Form and Content

by Moritz Schlick

I. The Nature of Expression.

1. Language.

Human civilisation rests entirely on the possibility of communication of thoughts. There would be no cooperation between human beings if man could not exchange ideas with his fellow men; there would be no arts, no science, if knowledge could not be handed down from one generation to the next.

Communication requires some sort of vehicle which carries the message through space and time. The most common vehicle consists of certain articulated sounds called Speech; but for many purposes spoken words would be useless on account of their transitory character: in such cases we use certain enduring marks of ink, pencil, chalk, engravings in stone or brass, or similar devices. Any system of lasting marks serving the purpose of communication we shall call Writing.

Speech and Writing are two different kinds of Language. They may not be entirely distinct from each other, the difference between them may be one of degree rather than of essence, but at present we are not concerned with this difference, nor indeed with any differences between various kinds of speech or writing; we are interested only in those characteristics which all the different methods of communication have in common and which are the essential characteristics of Language. There are innumerable methods of conveying thoughts, as a matter of fact almost anything in the world can be used as a vehicle of communication, and modern technical skill has developed some of the possibilities: electric currents, gramophone records, radio waves, and so on.

All these possible systems must have certain common properties (otherwise they could not serve a common purpose), and it is these properties which constitute the nature of language. We shall always use the word “language” in its largest sense, in which it denotes any system of things or procedures or events considered as a means of communication of thoughts. In everyday life we find nothing mysterious in the fact of the existence of Language; but although it is true that there is nothing mysterious about it, it seems strange that philosophers have not paid a little more attention to it and have not (as it is the philosopher’s business to do) wondered a little more at this apparently simple phenomenon which we all take for granted as part of our life like walking, eating or sleeping, but which hardly ever has been properly understood. The whole history of philosophy might have taken a very different course if the minds of the great thinkers had been mor deeply impressed by the remarkable fact that there is such a thing as language.

2. Expression of one fact by another.

Is it not astonishing that by hearing certain sounds issuing from the mouth of a person, or by looking at a few black marks on a piece of paper I can become aware of the fact that a volcano on a distant island has had an eruption, or that Mr So-and-so has been elected president of the republic of So-and-so? The marks on the piece of paper and the eruption of the volcano are two entirely distinct and different facts, there is apparently no similarity between them, and yet knowledge of the one conveys to me knowledge of the other. How is this possible? What peculiar relation is there between the two?

We say that one fact (the arrangement of little black marks) expresses the other (the eruption of the volcano), so the particular relation between them is called Expression. In order to understand language we must investigate the nature of Expression. How can certain facts “speak of” other facts? That is our problem.

It is not a difficult problem, I think; but even the simplest question deserves to be taken seriously, and it seems that most philosophers have thought it a little too easy, have given the answer rashly and thereby failed to gain an insight which, as I hope to show, might have prevented most of the misery of traditional philosophy.

3. Representation by symbols.

How is it possible that by perceiving one thing we can become aware of another thing which is evidently in no way present in the first one?

The first answer one feels tempted to give to this question is something like this: In order to understand Expression, one might say, it is sufficient to point to the simple fact of representation, i.e. a sort of correspondence between two things which we establish arbitrarily by agreeing that the one shall stand for the other, shall replace it in some given context, serve as a sign or symbol for the other, or, in short, signify it.

As for a playing child a piece of wood may mean a ship, or as for a general engaged in battle a couple of strokes on his map may represent a marching army — in a similar way our words and all our signs for words are symbols which, partly by arbitrary agreement and partly by accidental usage, stand for the things cf which they are symbols. Is it not natural to suppose that in the same way our sentences or propositions stand for the facts which they express?

A child, when learning to speak, has to be taught this prëestablished correspondence between the words and the world: this seems to be everything that is required to enable him to use the symbolism which is called his native language. He becomes able to express his thoughts and his expression can be understood because both he and those to whom he is speaking know by heart which particular thing is represented by each particular symbol. In this way the possibility of representing things by signs appears to account for the possibility of language, and nothing else seems to be needed to explain the nature of expression. But a little closer examination of the matter will easily convince us that this account is far from being satisfactory. It does not help us to understand that particular property without which a symbolism cannot be a language capable of really "expressing" anything.

