The Analysis of Mind

reference of a proposition, according to this definition, unless we know whether the proposition is true or false. To avoid this inconvenience, it is better to adopt a slightly different phraseology, and say: The "meaning" of the proposition "to-day is Tuesday" consists in pointing to the fact "to-day is Tuesday" if that is a fact, or away from the fact "to-day is not Tuesday" if that is a fact. The "meaning" of the proposition "to-day is not Tuesday" will be exactly the opposite. By this hypothetical form we are able to speak of the meaning of a proposition without knowing whether it is true or false. According to this definition, we know the meaning of a proposition when we know what would make it true and what would make it false, even if we do not know whether it is in fact true or false. The meaning of a proposition is derivative from the meanings of its constituent words. Propositions occur in pairs, distinguished (in simple cases) by the absence or presence of the word "not." Two such propositions have the same objective, but opposite meanings: when one is true, the other is false, and when one is false, the other is true. The purely formal definition of truth and falsehood offers little difficulty. What is required is a formal expression of the fact that a proposition is true when it points towards its objective, and false when it points away from it, In very simple cases we can give a very simple account of this: we can say that true propositions actually resemble their objectives in a way in which false propositions do not. But for this purpose it is necessary to revert to image-propositions instead of word-propositions. Let us take again the illustration of a memory-image of a familiar room, and let us suppose that in the image the window is to the left of the door. If in fact the window is to the left of the door, there is a correspondence between the image and the objective; there is the same relation between the window and the door as between the images of them. The image-memory consists of the image of the window to the left of the image of the door. When this is true, the very same relation relates the terms of the objective (namely the window and the door) as relates the images which mean them. In this case the correspondence which constitutes truth is very simple. In the case we have just been considering the objective consists of two parts with a certain relation (that of left-to-right), and the proposition consists of images of these parts with the very same relation. The same proposition, if it were false, would have a less simple formal relation to its objective. If the image-proposition consists of an image of the window to the left of an image of the door, while in fact the window is not to the left of the door, the proposition does not result from the objective by the mere substitution of images for their prototypes. Thus in this unusually simple case we can say that a true proposition "corresponds" to its objective in a formal sense in which a false proposition does not. Perhaps it may be possible to modify this notion of formal correspondence in such a way as to be more widely applicable, but if so, the modifications required will be by no means slight. The reasons for this must now be considered. To begin with, the simple type of correspondence we have been exhibiting can hardly occur when words are substituted for images, because, in word-propositions, relations are usually expressed by words, which are not themselves relations. Take such a proposition as "Socrates precedes Plato." Here the word "precedes" is just as solid as the words "Socrates" and "Plato"; it MEANS a relation, but is not a relation. Thus the objective which makes our proposition true consists of TWO terms with a relation between them, whereas our proposition consists of THREE terms with a relation of order between them. Of course, it would be perfectly possible, theoretically, to indicate a few chosen relations, not by words, but by relations between the other words. "Socrates-Plato" might be used to mean "Socrates precedes Plato"; "Plato-Socrates" might be used to mean "Plato was born before Socrates and died after him"; and so on. But the possibilities of such a method would be very limited. For aught I know, there may be languages that use it, but they are not among the languages with which I am acquainted. And in any case, in view of the multiplicity of relations that we wish to express, no language could advance far without words for relations. But as soon as we have words for relations, word-propositions have necessarily more terms than the facts to which they refer, and cannot therefore correspond so simply with their objectives as some image-propositions can. The consideration of negative propositions and negative facts introduces further complications. An image-proposition is necessarily positive: we can image the window to the left of the door, or to the right of the door, but we can form no image of the bare negative "the window not to the left of the door." We can DISBELIEVE the image-proposition expressed by "the window to the left of the door," and our disbelief will be true if the window is not to the left of the door. But we can form no image of the fact that the window is not to the left of the door. Attempts have often been made to deny such negative facts, but, for reasons which I have given elsewhere,* I believe these attempts to be mistaken, and I shall assume that there are negative facts. * "Monist," January, 1919, p. 42 ff. Word-propositions, like image-propositions, are always positive facts. The fact that Socrates precedes Plato is symbolized in English by the fact that the word "precedes" occurs between the words "Socrates" and "Plato." But we cannot symbolize the fact that Plato does not precede Socrates by not putting the word "precedes" between "Plato" and "Socrates." A negative fact is not sensible, and language, being intended for communication, has to be sensible. Therefore we symbolize the fact that Plato does not precede Socrates by putting the words "does not precede" between "Plato" and "Socrates." We thus obtain a series of words which is just as positive a fact as the series "Socrates precedes Plato." The propositions asserting negative facts are themselves positive facts; they are merely different positive facts from those asserting positive facts. We have thus, as regards the opposition of positive and negative, three different sorts of duality, according as we are dealing with facts, image-propositions, or word-propositions. We have, namely: (1) Positive and negative facts; (2) Image-propositions, which may be believed or disbelieved, but do not allow any duality of content corresponding to positive and negative facts; (3) Word-propositions, which are always positive facts, but are of two kinds: one verified by a positive objective, the other by a negative objective. Owing to these complications, the simplest type of correspondence is impossible when either negative facts or negative propositions are involved. Even when we confine ourselves to relations between two terms which are both imaged, it may be impossible to form an image-proposition in which the relation of the terms is represented by the same relation of the images. Suppose we say "Caesar was 2,000 years before Foch," we express a certain temporal relation between Caesar and Foch; but we cannot allow 2,000 years to elapse between our image of Caesar and our image of Foch. This is perhaps not a fair example, since "2,000 years before" is not a direct relation. But take a case where the relation is direct, say, "the sun is brighter than the moon." We can form visual images of sunshine and moonshine, and it may happen that our image of the sunshine is the brighter of the two, but this is by no means either necessary or sufficient. The act of comparison, implied in our judgment, is something more than the mere coexistence of two images, one of which is in fact brighter than the other. It would take us too far from our main topic if we were to go into the question what actually occurs when we make this judgment. Enough has been said to show that the correspondence between the belief and its objective is more complicated in this case than in that of the window to the left of the door, and this was all that had to be proved. In spite of these complications, the general nature of the formal correspondence which makes truth is clear from our instances. In the case of the simpler kind of propositions, namely those that I call "atomic" propositions, where there is only one word expressing a relation, the objective which would verify our proposition, assuming that the word "not" is absent, is obtained by replacing each word by what it means, the word meaning a relation being replaced by this relation among the meanings of the other words. For example, if the proposition is "Socrates precedes Plato," the objective which verifies it results from replacing the word "Socrates" by Socrates, the word "Plato" by Plato, and the word "precedes" by the relation of preceding between Socrates and Plato. If the result of this process is a fact, the proposition is true; if not, it is false. When our proposition is "Socrates does not precede Plato," the conditions of truth and falsehood are exactly reversed. More complicated propositions can be dealt with on the same lines. In fact, the purely formal question, which has occupied us in this last section, offers no very formidable difficulties. I do not believe that the above formal theory is untrue, but I do believe that it is inadequate. It does not, for example, throw any light upon our preference for true beliefs rather than false ones. This preference is only explicable by taking account of the causal efficacy of beliefs, and of the greater appropriateness of the responses resulting from true beliefs. But appropriateness depends upon purpose, and purpose thus becomes a vital part of theory of knowledge.