Introduction to Wittgenstein’s Tractatus
Companion to Wittgenstein’s Tractatus
Letters from Ludwig Wittgenstein with a Memoir by Paul Engelmann
Wittgenstein: The Philosophical Investigations: A Collection of Critical Essays
Remarks on the Foundation of Mathematics
Lectures and Conversations on Aesthetics, Psychology, and Religious Belief [including the Conversations on Freud]
In the history of western philosophy, at least since the time of Descartes, it is possible to discern a definite pattern which is often repeated. First there is a period of expansion, and then follows a period of criticism and contraction. In the period of expansion a certain set of ideas will have won general acceptance, and they will be developed and applied to the whole range of human thought and experience. At such times philosophy is likely to encroach on other disciplines—on the physical sciences in the seventeenth century, more recently on psychology, and most recently on linguistics—and the central ideas will probably go too long unexamined. It is especially likely that the competence and credentials of philosophy itself will be left unquestioned. How, for example, should philosophical truths be classified? Do they belong to the realm of contingency, because they state things that might have been otherwise—such as the fact that Eisenhower was President? Or do they belong to the realm of necessity, because what they state could not have been otherwise? Eisenhower might not have been President, but it is necessarily true that he was younger than his mother, and that 7+5=12. To put the same question linguistically—are philosophical truths expressed in factual propositions or in a priori propositions?
When such questions are asked, a period of criticism begins. The vague persuasiveness of philosophy is analyzed, and there is a demand for a precise specification of the kind of statement which philosophers may legitimately make, and of the grounds on which they should be accepted. When philosophy criticizes itself in this way, the result is usually a certain contraction. If it has grown into some other discipline, such as psychology, and has become intertwined with it, those branches will be cut back, and a definite limit will be set to its competence. There are various ways in which this self-criticism may develop, but since the Renaissance the most important step has always been to inquire whether philosophy is a factual discipline, like the sciences, and, if not, how far removed from them it is. One method of arriving at an answer to this question would be to take factual discourse first and to try to determine its limits, and then to ask whether philosophy falls within those limits. This would be an indirect approach to the question what philosophy ought to be.
About the turn of the last century, philosophy in England, largely under the influence of the work of Moore and Russell in Cambridge, began to move into a phase of criticism and contraction. Looking back on it now we can see that they started the most important movement of this kind since Kant. There is, of course, a difference between their view of what philosophy ought to be and Kant’s view. They believed that the correct procedure would be the detailed analysis of the meanings of the various kinds of things that people say, including the things that philosophers say, whereas Kant believed it to be a very general analysis of the powers and limitations of human thought. But since sentences ought to be intelligible and thoughts ought to be expressible, this difference is not so great as it looks. There is, in any case, a striking similarity between their view of what was wrong with the philosophy of the period of expansion which their work was to supersede and Kant’s view of what was wrong with the philosophy which was related in a similar way to his work. In both cases the criticism was that philosophy was insecurely balanced between contingency and necessity. If philosophy was really like a science, why were its results not based on observation and experiment? If, on the other hand, it was really like mathematics, why was there so much disagreement about the validity of its arguments?
Wittgenstein’s Tractatus Logico-Philosophicus, which was first published in 1921, is in part an attempt to determine what philosophy ought to be, and particularly what its relationship to factual disciplines really is. It is also much more than this, because such an undertaking necessarily leads on to an investigation of the difference between factual and a priori propositions, and so to a general theory about the various kinds of things that people say, and the grounds on which they should be accepted. But one of Wittgenstein’s motives for seeking a general theory of meaning and truth—the one which he emphasizes in the Preface to the Tractatus—was that he wanted to put philosophy in its proper place. He wanted to show that it cannot do one of the things which it has often been expected to do: it cannot establish religion and morality on a factual basis, because it is not another factual discipline like the sciences, but more general in its scope—in short, traditional metaphysics is not possible.
His method of placing philosophy is indirect. He takes factual discourse first, and tries to determine its limits, in order to see whether philosophy falls within those limits. So after announcing in the Preface that the Tractatus deals with the problems of philosophy, he says that the aim of the book is to plot the limit of language, within which everything that can be asserted truly or falsely will have to find a place. The two projects are connected because, according to him, the traditional problems of philosophy arose from linguistic misunderstandings—not, of course, from particular failures to communicate with other people, but from general misconceptions, and especially from the inability to see all the differences between different kinds of discourse. It is, for example, obvious that morality is not a science, but the full extent of the differences between moral and scientific discourse is far from obvious.
When Wittgenstein says that the aim of the Tractatus is to plot the limit of language, he means that its aim is to plot the limit of factual language. Although it is clear why he believed this task to be important, it is not so clear why he describes it in the way that he does. Whatever the exact scope of factual discourse—and this too is uncertain—it is obvious that not all discourse is factual. So does non-factual discourse not count as language? Is there something wrong with all non-factual discourse? Does his equation of language with factual discourse express a kind of positivistic intolerance? These are crucial questions in the interpretation of his philosophy. For beyond the limit of language there is only nonsense, and so, given the equation of language with factual discourse, all non-factual discourse will be nonsense—a conclusion that will be as harsh and intolerant as it sounds, unless either the term “factual discourse” is being used to include more than is commonly allowed, or there is some subtle distinction between good nonsense and bad nonsense.
Perhaps, however, it is not quite accurate to say that nonsense lies beyond the limit of language. For the task of plotting the limit is rather like calculating the curvature of space, because there is nothing outside it. Nonsense is nowhere, and the line between sense and nonsense can be drawn only from some point of vantage within language. Now if “language” means “factual discourse,” the point of origin of this geometrical construction must lie somewhere within the factual assertions that people actually make, or, at least, somewhere within some of them. If we did not live in a world of factual meaning, we could not imagine what such a life would be like, because to imagine something is to put together certain words, or perhaps certain ideas, in such a way that the result—a sentence or a thought—has a meaning, even if it is not true.