4. Expression as contrasted with representation.

If we want to study a language we shall certainly begin by learning its vocabulary, i.e. the signification of its words. That is necessary, but not sufficient. We must study its grammar also. But do we not learn the grammar in exactly the same way as the vocabulary, by being taught what particular construction corresponds to a particular fact? In a certain sense that may be so, but before drawing any further conclusions we shall do well to remark that a psychological investigation of the way in which a language is learned may not help us at all to understand the nature of language in general. The philosopher is concerned only with the essence or possibility of expression, the psychologist has to take the possibility for granted and shows only the way in which a learning child avails himself of it.

In reality Expression is entirely different from mere Representation, it is much more and cannot be derived from it. Genuine speech is something entirely new as compared with the simple repetition of signs whose meanings have been learned by heart. A parrot utters significant sentences, but it does not really "speak" in the proper sense of the word.

It is true, of course, that language is composed of words and that words are symbols in the sense explained, but that does not explain the possibility of expression. If language were nothing but a system of signs with fixed significations it would never be capable of communicating new facts. If its function consisted solely in representing thoughts or facts by means of symbols it could represent only such thoughts or facts to which a sign had been attached beforehand; a new fact would be one to which no symbol had been assigned, it would therefore be impossible to communicate it.

There would have to be as many signs (names) as there are facts; if a new fact occurred it could not be mentioned, because there would be no name to call it by.

This state of affairs is made very clear by what is often called the "language" of certain animals such as bees and ants. Their means of communication are not a language in our sense of the word at all, but only a number of signs or signals, each of which stands for a particular class of facts, as "there is honey", "there is danger", and so forth. In the case of the parrot there is, in most instances even less than this, its words being usually mere mechanical repetitions of sounds. The signals of bees and ants represent or indicate certain occurrences, they do not express them. They are restricted to these particular kinds of events and cannot represent anything else.

The essential characteristic of language, on the other hand, is its capability of expressing facts, and this involves the capability of expressing new facts, or indeed any facts. A school boy opens his copy of Xenophon’s Anabasis, and by reading the first sentence of the book he learns the fact, which (let us assume) is entirely new to him, that king Darius had two sons. He knows what particular fact is expressed by that particular sentence, although he never came across that sentence before and certainly did not know the fact before. He, therefore, cannot have learned that the one corresponds to the other. It is a necessary conclusion that the proposition and the fact which it expresses must naturally or essentially correspond to one another, they must have something in common. It is this common feature that we have to discover.

Nearly every day in our lives we learn the most important facts by looking at rows of little black marks of a very limited variety of shapes. And this variety can be reduced to an astonishing simplicity: The Morse alphabet manages to express any thought which has ever entered or ever will enter into any human mind by means of the simplest of signs, a dot and a dash.

How is this done? What makes expression possible? A first answer seems to present itself without difficulty: evidently it is the arrangement, the peculiar order or combination of signs which constitutes the essence of language. It is because a limited number of symbols can be arranged in an unlimited number of different ways that any set of symbols can be used to express any facts. I might use a chair in my room, for instance as a means of saying anything I like. All I need to do is to select a number of different positions of the chair in the room and agree that each one shall correspond to a letter of the alphabet. By this agreement I shall have constructed a new language which will consist in changing the position of the chair; and by moving it about in the room I shall be able to express all the plays of Shakespeare with the same perfection as the best of the printed editions.

The same set of signs which was used to describe a certain state of affairs can, by means of a rearrangement, be used to describe an entirely different state of affairs in such a way that we know the meaning of the new combination without having it explained to us. This last property is the important point which distinguishes Expression from mere Representation; it is the only essential point. If the new arrangement of the old signs were nothing but a new symbol it would not symbolize anything before a new signification had been given to it by a special definition; but an expression expresses its own meaning, it cannot be given a meaning post festum. Let us illustrate the difference by an example. If I know that the sign Ⅿ stands for a certain sound, we have to do with a mere representation, and therefore the same sign turned upside down ꟽ will have no signification until someone has explained to us that, by arbitrary convention, it shall represent a certain other sound (double-u) ; so in this case we have only formed a new sign out of an old one.

Now let us take an example of a real Expression. If we understand the meaning of the proposition “the ring is lying on the book”, and if we rearrange the parts of it so as to form the sentence “the book is lying on the ring”, we understand the meaning of the second proposition immediately, without explanation. We do not have to wait till a meaning is assigned to it, the meaning is determined by the sentence itself. If we know which state of affairs is described by the first proposition, we necessarily know also which fact is described by the second one; there is no doubt or ambiguity. Let us repeat: the signification of a simple symbol (a name) has to be explained separately, the meaning of an expression (a proposition) explains itself, if only the vocabulary and the grammar of the language are known.

