is what the proposition “says”). The arrows represent reference. Next draw an arrow pointing right; this indicates entailment—the logical consequences of the proposition. These are other propositions, “q”, “r”, etc. Finally, draw an arrow pointing left: this points to the logical connectives, “and”, “or”, and “not”. According to Wittgenstein, and I agree, even elementary propositions contain the possibility of composition with these logical concepts; they are implicit in the proposition. So, we now have a diagram in which “p” occurs in the center and lines radiate out to other points of logical space. These points include the two truth-values, the reference of the terms of the proposition, the operation of predication, the logical consequences of the proposition, and the truth-functional connectives. The anatomy of the proposition takes in all these things, so it is not an isolated unit, an indivisible atom. Nor is it best represented by an ordered pair of object and property; it has a lot more inner complexity than that (it is octopus-like). The diagram depicts the proposition as having a certain kind of formal structure with which we are familiar—the structure of a physical atom such as an atom of oxygen. In particular, it has a nucleus and a surrounding “shell” of “particles”. What is that nucleus? That is what Wittgenstein says he doesn’t know (he understands the rest). It isn’t that the proposition is just the sum-total of what the arrows point to; it has something at the center of this array. It has a nucleus that generates and explains the array—something where the “mass” is concentrated. This is intuitively correct: we have the feeling (impression, conviction) that the proposition consists of a kernel that underlies its various connections, but we can’t pinpoint what that is. Is it a picture? But that theory runs into well-known problems and doesn’t really explain the array. It can’t be a mere sentence, a sequence or marks or sounds, because that is just a physical thing. It can’t be a mental image, for innumerable reasons. It can’t be a mere point in logical space (too simple).  So, what is it? It has a mysterious nature. How can it contain the things to which the arrows point? But it is not externally related to them; the connections are logical. It both is those things and yet stands apart from them. It is logically eukaryotic, but doesn’t have the architecture of a biological cell. What is this peculiar tentacled entity that essentially comprises the things indicated by the arrows? It eludes our grasp. So, we don’t really understand the basic concept of logic, the concept of a proposition. Yet we can draw a diagram of it, perhaps marveling at the remarkable powers of this elusive creature. It seems like nothing else we are familiar with (neither atom nor cell), though it has a nucleus-shell structure. We say of it that it must have one or the other truth-value, that it performs the act of predication on subject and predicate, that it entails other propositions, that it is subject to truth-functional composition: but what it is escapes us. It doesn’t seem like a thing at all—an object, simple or complex. It is what makes logic possible, and it is what makes belief and other attitudes possible, and it is what sentences express—but its nature is frustratingly opaque. A picture is much easier to understand, because you can see a picture and it doesn’t have the array of properties depicted in the diagram—hence the temptation to assimilate propositions to pictures. But a proposition is really nothing like a picture and presents far greater problems of comprehension. You have to sympathize with Wittgenstein’s puzzlement.[1]

[1] He agonized over the problem at the time of the Tractatus, but later dropped the whole idea of the proposition. Frege, Russell, and others were also much exercised by the problem, but today it is seldom broached. Contemporary theories of propositions don’t seem to me to make much headway with what was troubling Wittgenstein (propositions as sentences, propositions as psychological entities, propositions as sets of possible worlds, propositions as n-tuples of senses, etc.). Things are a lot more difficult than people imagine.