But the general area, within which the construction certainly had to start, contained a variety of possible points of origin, among which a choice needed to be made. It would be possible to start from empirically based factual propositions, on the ground that at least they have meanings. Or it might be better to include under the heading “factual discourse” more than is always allowed. If religious discourse were included, and other similar relaxations were allowed, it would be possible to take several points of origin and to give the space of factual meaning a more sinuous curve, which would allow for the gravitational pull of whatever it is that is happening in less scientific fields of thought.
There are also other questions which need to be asked about Wittgenstein’s attempt to plot the limit of language. For in order to understand his choice of a point of origin, we need to know something about his theory of logical analysis. Now he began to develop the ideas which went into the Tractatus soon after he first arrived in Cambridge in 1912, and like Russell, with whom he worked, he did not take ordinary factual propositions in the form in which they are current in everyday life and in scientific discourse. He believed that language disguises thought, and that the real forms of our thoughts would be apparent only when the language in which they are expressed had been analyzed and broken down into its basic components. His idea was that the assertion of an ordinary factual proposition is a gross move, which contains within itself a number—perhaps a very large number—of minute moves.
For instance, merely to assert that the watch is lying on the table is to assert by implication quite a large number of other propositions. These implied propositions would be propositions about the mechanism inside the case of the watch—or, at least, this is the natural view to take of the implications of the original assertion. (There is also another possible view about them—that they would be propositions about people’s sensory experiences.) Of course, Wittgenstein was not recommending that the assertion of each of these implied propositions should be a separate move in everyday life. The grossness of ordinary factual propositions is a blessing. But he did think that an exact account of what they mean could be given only if they were analyzed into their basic components, which he called “elementary propositions.”
This raises further questions about the point of origin which Wittgenstein used in the Tractatus. If we are analyzing ordinary factual propositions, how far shall we have to go before we reach the elementary propositions which will reveal the real forms of our thoughts? This is not a question about the scope of factual discourse, but a question about its depth. How are we to know when analysis has gone deep enough? Do we even know the general direction which it ought to take? Should the statement about the watch be analyzed into statements about its mechanical parts, as has just been suggested? Or should it be analyzed into statements about the sensory experiences (sense-data) which a person would get if he examined it—e.g., into statements about the visual impressions which he would get if he looked at it?
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.
This distinction between the usable and the unusable parts of Wittgenstein’s early theory of analysis can be related to his attempt to plot the limit of language. That undertaking requires not only a point of origin but also a formula to fix the limit in relation to it. The exact location of the point of origin—elementary propositions—is something of a mystery, but there is nothing mysterious about the formula. Wittgenstein’s idea was that the way to fix the limit is to find a formula for constructing all the propositions which would fall within the limit—i.e., a formula for constructing any factual proposition. The formula which he adopts is to take a set of elementary propositions, and to form all possible combinations of their truth and falsity, and then to specify which of these combinations shall not be realized if the proposition which is being constructed is true. For he believed that the truth or falsity of any factual proposition depends solely on the truth or falsity of the elementary propositions in its final analysis. To put the point in the usual logical terminology, any factual proposition is a truth-function of elementary propositions, or—to put it in a way that relates it to the previous discussion—the sense of a factual proposition depends on what has to be the case if it is true, and ultimately, when its sense has been ground down to the finest possible grains, on the requirement that certain combinations of the truth and falsity of elementary propositions shall not be realized, if it is true.
Although elementary propositions, to which this formula is applied, are somewhat mysterious, the formula itself is clear enough. It is also clear that it runs into difficulties. For it does not seem to allow for all the ways in which propositions are constructed. It explains the construction of such a proposition as “Either the watch is on the table, or it is on the desk.” But the proposition “I believe that the watch is on the table” seems to be constructed in a different way. Certainly, its truth or falsity does not depend on the truth or falsity of the proposition “The watch is on the table,” which is one of its components.
It is perhaps surprising that Wittgenstein’s elementary propositions should be so inaccessible and mysterious, because they are deduced from a theory of analysis constructed out of material which he got from Russell, and which in Russell’s hands took a less recondite form. Russell’s system is really a version of Hume’s empiricism, presented not as a theory about the mind—which is the way in which Hume presented it—but as a theory about language, and, therefore, based on Russell’s new ideas in logic rather than on the primitive psychology of the eighteenth century. It is clear and cool, and its doctrines and the spirit in which they are developed are Humean, even if the arguments on which they are based are not Humean. The analysis of all factual propositions is supposed to terminate in sense-datum propositions. Nothing could be less recondite.
But when Wittgenstein took over the logical ideas on which Russell’s theory of analysis was based, he developed them in the darker manner of German Idealism. The Tractatus belongs to the same tradition as the work of Freud. It is, of course, neither a psychological treatise nor a philosophical treatise presented in psychological terms. But it offers a speculative theory about something which is usually supposed to take place in the clear light of consciousness—the correlation of words with things through which factual propositions acquire their senses. In the case of elementary propositions this correlation takes place in total obscurity. If it is something that we do, we do not do it consciously or intentionally.
In his Memoir Engelmann connects the darkness at the center of Wittgenstein’s construction of factual discourse with the mysteriousness of certain kinds of non-factual discourse. One connection—an obvious one—is that Wittgenstein could not plot the limit of factual discourse without saying something about at least one kind of non-factual discourse, namely philosophy. What he says about it is that, like religion, morality, and aesthetics, it cannot be expressed in factual propositions, and this is one of the most important findings of the Tractatus. But he also says something more positive about philosophy. It is an organized investigation of a well-defined field. It is not a science, distinguished from other sciences only by its extreme generality. For science studies things that might have been otherwise, and, however general its results may be, they belong to the realm of contingency, whereas philosophy studies the realm of necessity. So philosophical results will be expressed in propositions which are in some way or other necessarily true, a priori propositions. When Wittgenstein claims that all factual propositions are analyzable into elementary propositions, and that the words in elementary propositions are correlated with simple existents, this is a philosophical claim that these things are necessarily so. Although it is a claim about the structure of factual discourse, and ultimately about the structure of reality, it does not itself belong to factual discourse, because a priori propositions do not have factual sense. So at the center of the realm of contingency there are truths of the kind which traditional metaphysicians tried to express in factual propositions, but which cannot be expressed in factual propositions. Inside the world of factual meaning the pressure of other modes of thought can be felt.