5. Structure and material.

Thus far we have found that the possibility of expression seems to depend on the possibility of arranging signs in different ways, in other words, that the essential feature of expression is Order. Speech is based on a temporal order of signs, writing on a spatial order. When we read a written sentence aloud its spatial order is translated into the temporal order of the spoken sentence. The possibility of such a translation proves that the particular spatial or temporal character of different languages is not relevant for the expression; the order which is essential for it must be of a more general or abstract kind, it must be something that belongs to speech just as well as to writing, or indeed to any other kind of language. It is not spatial order that is required, nor temporal order, nor any other particular order, but just Order in general. It is the kind of thing with which Logic is concerned, and we may, therefore, call it Logical Order, or simply Structure. One and the same fact may be expressed in a thousand different languages, and the thousand different propositions will all have the same structure, and the fact which they express will have the same structure, too, for it is just for this reason that all those propositions express just this particular fact. A language must, in principle, be able to express any facts by its propositions, anything that can possibly happen must be capable of being expressed by language. In order to describe the world we must be able to speak of all possible facts including those which do not exist at all, for language must be able to deny their existence.

One might think that in saying this we are making rather bold a priori statements about the world. For are we not implying that all possible things or events in the world must conform to certain conditions, must possess a certain kind of order which will enable us to grasp them by means of our expressions? And would this not mean a metaphysical presupposition which can never be justified?

It is of the highest importance to see that in maintaining that all facts must have a structure we are not making any presuppositions about the facts at all, we are saying only that facts are facts, which is, as will probably be admitted, saying nothing about them. Some philosophers have discussed the possibility of the world’s being “irrational”, which probably means that we could have no knowledge of it, form no true propositions about it.

These philosophers might object to my view by asking: How do you know that everything has a logical structure? is it not possible that the world or part of it may be entirely without order? I answer that this question is the result of a misunderstanding. The order of which I speak is of such a general nature that it would be meaningless to speak of anything as not possessing it. To say that a fact has a structure is to assert nothing of it; it is a mere tautological statement. This will become clearer as we proceed; but I think it will be admitted at the beginning that the possibility of describing or expressing a fact cannot be regarded as a genuine “property” of the fact which it may possess or not possess.

It seems impossible to speak of Form and of Structure without implying the existence of something that has the structure or form. It seems natural to ask: What is the Material which possesses a certain structure? What is the Content which corresponds to the Form?

Very soon we shall feel certain misgivings as to whether there is any sense in a question of this sort, but at present we will put off these doubts and endeavour to understand Structure by trying to distinguish it from that which has the structure. Such a distinction appears to be not only reasonable but even necessary, for our examples seem to show that the same material may take many different structures, or even any structure; and that the same structure may belong to any material, or at least to any number of different materials. A sheet of music with its words and notes is as different as can be from the record on a gramophone disk, and different from the motions of the singer’s larynx and the motions of the pianist’s fingers: nevertheless all these things may be perfect expressions of one and the same song, which means that the structure of the melody (and of everything else which constitutes the “song”) must in some way be contained in them. On the other hand it goes without saying that a gramophone disk, for instance, must be regarded as a material which is capable of expressing anything that can be expressed, i.e. capable of taking any possible structure. The difference between structure and material, between form and content is, roughly speaking, the difference between that which can be expressed and that which cannot be expressed. The fundamental importance for philosophy of that which is vaguely indicated by this distiction can hardly be exaggerated. We shall avoid all the typical mistakes of traditional philosophy if we bear in mind that the inexpressible cannot be expressed, not even by the philosopher.

6. Communicability of Structure.

We have seen that Expression serves as a means for Communication and that the latter is rendered possible by the former. Undoubtedly a thought cannot be communicated without having been expressed before; we may, therefore, regard communicability as a criterion of expressibility, i.e. of structure, and throw some light on the distinction of form and content by examining some particular instances of communication. There is a green leaf lying on my desk. My fingers touch it, my eyes see it, I am aware of its shape, its colour, its approximate weight, and so on. You, who are not present in my room, are not aware of any of these properties, but it is possible for me to communicate them to you by describing the leaf. The description expresses its properties; how is it effected, and are there any limits to it? From what has been said before we might be led to think that there must be two kinds of properties: those which can be described and communicated, and those which cannot; the former constituting the structure of the leaf, the latter its material or content. But that would be a mistake, for in a certain sense a complete description can be given of all the properties of the leaf, and it is not in this simple way that we arrive at the distinction between form and content.

