Some of these questions of interpretation have never been controversial ones. For instance, Wittgenstein makes it quite clear that he did not include the propositions of religion, morality, or aesthetics among factual propositions. They are all explicitly excluded at the end of the Tractatus, so that there is no doubt that their analyses are not supposed to yield elementary propositions. On the other hand it is true that his theory of language (i.e., of factual discourse) does not contain anything which necessarily restricts its application to empirically based factual propositions. For example, although he applies the German equivalent of Russell’s term “acquaintance” (kennen) to knowledge of the things which would be mentioned in elementary propositions, he never identifies acquaintance with sense-perception. So he may seem to be allowing for the possibility that factual discourse need not always have an empirical basis. But the explicit exclusions at the end of the Tractatus make it evident that this cannot have been his intention. So when Schlick and Carnap and the other philosophers of the Vienna Circle took the Tractatus as their model, and applied its theory of language to empirically based factual propositions, they were applying it in the way in which its author intended it to be applied. The Notebooks 1914-1916 in which Wittgenstein worked out the ideas of the Tractatus make this intention particularly clear.
But it is not so clear what direction the analysis of factual propositions was supposed to take. Here the main choice is between an analysis which keeps to propositions about the physical world and an analysis which at some point abandons propositions about the physical world and goes over to propositions about the sensory experiences of observers (sense-datum propositions). The first kind of analysis is the one that recommends itself to common sense. The choice of this kind of analysis may also be justified on the ground that it is the simplest way of systematizing the findings of science. A philosopher who chooses the second kind of analysis will probably choose it because of his theory of knowledge. He will argue that, since we have no direct knowledge of anything beyond our own sense-data, all factual propositions must be analyzable without residue into propositions about our own sense-data. If there were a residue which could not be analyzed in this way, it would represent something unknowable. Russell used this kind of argument for the analysis of all factual propositions into sense-datum propositions. But was this Wittgenstein’s view too? If so, his elementary propositions—the point of origin of his survey of factual discourse—would be sense-datum propositions.
Elizabeth Anscombe, whose book opens with a discussion of this controversial question, argues that the elementary propositions of the Tractatus cannot be sense-datum propositions. Her argument is that Wittgenstein says that elementary propositions are logically independent of one another (the truth or the falsity of one elementary proposition does not imply the truth or the falsity of any other elementary proposition); but sense-datum propositions are not logically independent of one another—for example, the truth of the proposition that a certain visual impression is yellow does imply the falsity of the proposition that it is blue; therefore, elementary propositions cannot be sense-datum propositions. But this argument only proves that they cannot be sense-datum propositions containing predicates like “blue” and “yellow.” It is possible that Wittgenstein believed that sense-datum propositions containing such predicates could be analyzed into sense-datum propositions which did not contain any such predicates. If so, his elementary propositions might still be sense-datum propositions.
But were they sense-datum propositions? If it is difficult to extract a definite answer to this question from the text of the Tractatus, at least it is possible to explain why it is difficult. The reason is that Wittgenstein’s theory of language was intended to be an entirely general theory, deduced from the barest essentials of the symbolization of facts. So he did not want its application to be restricted, like the application of Russell’s theory of language, by some argument drawn from the theory of knowledge. He intended it to be applied to empirically based factual propositions, but he did not wish to be more specific than that.
If Wittgenstein leaves it uncertain what sort of proposition an elementary proposition would be, why is he so certain that there must be elementary propositions, and that all other factual propositions must be analyzable into them? It would be understandable if a philosopher specified a certain kind of proposition, and then argued that all factual propositions are analyzable into propositions of that kind—this is a familiar pattern of argument. But it is puzzling to find Wittgenstein arguing in this way about an unspecified kind of proposition. How can he? This question is easier to answer than the last one. The answer can be given in two parts, both of which will require some explanation. First, he does give a specification for elementary propositions, the specification on which Elizabeth Anscombe’s argument relied: they must be logically independent of one another. Of course, this is not the kind of specification which was being sought just now. It specifies them not by their subject-matter, but by their logical properties. But from Wittgenstein’s point of view this is, as will soon become apparent, a more important way of specifying them. Secondly, he uses a very general argument, based on the essential nature of factual discourse, in order to show that all factual propositions must be analyzable into elementary propositions which are logically independent of one another.