This connection between the philosophical study of factual discourse and other non-factual disciplines is a negative one. Neither religion nor morality nor aesthetics nor philosophy can be expressed in factual propositions. Nevertheless it is an important connection, because it shows that, when Wittgenstein places a certain kind of discourse outside factual language, he is not thereby condemning it. Such exclusions are certainly divisive, but they are not intolerant. In fact—to answer one of the questions that was posed earlier—he does distinguish between good and bad nonsense. There is the complete nonsense which is produced when someone tries to take factual propositions beyond their limit. Some of the doctrines of traditional metaphysicians belong to this category: they do not have factual sense, although they purport to have it. But there are also two other categories of “non-sense” which are not condemned. There are a priori propositions which neither have nor purport to have factual sense, and there are propositions such as those of religion and morality which express things that cannot be expressed in a factual way, although they are often cast in a form which suggests, most misleadingly, that their mode of expression is factual.
The peculiarity of philosophy, which differentiates it from other non-factual disciplines, is that its results are expressed in a priori propositions. This peculiarity is, of course, a direct consequence of the thesis that philosophy is linguistic analysis. For the statement that a particular proposition can be analyzed in a certain way is a statement which, given the meaning of the proposition to be analyzed, and the meaning of the analysis, is necessarily true, or a priori. But this is not a complete explanation of the fact that philosophical results are expressed in a priori propositions. For the theory of elementary propositions and the ontology which Wittgenstein deduced from it are also philosophical results expressed in a priori propositions. They are, of course, results of a very different kind. It is one thing to give the analysis of a certain kind of proposition, and quite another thing to offer a general thesis about the structure of factual discourse and the structure of reality. But both alike would be expressed in a priori philosophical propositions.
The distinction between these two kinds of results is, of course, the distinction between the usable and the unusable parts of the theory of analysis which is expounded in the Tractatus. The unusable part was Wittgenstein’s general and highly speculative theory of elementary propositions, and the ontology which he deduced from it. The usable part of the theory of analysis was detached by other philosophers in the period between the two wars and worked out separately. It contained three leading ideas. The first idea is that a factual proposition is a truth-function of the propositions which occur at any stage in its analysis, whether it be the final stage or not; the second idea is that the connection between a proposition and its analysis—sameness of meaning—will be expressed in an a priori philosophical proposition; and the third idea is that all a priori propositions lack factual sense.
It was inevitable that Wittgenstein’s attempt to place philosophy in relation to factual disciplines should raise the question how it is related to a priori disciplines. It was also inevitable that this question—to which the answer given was that it is an a priori discipline of a peculiar kind—should lead on to the question, what the difference between factual and a priori propositions really is. This trail of questions leads to the center of the system of the Tractatus. The easiest way to follow it is to take the three ideas which comprise the usable part of Wittgenstein’s theory of analysis, and to examine them more closely, in order to see why they seemed to him to point unmistakably toward the more speculative part of the theory.
A factual proposition is a truth-function of the propositions which occur in its analysis. This means that a factual proposition, provided that it is not elementary, is a compound proposition, which says what its components say, no more and no less. For example, if a factual proposition, p, can be analyzed as a conjunction of two factual propositions, q and r, then p is true if both q and r are true, but in all other cases it is false. Now there are two other types of truth-function besides factual propositions. There are truth-functions which are true in all cases, and these are tautologies—e.g., the tautology, p or not-p, is always true, whether p itself, which is its only component, is true or false: and there are truth-functions which are false in all cases, and these are contradictions—e.g., the contradiction, p and not-p, is always false.
These two further types of truth-function lack factual sense, because considered as messages they are self-cancelling. Someone who begins by saying, “p…,” and continues by saying, “…and not-p” cancels the sense of the first part of his utterance, and produces a contradiction. The continuation, “…or not-p,” which produces a tautology, cancels the sense of p in a different way. For, whereas a contradiction cannot be true, whatever happens, a tautology must be true, whatever happens. So tautologies and contradictions are not messages. They do not express what is the case, but what must be the case, and what cannot be the case. They themselves lack factual sense, but they express the necessary connections between other propositions which do have factual sense. An argument is valid if the combination of its premises and its conclusion is a tautology: given the premises the conclusion must be true. For example, it is tautological to say that, given p, and given if p, then q, q must be true. To put the same point negatively, an argument is valid if the combination of its premises and the negation of its conclusion is a contradiction. In short, the propositions of logic are not theories about the nature of reality, but tautologies, which lack factual sense.
This theory of logical necessity is so simple and elegant that it attracts all the attention, and Wittgenstein’s next step sometimes goes unnoticed. His next step is to argue that, though the propositions of logic are tautologies and not theories about the nature of reality, the fact that logic exists does indicate something about the nature of reality—it indicates that reality consists ultimately of simple things. His argument for this connection between the existence of logic and his ontology can be broken down into stages. The existence of logic depends on the possibility of combining factual propositions to form tautologies. But that requires the possibility of first constructing factual propositions, without which there would be nothing to combine; and this, in its turn, involves the possibility of elementary propositions and the ultimate granulation of reality. Read in this direction, the argument is a transcendental one, which, in the spirit of Kant, seeks to show how the a priori propositions of logic are possible. They are possible only because reality consists ultimately of simple things. From this point the argument can be traced back in the reverse direction—from simple things to elementary propositions, and thence by the application of the truth-functional formula to the limit of language, which is fixed by the possible permutations and combinations of elementary propositions, however much this may be disguised by the convenient grossness of ordinary factual discourse.