The size of the leaf will be described by giving its various measurements, say, in inches; its shape will be communicated by mentioning its similarity to the shape of some well known object (“heart-shaped” etc.) or by giving a drawing of its contour, which, theoretically speaking, could be replaced by a mathematical equation representing the curve of the contour. Similarly, a description of the colour can be given by certain combinations of words such as “dark yellowish green”, “a little darker than the green dress of a certain Madonna by Raphael”, and so forth; and if this does not seem definite enough, I might state the exact physical circumstances under which light of that particular green colour is produced; or, finally, I might send you a piece of paper with a green spot on it and write underneath: “This colour is exactly like that of the leaf on my desk.” In this way I could go on and answer all the questions you could possibly ask about the leaf, without any exception.

All my answers, all my descriptions of the leaf are propositions by which I can communicate to you the whole of my knowledge about the leaf. This knowledge is knowledge of a certain set of facts, and if our former arguments are true my propositions express these facts by conveying to you their logical structure, and nothing but their logical structure.

Most people will find it difficult to see that this is so; they will be inclined to believe that my descriptions contain information about the “material” as well as about the structure of the facts which they express. Even the statements concerning the shape and the size of the leaf do not seem to be purely formal in the sense explained, for spatial structure, although "space" may justly be considered as a "form" of natural things or events, is no itself logical structure, for how could it be "spatial" if not by virtue of its content? If the shape of the leaf were described by the equation of its boundary curve it would probably be admitted that the mere equation as such contained nothing intrinsically spatial and could, therefore, impart nothing but the logical properties of the curve. But on the other hand the equation itself does not communicate anything anyway; it pictures the outline of the leaf only in connection with, and by means of, an explanation of the terms composing the formula, the terms must be interpreted as signifying spatial quantities (coordinates), and it is in this way that the content "space" seems to be brought into description: indirectly but no less essentially than appears to be done by actually repeating the contour in a pencil drawing. — Under these circumstances it seems difficult to understand and prove our assertion that only structure can be communicated and that content is inexpressible; it does not appear to be true even for the spatial form of our leaf — how could it be true for its colour!

Later on we shall have occasion to speak of spatial form — so we may put off the consideration of this point and confine ourselves to the analysis of expressions which deal with "quality", that is in our case: with the greenness of the leaf. How do those expressions communicate the colour, and in what sense is it true that they communicate nothing but its structure ? What can we mean by the "structure" of a quality?

7. Structure and internal relations.

Let us first examine the verbal expressions of our ordinary language, i.e. the sentences and their words by which I give a description of our particular green colour. We easily discover an essential feature which they all have in common: they assign to the "green" a certain place within a comprehensive system of shades, they speak of it as belonging to a certain order of colours. They assert, for instance, that it is a bright green, or a rich green, or a bluish green, that it is similar to this, less similar to that, equally dark as that, and so on; in other words, they try to describe the green by comparing it to other colours. Evidently it belongs to the intrinsic nature of our green that it occupies a definite position in a range of colours and in a scale of brightness, and this position is determined by relations of similarity and dissimilarity to the other elements (shades) of the whole system.

These relations which hold between the elements of the system of colours are, obviously, internal relations, for it is customary to call a relation internal if it relates two (or more) terms in such a way that the terms cannot possibly exist without the relation existing between them — in other words, if the relation is necessarily implied by the very nature of the terms. Thus, all relations between numbers are internal: it is in the nature of six and twelve that the one is half of the other, and it would be nonsense to suppose that instances might be found in which twelve would not be twice as much as six. Similarly, it is not an accidental property of green to range between yellow and blue, but it is essential for green to be related to blue and yellow in this particular way, and a colour which were not so related to them could not possibly be called "green", unless we decide to give to this word an entirely new meaning. In this way every quality (for instance, the qualities of sensation; sound, smell, heat etc. as well as colour) is interconnected with all others by internal relations which determine its place in the system of qualities. It is nothing but this circumstance which I mean to indicate by saying that the quality has a certain definite logical structure.

It will help to make matters clearer if I say a few words about "external" relations. The relation holding between the leaf and the desk is "external", because it is in no way essential for the leaf to be lying there, nor does it belong to the nature of the desk to have the leaf lying on it. The surface of the desk might just as well be empty, and the leaf might be somewhere else. If the leaf happens to have the same colour as a blotter lying next to it, the colour similarity between the two objects is an external relation, for the blotting paper might just as well have been dyed with a different colour. You will notice this important difference: the relation of similarity between the two coloured objects is external, but the relation of similarity between the particular colours as such is internal.