The argument has two premises. The first premise is that every factual proposition must have a precise sense. Now the sense of a proposition is a function of its implications: it depends on what has to be the case if the proposition is true. So if a proposition must have a precise sense, it must be possible to draw a sharp line around everything that would have to be the case if it were true. Wittgenstein owed this idea to Frege. His argument also requires a second premise: that a factual proposition has sense only because words represent things, just as a diagram says something only if its parts represent things.
The second premise needs to be refined in order to allow for the possibility that a factual proposition might have a sense even if it contained a word which happened to represent something that did not exist. This can happen, just as it can happen that a certain part of a diagram represents something that does not exist—perhaps an invention. But what can be said in such cases is that, if the whole diagram is going to be intelligible, that particular part of it must be divisible into smaller parts which represent things that do exist—for example, the first man to think of a watch-spring could produce a diagram of it only by drawing a wheel and an axle, and by showing the tension, and these things would already exist; and, similarly, it can be said that, if the factual proposition has a sense, the word which happens to represent a non-existent thing must be analyzable into other words which represent existent things. For representation, which is essential to the symbolization of facts, is based ultimately on the correlation of words with existent things.
Starting from these two premises Wittgenstein argues for the conclusion that every factual proposition can be analyzed into elementary propositions. The argument depends on the specification of elementary propositions—that they must be logically independent of one another. From this it follows that the words which they contain cannot represent anything complex, such as colors. For if their words did represent complex things, elementary propositions could not be logically independent of one another. Only absolutely simple things can be represented by the words in elementary propositions. Wittgenstein argues that the analysis of any factual proposition must continue until it reaches a point at which the words represent simple existents, and so the propositions are elementary.
This part of his argument is an attempt to destroy the hypothesis that the things that are represented by words are all complex. He tries to destroy it by pointing out that, when a particular complex thing exists, a proposition which dissects its complexity and describes it in detail must be true. So if the analysis of a factual proposition stopped at a point at which a word represented a complex existent, a further proposition, which described the complexity of that existent would have to be true. But if the truth of the further proposition were required by the sense, and therefore by the truth, of the original factual proposition, the further proposition would state something which would have to be the case if the original proposition were true. But then from the premise that every proposition must have a precise sense, it follows that the further proposition should be included as part of the sense of the original proposition, just as the details of anything complex, which is represented by a part of a picture should be included in the message conveyed by the picture. The same doctrine requires that there should be an end to this process of aggrandizement. A country whose frontier was always a little further out than at any moment it was deemed to be would not really have a frontier. There must be a definite limit to what is being asserted, and so there must be a definite limit to the granulation of the view which is presented by a picture or a factual proposition.
This is a very abstract argument, and Wittgenstein did not claim to be able to illustrate its conclusion by giving actual examples of elementary propositions, or of the simple existents represented by the words which they contained. He thought that he had proved on theoretical grounds that the analysis of factual propositions must end in elementary propositions, but in practice it had not got so far. In practice the analysis of a factual proposition proceeds by setting out separately everything that has to be the case if it is true, and then, if necessary, by taking some of these items and treating them in the same way, without making any use of the presumption that the process will terminate in elementary propositions.
No doubt this helps to explain the kind of influence which was exerted by Wittgenstein’s theory of analysis between the two wars. His description of the process of analysis gave linguistic philosophers a guide and a program which they could at least begin to carry out. They could, for example, begin to work on the task of analyzing propositions about the physical world into propositions about people’s sense-data: or, alternatively, their analyses might never go over into propositions about sense-data, and they might try to translate propositions about theoretical entities, such as electrons, into propositions about things and processes that are observable in laboratories, and, in the social sciences, propositions about nations or corporations might be translated into propositions about individuals. But, however useful Wittgenstein’s description of the process of analysis might be, his description of elementary propositions gave more inspiration than guidance, like the pictures which are sometimes found inset in old maps.