So the task which Wittgenstein undertook in the Tractatus was really an investigation of the foundations of logic. His Notebooks show that this was how it began, and the other aspect of it, which he emphasizes in the Preface to the Tractatus—the fixing of the limit of language—emerged later. The two aspects are connected because logic reveals the structure of factual discourse, and so reveals the structure of reality, which factual discourse reflects. It is for logic to reveal these two structures, which are really one, because they are given in advance of experience—a priori. Experience can only give us a world of facts—everything that is contingently the case—but this world floats in a space of possibilities, which is given a priori. The limit of the space of possibilities, which is reflected in the limit of factual discourse, is given by logic. For the point of origin from which the limit is calculated is determined by logic, and the truth-functional formula, according to which it is calculated, is a logical formula.
So though the propositions of logic are tautologies and lack factual sense, it is logic that reveals the essential structure of reality. The point is sometimes overlooked, because it might be thought that, if the propositions of logic are tautologies, that is only because we happen to have chosen a language in which tautologies are produced when certain propositions are combined. So it might appear that a different choice would have produced a different result, and that all logical truths are true merely by convention. But this was not Wittgenstein’s view. He held that, although we have certain options—that this word should have this meaning, and that word that meaning—the general framework of any factual language is fixed objectively in advance. The general framework is a truth-functional structure based on elementary propositions. When human beings devise a particular factual language, they must connect it up to this pre-existing structure. They have certain options about the ways in which they make the connection, but the structure itself is rigid.
The Tractatus is a philosophical study of this structure, and the medium through which it works is logic. This explains why the book contains so little detailed analysis of particular types of proposition. Wittgenstein is concerned with the general theory of factual language, and with the general theory of reality which he believed that he could deduce from it. He was not much concerned with what seemed to him to be the comparatively trivial details of particular analyses. Now the general theory of language and the ontology do not themselves belong to factual discourse. That is one connection between the darkness at the center of Wittgenstein’s theory of factual discourse and the mysteriousness of certain kinds of non-factual discourse—such things cannot be expressed in factual propositions. But there is also another connection. Wittgenstein’s ontology and part of his theory of language—the part which deals with elementary propositions—are intrinsically mysterious. It is not that they can be fully and clearly expounded in language whose only disadvantage—if it is one—is that it is not factual language. The exposition of them is necessarily sketchy and impossible to illustrate with examples, because they are speculative theories. Even if his arguments proved that these things must be so, they could not be seen to be so.
Ten years later Wittgenstein had begun to dismantle parts of this system, but not in full view of the usual public. In fact, out of the mass of written work which he produced between the late 1920s and his death in 1951 only one brief article was published in his lifetime. In this period his ideas became known through discussions with small groups and lectures to restricted audiences. The result was that, at a time when some of the ideas of the Tractatus were being modified, they continued to exert an influence which was, perhaps, greater than it would otherwise have been. The theory of analysis, or at least the usable part of it, was taken as a model by analytical philosophers in this period.
The model suggested that all factual propositions are truth-functional compounds of simpler propositions. So it appeared that the way to deal with a type of factual proposition which raises a philosophical problem would be to analyze it into its simpler and more explicit components. Thus in the realm of contingency philosophy became the search for translations which would reveal all the implications of the various types of factual proposition and the real nature of their subject matter. Factual propositions whose meaning appears on first inspection to be rather nebulous, such as propositions about social or political groups, or propositions about electrons, would be analyzed in a way that made their implications absolutely clear. Similarly, in the realm of necessity, if all a priori propositions are reducible to tautologies, the way to deal with a puzzling proposition, which is evidently a priori, and yet which does not seem to be tautological, would be to translate it into a form in which it was demonstrably tautological. For example, it is evidently an a priori truth that we cannot travel backwards in time, and, though it does not seem to be a tautology in this form, it could be hoped that it would be possible to translate it into a tautology if an adequate analysis of temporal terms could be found.
Wittgenstein’s modification of the second of these two ideas began in 1929, and can be seen in Philosophische Bemerkungen. All a priori propositions would be reducible to tautologies only if the kind of final analysis which is described in the Tractatus could be achieved. But in the Bemerkungen he admits that it cannot be achieved. He had always conceded that he had not been able to produce final analyses of that kind. But he had thought that they existed and awaited discovery. This is what he retracted in 1929.
In order to understand the retractation, it is necessary to remember the specification of elementary propositions: they are logically independent of one another. Now ordinary factual propositions are not logically independent of one another. For example, a proposition describing a certain area as blue is incompatible with another proposition describing it as yellow. In the Tractatus Wittgenstein had explained this incompatibility by saying that colors have a certain internal complexity. His idea was that propositions in which colors are mentioned could be analyzed down into elementary propositions which would mention things with no internal complexity. If this kind of analysis could be achieved, an a priori proposition such as “Nothing can be blue and yellow simultaneously” would be demonstrated to be a tautology, and its negation, “Something can be blue and yellow simultaneously,” would be demonstrated to be a contradiction. For in the final analysis of the proposition “This thing is blue” there would be found one or more elementary propositions the negation of which would be found in the final analysis of the proposition “This thing is yellow.” Now if a proposition is combined with its negation, the result is a contradiction. So in the final analysis the proposition which is produced when the two color propositions are combined—“This thing is both blue and yellow simultaneously”—would turn out to be a contradiction, and its negation would therefore be a tautology.
If this program could be carried out, the necessary truth of all a priori propositions, except those which give the ontology of the Tractatus, would be shown to be merely the result of the fact that certain combinations of elementary propositions are tautologies. The necessary truth of an a priori proposition would never depend on the specific natures of the things mentioned in elementary propositions because those things would have no internal complexity. This is why the elementary propositions which mention those things would be logically independent of one another. However, the fact that certain combinations of them are tautologies would reveal something about the nature of reality—it would reveal the general structure of reality, which is objectively necessary. To put the same point the other way round, the general structure of reality would necessarily be reflected in the logical grammar of any factual language which human beings may devise. But, according to Wittgenstein’s earlier theory, there would be no further sources of necessity in the nature of things. If we put on one side the necessary truths about the general structure of reality which give the ontology of the Tractatus, there would be no residual sources of necessity left in the nature of things.