It is clear that in speaking of colours or other "qualities" we can refer to them only as external properties of something: we have to define a certain flavour as the sweetness of sugar, a certain colour as the green of a meadow, a certain sound as the sound produced by a tuning fork of a particular description, and so on.

In this way it becomes evident that propositions express facts in the world by speaking of objects and their external properties and relations. And it would be a serious misunderstanding of our statements if you believed that propositions could speak of logical structures or express them in the same sense in which we speak of objects and express facts. Strictly speaking none of our sentences about the green leaf expresses the internal structure of the green; nevertheless it is revealed by them in a certain way, or — to use Wittgenstein's term — it is shown forth by them. The structure of "green" shows itself in the various possibilities of using the word "green", it is revealed by its grammar. A language does not, of course, express its own grammar, but it shows itself in the use of the language.

All the statements that can be made in any language about the colour of our leaf speak only of its external properties and relations. They tell us where to find it (i.e. what position it occupies relatively to other things), how it is distinguished from the colour of other objects, under what circumstances it may be produced, and so forth — in other words, they express certain facts into which the green of the leaf enters as a part or element. And the way in which the word "green" occurs in these sentences reveals the internal structure of that part or element.

8. Inexpressibility of content.

If it is true that verbal sentences, the propositions of our spoken language, can communicate nothing but the logical structure of the green colour, ' then they seem to be unable to express the most important thing about it, namely that ineffable quality of greenness which appears to constitute its very nature, its true essence, in short, its Content. Obviously this content is accessible only to beings endowed with eyesight and power of colour perception, it could not possibly be conveyed to a person born blind. Shall we conclude that such a person could not understand any of our statements about the colour of the leaf, that they must be quite meaningless to him because he can never possess the content whose structure they reveal? This conclusion would not be justified. On the contrary, the proposition describing the greenness can communicate to the blind man just as much as they do to a seeing person, namely, that it is something possessing a certain structure or belonging to a certain system of internal relations. Since Content is essentially incommunicable by language, it cannot be conveyed to a seeing man any more or any better than to a blind one. You will say that nevertheless there is an enormous difference between the two: the seeing man will understand the propositions about colour in a way in which the blind man is unable to understand them, and you will add that the first way is the only right way and that the blind man can never grasp the "true meaning" of those propositions.

Nobody can deny the difference of the two cases, but let us carefully examine its real nature. The difference is not due to an impossibility of communicating to the one something which could not be communicated to the other, but it is due to the fact that a different interpretation takes place in the two cases. What you call the "understanding of the true meaning" is an act of interpretation which might be described as the filling in of an empty frame: the communicated structure is filled with content by the understanding individual. The material is furnished by the individual himself, derived from his own experience. The seeing person fills in material supplied by his visual experience, i.e. material he has acquired by the use of his eyes, while the blind person will fill in some other "content", i.e. some material which is acquired by some other sense organ, as the ear, or some of the sense organs located in the skin.

(These different interpretations are possible because, as we pointed out before, almost any material may take any structure. It is well known that psychologists and physiologists try to represent the system of colours in a spatial picture, e.g. a double cone, each point of which is supposed to correspond to a particular shade of colour, and the relations of similarity between the colours are represented by relations of spatial neighbourhood between the points. The whole scheme is nothing but the construction of a system of points whose spatial relations have the same structure as the internal relations between the colours. We know that a blind man is perfectly familiar with the structure of "space", which to him is a certain order of tactual or kinaesthetic sensations. With the help of this material he is able to build up any spatial structures, and, therefore, also the structure of the system of colours, because it can be represented by a spatial picture like that of the double cone or a similar device.)

The description of a coloured object does not communicate content to any one, whether blind or seeing, but leaves it to him to provide it from his own stock. You will probably say that only the seeing person will really provide "colour", whereas a blind man will provide some other content, and you will assert that the latter, although he will think that he understands the description perfectly well, is in reality very far from it, because the "true" interpretation must be given in terms of "colours", and nothing else can take their place.

I answer that you are quite right if by "colour" you mean something which has to do with vision, i.e. involves the use of certain particular sense organs called "eyes". You are at liberty to say, by way of definition, that an interpretation shall be acknowledged as true only in the case of a person capable of using his eyes in a normal way. This would be perfectly legitimate If I should ask you whether or not Mr. X could properly understand a description of, say, a coloured picture, you could submit him to certain experiments (which would consist in observing his reactions to colours presented to his eyes), and the results would enable you to answer my question with either yes or no (in the latter case you would declare Mr. X to be blind or colour-blind).