In the Bemerkungen he admits that this theory of necessity will not work in all cases. He had come to think that the necessary truth of certain specific a priori propositions cannot be explained by reducing them to tautologies. His reason for this retractation was that he no longer found it possible to believe that there would be no incompatibilities between the words contained in the elementary propositions into which he thought that all factual propositions are analyzable. Suppose, for example, that incompatibilities of colors were explained by analyzing propositions about them into propositions about the velocities of particles. Then the same situation would recur at a lower level of analysis, because there would be a wide range of velocities which would be incompatible with one another. So Wittgenstein conceded that elementary propositions would not be logically independent of one another. They would contain words which produced certain incompatibilities between them, just as color words do, and it would not be possible to reduce these incompatibilities to contradictions by further analysis. All that the philosopher can do is to note the incompatibilities and treat them as irreducible features of the logical grammar of the words.
It is one of the merits of Max Black’s Companion to the Tractatus that he emphasizes the continuity of Wittgenstein’s philosophical development by frequent quotation from his later writings. In this particular case the retractation does not amount to a complete abandonment of the earlier point of view. Of course, it puts the original theory of elementary propositions in jeopardy, because it was through their logical independence that elementary propositions were specified in the Tractatus. But whatever its effect on his view about the terminus of analysis, it leaves his view about the process of analysis—the usable part of the original theory—unchanged.
There is also another important idea which survives the change. Wittgenstein still maintains that the essential nature of things cannot be described in factual propositions, but can only be revealed in the a priori connections between factual propositions. The difference is that in the Tractatus what was supposed to be revealed in this way was only the most general structure of reality, which is reflected in the truth-functional structure of all factual discourse. The doctrine was that reality consists essentially of simple things, and that this basic structure is revealed in any a priori connection between a pair of factual propositions. For it was supposed that any such connection could be reduced to a tautology or a contradiction, and that the existence of this tautology or contradiction made only a very general demand on reality: all that was required was that reality should consist of simple things. But in the Bemerkungen he allows that it is not always possible to explain an a priori connection between two factual propositions by reducing it to a tautology or contradiction. Sometimes this explanation will work, but his new view was that some a priori connections depend on words which cannot be analyzed in this way, and that in such cases a truth-functional reduction to tautology or contradiction is not possible. When he finds an a priori connection of this latter kind, he can still say that it is a feature of the logical grammar of the words, but in such a case what the logical grammar of the words reveals about the structure of reality will be something very specific, rather than its general truth-functional framework. For example, the structure of the spectrum of colors, or the structure of the range of sounds would be revealed in this way. In fact, Wittgenstein’s new view was that there are many specific features of the structure of reality which are reflected in the logical grammar of the words which we use to divide and classify what we experience.
At this point it is important to observe what made the earlier theory of necessity succeed in those cases in which it did succeed. There are two kinds of case. First, there are a priori propositions which depend on definitions, and in such cases we can see how the definition confers necessary truth on the proposition, and we can often see that the definition is merely a convention which need not have been adopted. For instance, the a priori proposition “All planets move round the sun” owes its necessary truth to the definition of the word “planet” as “a heavenly body in orbit around the sun.” We can see how this definition works, and we can see that it need never have been adopted. Therefore, in order to explain this kind of a priori proposition, we do not have to appeal to the nature of things.
Secondly, there are the truths of logic, and in their case too the explanation of necessary truth avoids any direct appeal to the nature of things. There is, of course, an indirect appeal, because tautologies reveal the general structure of reality. But there is no direct appeal, because tautologies are not theories with factual sense. So in both these types of case the appeal to logical grammar is successful because it eliminates any direct appeal to the nature of things. But when Wittgenstein extended the scope of this explanation of a priori propositions by appealing to the logical grammar of descriptive words which, according to the earlier theory ought to be definable, but which in fact are not definable, it was not so clear whether it was successful. Can incompatibilities of colors be explained by the observation that they depend on the logical grammar of color-words? It is not even clear how this explanation was meant to be taken. When Moore heard him lecturing on this point in Cambridge in 1933, he was puzzled. He wondered what the ultimate source of the necessity was supposed to be in such cases. For example, was the proposition, “Nothing can be blue and yellow simultaneously” supposed to owe its necessary truth in the last resort to the logical grammar of the words, or to the nature of the things to which we apply the words?
Now when Wittgenstein wrote the Tractatus, he believed that, though the propositions of logic lack factual sense, they reveal the general structure of reality. So when he changed his theory of elementary propositions, and allowed that they might contain incompatible words, it would be natural to assume that his new view was that the logical grammar of those words revealed specific features of the structure of reality. But the way in which his ideas about necessary truth actually developed was more complex than this. For in the early 1930s his work on the foundations of mathematics was leading him toward a more conventionalist theory of necessary truth. He was beginning to think that all necessary truth depends on conventions which need not have been adopted.
This tendency to conventionalism complicates the development of his ideas. One line of development has already been described: instead of claiming to find a single basic pattern in reality—the pattern of simple things arranged in various ways—he came to think that the logical grammar of unanalyzable words reveals a multitude of more specific patterns in reality. But at the same time his shift toward conventionalism was changing the very meaning of the thesis that the structure of reality exhibits this pattern, or that pattern. He was moving away from the view that the structure of reality is a rigid framework, fixed in advance, and toward the view that it is a projection of human thought. In his theory of necessity conventionalism was replacing objectivism, and, in his account of the way in which we divide and classify what we experience, nominalism was replacing realism. So, although he located the source of specific necessary truths in the nature of things, he was beginning to take an entirely different view of this location. According to his new view, it would be nearer the truth to regard it as our creation. This shift toward anthropocentric theories is one of the two most important developments in his later philosophy.