Nothing can be said against this procedure, which, as we know, is actually used in certain tests, but I cannot agree with you if you think that it is based on anything more than an arbitrary, though very sensible, definition. I suspect that you are inclined to argue somewhat on the following line: "If I observe a man using his eyes in a similar way in which I use my own I am justified in believing that he experiences in his consciousness exactly the same kind of sensations as I do when the same objects are presented to my eyes, so that he will be able to fill a given structure with the same content which I have in mind when I try to communicate to him what I have seen. I must necessarily regard his interpretation as the only right one, because only he can use the right content for it".

This argument speaks of visual sensations not only as of something which has certain relations to sense organs (or, which would amount to the same, to certain brain centers), but as of something that is made up of content, which is evidently regarded as the intrinsic nature of certain "states of consciousness". Later on we shall see that this whole argument is really meaningless; but before we proceed to show this we will for some time remain on a level on which there seems to be some sense in phrases of this sort. This will involve the use of incorrect language on our part, but for the sake of clarity we shall not be afraid of it and shall add the necessary corrections in due time.

The above argument, or a similar one, occurs in many metaphysical discussions, and we shall have to explain later that it must be regarded as the typical argument in metaphysics. The metaphysicians who use it ascribe to it the character of an inference by analogy and are therefore willing to admit that the conclusion is not absolutely certain. They say that it is just "highly probable" that the visual perceptions of two individuals have practically the same content when they look at the same object and are both in possession of sound eyes and optical nerves and brain centres. We declare ourselves satisfied with this admission and call our philosopher's attention to the fact that, according to him, there is a possibility, however faint, that the content of one person's visual perception may be altogether different from that of another person's. He would have to admit that possibly the content which arises in the first man's mind when he is looking at something might be similar to, or even the same as, the content of the perceptions which arise in the second man's mind when he is listening to something.

In other words: what the first person calls "colour" would be called "sound" by the second person, if he could experience the content of the first one. If the second man could suddenly enter into the first one's mind he might exclaim: "Oh, now I am hearing with my eyes and seeing with my ears!" (The reader will bear in mind that I am speaking as if there were real meaning in the metaphysicians' first argument.)

Now, since such an exchange of personalities cannot possibly take place (and this impossibility is not just an empirical or a practical one, but, as we shall understand later, a logical impossibility, i.e. there is no sense in the assumption) the supposed difference of content could never be discovered as long as we assume the order and structure of all the perceptions to remain the same. For this assumption means that all reactions by which the perceptive faculties could be tested (including utterances of speech) would be exactly the same for the two individuals. Both of them would say that they were seeing with their eyes and hearing with their ears, they would call the objects and their qualities by the same names, their judgments about all similarities and differences of sounds, colours, sizes etc. would agree in every respect, in short, they would understand each other perfectly. And yet in spite of all this the content of all their experiences and thoughts would be absolutely and incomparably different (I am always using the language of the metaphysician), they would be living in two entirely different worlds of content.

Thus we see that there may be complete understanding between individuals even if there is no similarity between the contents of their minds, and we conclude that understanding and meaning are quite independent of Content and have nothing whatever to do with it.

This result remains valid (although it should be formulated in more correct language), and we see that wherever words like "colour", "sound", "feeling" etc. occur in our sentences they can never stand for Content. They have meaning only is so far as they stand for certain structures. The structures corresponding to the word "colour" occur, as we know empirically, in connection with the use of the organs called "eyes". People who do not possess these organs or lack the capacity of using them in the ordinary way are called "blind" or "colour blind" etc. And if we assert that e.g. colour blind persons are not able properly to understand a proposition about colours we assert nothing but that certain structures do not occur in their experience — a fact which shows itself in the set of their responses — , and we do not assert anything about their inability of filling structures with the "right content".

In so far as a blind man is actually capable of building up structures identical with those of the colour system, he does understand communications concerning coloured things, and in so far he is in possession of the logical form of colours. He is not able to use his knowledge in the same way as a normal person — he cannot, for instance, be a painter — but that is not on account of lack of some particular content, but because the different structures which play important parts in his life do not have the same connections and relationships among each other as exist in the life of a seeing person. We must not fall into the error to say that this is so because his optical apparatus (eyes and optical centers) do not function properly; for in reality the statement that there is something wrong with his perceptive faculties is identical with the statement that the structures which determine the general character of his conscious life are connected or disconnected in a way which differs in a well defined manner from the lives of normal human beings. The latter statement might be formulated more shortly that the structure of the world of experience shows a well defined typical difference in the two cases. All these assertions, inspite of their different wording, have exactly the same meaning.

In this way we are always confronted with the same result: wherever it may at first seem necessary or possible to speak of content a closer examination shows that it is unnecessary and impossible. Everything we can possibly say and — which is more — everything we can possibly want to say is always said without mentioning content. Content cannot be mentioned, it is inexpressible.

If you should object that in this very sentence and in all the explanations presented on these pages I myself have continually been trying to say something about content I may remind you that I am deliberately using incorrect language at present, hoping to convince you in the end that I am not guilty of such a very crude contradiction.

It would be nonsense to regard the inexpressibility of content as a wonderful discovery or as a new deep insight. On the contrary, that nobody seriously denies it. It may not be stated expressis verbis, but it reveals itself in our every day actions. Even the man in the street would not try to explain to a blind person the essence of colour. The man in the street knows that the content which e.g. he believes to be indicated by the word "fear" cannot be communicated but must be learned by the experience of being afraid (one of Grimm's fairy tales treats of this subject), and so forth. It is important to notice that he knows such communication or expression to be impossible not because he has tried to do it in many ways and has failed each time, but because he cannot even try it, he can see no possible way of going about it; he is like a man who is asked to translate a sentence into a language with which he is not acquainted: the impossibility of this is not an empirical, but a logical one.

9. Why is content inexpressible?

I can imagine that beginners in philosophy (but, when we come to think of it, can anyone really be more than a beginner in philosophy?) may still entertain doubts in regard to our assertions, and it would be natural for them to ask: "You are making very categorical statements, but must they really be true ? How do you know that content might not be expressed after all, if one went about it in the right way? Why could not some means of doing it be discovered in the future? Even if it is impossible for human beings, could it not be achieved by beings of higher intellectual powers? Perhaps it is all a mistake, and a better philosopher might give us a different conviction? So where is your final proof?"

I answer that no proof is needed, because I have not asserted anything which can be believed or doubted. Our "assertion" of the inexpressibility of Content is a mere truism, it may be regarded as a tautology; and a tautology, properly speaking, does not assert anything. It does not impart any knowledge. As a matter of fact, I am not claiming to convey any knowledge to you when I say that content cannot be expressed, I am only trying to agree with you on the way in which we use our terms, especially the questionable word "content" itself. It is, if you like to put it that way, a matter of definition. Inexpressibility is not an accidental property of content which to our surprise we discover it to possess after we have been acquainted with it for some time, but we cannot get acquainted with it at all without knowing that this property belongs to its very nature.

All the insight we have gained thus far we have gained by simply considering carefully what we mean when we use the term "expression". Expression implies two facts: one that expresses and one that is being expressed. The former is a sort of picture of the latter, it repeats its structure in a different material. A picture must differ from the original in some way otherwise it would not be a picture at all, but simply the original itself, or perhaps an exact duplicate of it. Now there are cases in which the picture serves as a substitute for the original, we should prefer to have the original, but because for some reason or other it is unattainable, we have to be satisfied with a picture (as a lover who kisses the picture of his sweetheart during her absence); but there are also other cases where we do not care for the original at all — it may even be in our possession — , but where we want the picture for the picture's sake, our whole interest is turned to the expression and is turned away from that which is expressed.

It is these latter cases with which we are concerned in our present analysis: we are not interested in facts but in the way in which facts can be expressed. This means that we have nothing to do with content. To express is to leave content out of consideration. It is by its content that the original is distinguished from all its possible pictures, reproductions or representations. If we were to use old fashioned philosophical terms we might compare it to the "haecceitas" of the scholastics or speak of it as the "principium individuationis". The picture could not have the same content as the original (the reader must again excuse my incorrect language) without being the original itself, it would no longer be an expression of it. And it is the nature of expression into which we are inquiring here.

10. Transportation and expression.

There is still another way of formulating the insight we have gained. In ordinary life we may distinguish between communication by transportation and communication by expression. The first consists in simply taking the thing or fact in question and putting it in the presence of the person to whom it is to be communicated; the second consists in describing it to him or her, or sending a photograph or drawing of it, or telling about it in some way or other.