The other important development in his later philosophy is also connected with the theory of elementary propositions. In the period between the two wars the elementary propositions of the Tractatus were frequently identified with sense-datum propositions. Though this identification was not part of the theory itself, it is a possible application of it, and many analytic philosophers in this period made it almost automatically. Now it is often supposed that the sense-datum language could stand by itself as the firm substructure on which the remainder of empirical language could be built. The idea was not that this was the order of infant learning, but that the system of empirical language could be rearranged in this way. The point of the rearrangement, according to philosophers as diverse in viewpoint as Russell and C.I. Lewis, was that it would set the stage for the combat with Cartesian doubt. Although the sense-datum language was not learned first, it could have been learned first, and, if it had been, we would have started with propositions about our own sensory experiences which we could not doubt. For example, it was supposed that however doubtful I might be about the actual shape of a particular rock, I could not have any doubts about my visual impression of its shape. So each of us would train himself to use propositions about his own sensory experiences in the privacy of his mind, and then in one way or another we would all fight our way back to some sort of knowledge of the external world and establish communication with one another. Wittgenstein took this traditional picture of the relationship between minds and the physical world and turned it upside down. He argued that the so-called sense-datum language is, and must be, dependent on the language in which we describe the external world.
He developed this attack on the idea of a private language in his first posthumously published book, Philosophical Investigations, and it has had a profound effect on the analytic philosophy of the last fifteen years. There are more essays devoted to it in the excellent collection edited by George Pitcher than to any other single topic. Wittgenstein’s polemic would not have been so important if it had been developed only against theories of perception which assume that the sense-datum language could function independently of the language in which we describe the external world. What makes his arguments so important is that they traverse the whole philosophy of mind. They seek to prove that it would be equally impossible for emotions or desires or intentions to be reported in a private language. Public criteria are needed across the whole field of mental phenomena. This is a general challenge to the Cartesian assumption that our knowledge of the contents of our own minds is independent of our knowledge of the external world—an assumption which had dominated western philosophy for three centuries. The challenge is based on an idea which is neither original nor recondite: mental phenomena cannot be dissociated from their observable manifestations in behavior. But the way in which Wittgenstein develops this idea is elaborate and subtle. The obvious advantage of behaviorism is that it explains how one person can know so much of what goes on in the mind of another, and how we can communicate with one another about such things. Wittgenstein tries to keep this advantage without denying, as some behaviorists have done, that there is anything more to mental phenomena than observable behavior. But while he avoids this paradoxical denial, he takes care not to be misled by the patch-work of physical imagery which the mind has to borrow in order to form a view of itself. This delicate balance between three points is difficult to maintain, and not everyone agrees that he succeeded in maintaining it.
It is particularly important that the concept of intention is among those which are treated in this way. For this concept must lie somewhere near the center of any theory of meaning. At this point it is possible to trace two connections between Wittgenstein’s earlier and later theories of language, an obvious connection, and a deeper one. The obvious connection is that it is a mistake to suppose that the language of sense-datum propositions, with which elementary propositions were often identified by other philosophers, might stand alone. The deeper connection is that at a certain point in the development of his account of elementary propositions in the Tractatus, Wittgenstein stopped, when he might have gone on. He stopped at the correlation of words with simple things. If he had gone on to ask how such correlations could be made, he would have said more about people, and their intentions, and the rules which are associated with their intentions. A word is not brought to life by mere juxtaposition with the thing which it designates. Any attempt to say what more is needed inevitably brings in the philosophy of mind, which scarcely makes an appearance in the lunar landscape of the Tractatus.
The later theory puts language back in its place in human life, and this may give the false impression that all the old ideas have been superseded. Certainly, the abstract elegance of the Tractatus has gone. The point of origin of factual discourse no longer stands in the center like a surveyor’s landmark. There is, instead, a babel of different uses of language, all demanding an equal hearing by philosophers. The philosophical investigation of this diverse material is itself diversified. There is no longer a single recommended philosophical procedure. The old type of analysis, which deals with a puzzling type of proposition by translating it into a more detailed and explicit form, is not entirely given up. But more often Wittgenstein uses another method, which is to compare propositions and concepts taken from different areas of discourse, in order to draw attention to features of their logical grammar.
These comparisons are based on the actual use of the propositions and concepts in everyday life, and not on any theory about the ultimate basis of their meanings. If theories are involved they will not be philosophical theories, but the half-formed theories and vague imagery on the fringe of the consciousness of anyone who uses the propositions or concepts. For example, is the privacy of my mind like some kind of physical privacy? Are my secret thoughts like entries in my locked diary? Am I the ever present witness of them, or am I related to them in some other way? These questions probe the analogy between mental and physical phenomena. They may seem to be superficial, whereas the old method was at least an attempt to explore the depths. But the point of the new method is that the depths are on the surface. The features of our concepts are evident in the ways in which we use words. If we fail to see them, we have probably been misled by some primitive analogy between two areas of discourse. So the remedy is to take up the analogy and explore it in detail, in order to determine the point up to which it is valid, and beyond which it produces nonsense.
So the later exploration of language involves the same kind of incident as the earlier exploration. It leads us again and again to the limit of language, and there we are brought up short. This may happen because we feel that it must be possible to push an analogy a little further, or that at least it must be possible to explain why another step would produce nonsense. Or it may happen in a rather simpler way, if, for example, we ask why it is nonsensical to ascribe certain pairs of colors to the same area. In all such cases the philosopher can do little more than record that the limit has been reached, and describe the logical grammar of the relevant words which determines the position of the limit. He can, of course, try to loosen the grip of philosophical perplexity by inventing a slightly different logical grammar for the words, thereby shifting the limit to a new place. But he cannot describe the things in a way that would show what it is about them that forced us to give the words their present logical grammar. For the things did not force this choice on us.
At this point it is necessary to separate Wittgenstein’s later theory about the nature of philosophy from his later philosophical theory, if any, about the nature of things. His later theory about the nature of philosophy is built around the same central ideas as his earlier theory: philosophy is not a factual discipline, but an a priori discipline with certain distinctive features. It is an a priori discipline, because it investigates the structure of language and its account of that structure is based on the meanings of words. Its distinctive features are its scope and its detachment. It stands back from other disciplines and modes of thought, and it investigates all the varieties of discourse in which they find expression. But in the later period this investigation has become less systematic, partly because factual discourse no longer stands at the center. There is still the same concern with the limit of language, but it is now a much more intricate line, because it is plotted in relation to many different uses of language. The world of meaning of the Tractatus has exploded, leaving a number of separate systems each in its own space.
There is also another reason why the later investigation is less systematic. Instead of concentrating on truth-functional analysis, it more often uses the method of comparison, and the comparison of different types of proposition is a complicated and untidy process, particularly when it is illustrated by copious examples. Any attempt to theorize across the whole field of different types of discourse is disclaimed. In fact, the goal of philosophy is no longer supposed to be the production of theories, but the achievement of understanding through the activity of philosophizing. Wittgenstein is particularly hostile to the idea that philosophers should produce theories. He even equates the achievement of philosophical understanding with the removal of misunderstanding, and compares this process with psycho-analysis.
So it might be expected that his later work would contain no theory about the nature of things. But in fact it contains a repudiation of his earlier theory about the nature of things, and this repudiation might count as another such theory in its own right. If so, it would be classified as nominalism in ontology, and as conventionalism in logical theory.
His retractation of his earlier theory of elementary propositions, and of the ontology which he deduced from it, has already been described. After the retractation he might appear to be maintaining that the logic of factual discourse reveals not only the general structure of reality, but also many specific features of its structure. But at the same time he changed the very meaning of the thesis that the structure of reality exhibits this pattern, or that pattern. Instead of treating the structure of reality as a rigid framework, fixed in advance, he treated it as a projection of human thought.
This shift toward nominalism and conventionalism can be seen at many points in his later work. It is conspicuous in the criticism of the Tractatus which he develops at the beginning of Philosophical Investigations, where he dismisses his earlier ontology as an illusion, because it was offered as an objective account of the general structure of reality, but is in fact only an account of one of the ways in which we view reality. Here he is rejecting far more than the particular theory that reality consists ultimately of simple things. He is denying the general possibility of arguing in the way in which he had argued in the Tractatus for that theory or for any similar theory. His view now is that there is no valid argument from the present structure of language to the pre-existing structure of reality. This is a general condemnation of the kind of argument on which metaphysical systems most commonly rest—not only the metaphysical system of the Tractatus, which was avowedly expressed in propositions that do not belong to factual discourse, but also traditional metaphysical systems, which were expressed in propositions that were supposed to belong to factual discourse.
It is worth observing that in the Tractatus he had already rejected almost all arguments of this kind, and allowed only one exception—arguments from the nature of logic. For example, when he wrote the Tractatus, he did not think it possible to draw any philosophical conclusions from the a priori propositions of science. He pointed out that, though certain scientific laws—for example, Newton’s laws—are a priori propositions, that is only because we choose to adopt them, and the choice is not forced on us by any objective necessity in the phenomena of mechanics. On the contrary, Newton’s system is simply a framework or grid, through which we view the phenomena, and his laws merely determine the structure of the grid. But in the Tractatus he did not treat logic in this way. In the Remarks on the Foundations of Mathematics he extends the treatment to logic.
The anthropocentric theories, nominalism and conventionalism, are most plausible when they are applied to those rules of logical grammar which can be accepted or rejected independently of one another. For instance, the adoption of the definition of the word “planet” has no far-reaching consequences. Similarly—to take a case in which we do not depend on definitions in everyday life—it would be possible to divide up the spectrum of colors in a different way without many consequential changes in our conceptual framework (the color vocabularies of ancient Greek and Latin make distinctions which are not quite the same as our distinctions). It is true that in such cases there is often something which makes it natural to develop language in one way rather than in another way. Nominalists have usually admitted that, even if language does not uniquely reflect reality, there is something about the things themselves which makes a particular linguistic development a natural one.
Wittgenstein does not deny this. His point is only that the choice is not forced on us by the nature of things. The ultimate explanation of a necessary truth is only that we find it natural to develop language in accordance with it. Of course, there is much to be said in a general way about the concepts which are involved in any explanation of this kind, and it is at this point that his philosophy of mind comes in as an auxiliary to support his conventionalism. For the main theme in his study of the concept of following a rule is that, though a person’s application of a rule shows what the rule which he was following must have been, that rule did not dictate its own application. Even the person’s intention at the time could not prefigure all its own executions unequivocally. There will always be options which he did not think of in advance.
So necessary truth is a function of what we do with language, and we create it as we go—or, rather, we find that we have deposited it. But though this conventionalism provides a plausible account of options which are independent, or at least relatively independent of one another, it is much less convincing when Wittgenstein applies it to the a priori propositions of logic and mathematics. When the meaning of a logical or mathematical symbol has been fixed, it is hard to see what options are left, because it seems to follow that certain propositions must be accepted as necessarily true, and that certain proofs must be accepted as valid, even if nobody thought of these consequences in advance. Yet Wittgenstein insists in Remarks on the Foundations of Mathematics that there will always be options. This extreme conventionalism is the most paradoxical and perhaps the most vulnerable part of his later philosophy. The logical necessity, which, according to the Tractatus, reveals the general structure of reality, does not seem to depend on us. Though we may abandon the ontology of the Tractatus, it is difficult to abandon the objective theory of logical necessity with which it was associated.
The influence of Wittgenstein’s later ideas on the work of other philosophers has been close and penetrating. The Tractatus avoided details, and kept its distance from the actual work of logical analysis which it recommended. The later philosophy has entirely lost this aloofness, and exemplifies what it recommends in rich variety. The theory of language of the Tractatus was abstract and monolithic, and philosophers might well have been hesitant about its interpretation. But the much greater divisiveness of the new theory seems to make it possible to apply it to one problem without any thought of commitment to a similar application of it elsewhere. The single line dividing what can be said in factual propositions from what cannot be said in factual propositions has been replaced by a complicated network of lines dividing language into a great variety of different kinds of discourse, and then subdividing these types in innumerable different ways. The suggestion is that philosophy can and ought to be done in a piecemeal way without any attempt to construct general theories.
Theory or not, the achievement is a set of profound ideas about language and the mind, forged into a powerful instrument, which can be applied to the main problems of philosophy. The impacts that it makes on the philosophical controversies of the present day are clear. It is directed against certain forms of realism and objectivism, and, more generally, against any kind of systematic philosophy. In the philosophy of mind, what it offers is a carefully, but perhaps rather precariously balanced rival to behaviorism and Cartesian dualism.
There is one aspect of Wittgenstein’s philosophy of mind which deserves especial emphasis. C. K. Ogden, writing to Russell about the Tractatus on November 5, 1921, says, “I should very much like to know why all this account of signs and symbols cannot best be understood in relation to a thoroughgoing casual theory.” But this particular supplement cannot be added to the theory of the Tractatus. For Wittgenstein makes it very clear in the Bemerkungen that his view was that, whereas cause and effect are connected contingently, in an external way, the connection between a picture or a proposition and the fact which would verify it is an inner logical connection which depends on the intention of the user. According to him, this logical connection cannot be explained by bringing in some third, contingently connected thing, such as the experience of recognition. For a person might use a certain proposition to signify a particular fact, and later, when he was confronted with another, slightly different fact, he might have the experience of recognition, and so he might come to think mistakenly that this is what he had originally meant. He would, as it were, settle for a meaning which his original proposition did not have. This kind of mistake tends to occur when a person is asked whether this is the taste that he meant, or whether this is the color that he meant. It also affects aesthetic judgments, and in such cases it is sometimes more difficult to guard against it. But Wittgenstein’s point is that, even if this kind of mistake never occurred, it could occur, because the connection between the proposition, with its original meaning, and the later experience of recognition is only a contingent connection, and not a logical connection—not, as he often puts it, an inner connection. Similarly, the expression of a desire is internally connected with its object, and this connection cannot be explained by bringing in the feeling of satisfaction. For this feeling might be produced by something which was not the object of the original desire.
Wittgenstein makes the same point in the Conversations on Freud where he is criticizing the interpretation of the symbolism of dreams by free association. The person who had the dream may trace a path through the complicated maze of his associations, and this path may lead him to an interpretation of his dream, but according to Wittgenstein that does not prove that this is what his dream must have meant, or even that it had any meaning at all. In the Lectures on Aesthetics he makes what is essentially the same point, but its application to aesthetic judgments is more complicated. If someone complains that a door is too low (on aesthetic grounds, not on practical grounds), he does not mean that he has a feeling of discomfort which will be removed if the door were made higher. It may be true that his feeling of discomfort could be cured in this way, but it is one thing to describe the feeling prognostically by its cure, and quite another thing to describe it diagnostically by saying that at the time it was directed at a certain object, the lowness of the door. The success of the cure may suggest that the feeling was directed at that object, but it does not prove it. The connection between the feeling and its object is an inner logical connection, but it is only a contingent inference that, if the feeling vanishes when the door is made higher, it must have been directed at the lowness of the door. It might still have had a different object. This example, which is Wittgenstein’s, is characteristic of him. The case is a simple one, and nobody could suppose it likely that in such a case the cure would indicate the wrong object. But the example illustrates a feature of aesthetic judgments which according to him is essential to them, and which according to him cannot be given a causal analysis—they are directed at objects, or, to be more specific, at aspects of objects.
If, instead of considering a simple example like this one, we took a case in which the person who was making the aesthetic judgment found it difficult to formulate it precisely, the situation would be more problematical, but essentially the same. On the one hand, if Wittgenstein is right, no experiment which showed what changes in a work of art would lead to a retractation of the original adverse judgment could establish beyond all possible doubt what the aspect of the work against which it was directed must have been. But on the other hand, if we asked the person himself, he would begin by giving a vague and hesitant answer. How then could he arrive at a firmer and more precise answer? Wittgenstein suggests that the way for him to do this would be to make certain comparisons which would bring out the relevant aspect of this work of art. The point of the comparisons would be to reveal connections which run from the inner nature of the work, just as the comparisons which a philosopher makes in his study of the sense of a proposition reveal logical connections which run from the inner nature of the proposition.
Unfortunately, Wittgenstein does not develop this idea very fully in the Lectures on Aesthetics, and he does not make it clear how the comparisons which he has in mind would work. At one point he takes as an example a question about a piece of music: “Why do these bars give us such a peculiar impression?” He suggests that the answer to this question can be reached “only by peculiar kinds of comparisons, e.g., by an arrangement of certain musical figures, comparing their effect on us. ‘If we put in this chord it does not have that effect on us, if we put in this chord it does.’ ” Of course, Wittgenstein is not suggesting that this method will provide an absolutely certain indication of the aspect of the music which was the object of the original reaction. For here too the situation is essentially the same as it was in the simpler case of the door. The reaction to the slightly altered version might suggest that the original reaction had been directed at one aspect when in fact it had been directed at another aspect. His point is only that, in a case in which the person who is making the judgment is at a loss, the method which relies on alteration and comparison is the best available one.
These scattered examples illustrate a strong and constant tendency in Wittgenstein’s thinking, the tendency to treat the explanation of certain mental phenomena as a type of explanation which cannot be reduced to ordinary causal statements. Hume had hoped to devise a sort of mechanics of the mind, which would rival Newton’s achievement. Rightly or wrongly, Wittgenstein stands opposed to any attempt by modern empiricists to carry out anything like this program in any field which involves the mental phenomenon of intentionality or “directedness.” When I know what I mean, or what I intend to do, or what the object of my feeling is, Wittgenstein would deny that it is possible to give a causal analysis of what I know, or how I know it. It is always rash to predict the history of ideas, but at the moment it does look as if it is this element in his philosophy which will be most influential in the immediate future.