This distinction can well be made in everyday life, but it may prove misleading when we try to apply it to the subtle problem with which we are concerned. If I take the green leaf from my desk and send it to a friend he will see and touch the same leaf that I have seen and touched before, the leaf "itself" will have been transported to him. And yet it will not be quite the same leaf, as it certainly will have undergone certain changes in the meantime, and even if it had not changed there would be no identity in the logical sense, for some sentences about the leaf which were true propositions when the leaf was lying on my desk will not be so any more after it is in the hands of my friend (e.g. those referring to its place). In the strictest sense there is no transportation of an entity "remaining identically itself". Even the motion of a physical body through space is nothing but the transmission of a comparatively constant structure, or, still more correctly, it is a continuous series of events having approximately the same structures.

If (in the language of traditional metaphysics) I could take the greenness of a colrur which I am experiencing out of my own consciousness and put it into somebody else's, then he would have the green itself, and not an expression of it. We do not use the word "Expression" unless there is some other material which, as it were, carries the meaning of the expression, and this "other" excludes the original content. Expression involves some means of communication which does not (if it were at all possible) seize the fact or object itself, does not do anything to it, but leaves it entirely as it is and where it is, conveying to us only those of its features which it may share with other materials. I might be tempted to say: well, those features are the structure, and the rest (whether it be called "material" or otherwise) is Content, but such a figure of speech would be entirely misleading, as it seems to give an indirect description of content-which we know to be impossible. And I might be tempted to say that content cannot be expressed by language because the nature of language is expression, not transportation; but again this would give the wrong impression as if there were any sense in speaking of the transportation of content, and we know that there is not.

We can say that we express a fact by another fact (a sentence, a gesture, etc.), but to speak of expressing content is a contradiction in itself, like making music without sounds or painting without dyes. These things cannot be done not because they are too difficult and beyond human faculties, but because there are no such things: the sentences in which we seem to be speaking of them are meaningless in the same sense in which it is meaningless to speak of a "round square". (I need not remind the reader that the sentence "there is no round square" cannot be interpreted as asserting the non-existence of a certain thing called a round square, but must be understood as saying that the combination of words "round square" makes no sense.)

11. Is there no escape from language?

Thus far we have been discussing the nature of expression chiefly in regard to our ordinary language of words, at least we have taken from it most of our illustrations. Nevertheless our arguments have been of such a general nature that they hold for any kind of language, they include every possible sort of expression. I think this will be admitted readily, and there would be no reason for dwelling on it if we did not have to take precautions against certain misunderstandings which might arise from a failure to grasp the true function of expression.

One might be tempted to say: What, after all, is the final aim of language and expression ? Is it not to make the listener or reader acquainted with the fact which is to be communicated to him? And is not language only an indirect and roundabout way of doing this? Could it not be achieved in a more direct way by avoiding language and bringing the listener or beholder into immediate contact with the fact?

Thus one might think (and we shall see in our second lecture that most philosophers have thought it) that expression was just a means to an end which could also be attained in some other way. If, for instance, instead of describing our green leaf and talking so much about it, we produce the leaf itself: does not this act fulfill the same purpose as any expression, only much more perfectly? Does it not provide content itself (e.g. the green of the leaf) which, as we had to admit, cannot be grasped by any expression? In this way the only effect of all our arguments against the incommunicability of content might be the desire to avoid language and replace it by real acts of presentation which would have the advantage of making us acquainted with content as well as form.

You will notice that the act of making a person directly perceive a certain object or witness a certain fact is nothing but what we called "transportation" a little while ago. And we have treated it as not essentially different from the case of a verbal description. It is important to see that we were right in doing this. There can be no doubt that for many purposes this procedure of presenting the object itself is by far the best method of communication, but we must insist that from our point of view it is also a sort of language, or part of a language. It either has all the properties of expression (its advantages and defects), or it is no communication at all. If one morning the mail should bring you a letter containing nothing but a green leaf, you would not be able to make anything of it; you could record it as a simple fact, but it would not "mean" anything to you. On the other hand, the curious occurrence would have the character of a communication, it would be an actual message, if the leaf were accompanied by some explanation or if you had received some instruction concerning it. It might be a leaf someone promised to send to you from his garden, or there might be a note saying "I found this on my desk" or "please observe the colour of this leaf" or "this is the colour I spoke of yesterday" etc. In all these cases the object itself enters into language as part of it, it has exactly the same function that a picture or a description or any other sign would have: it is itself a symbol in the symbolism called "language". The only peculiarity of this case is that the symbol has the greatest possible similarity to the signified object.

Nothing can prevent us from making the signs out of which we construct our language as similar to the signified objects as we wish; this is even the most natural procedure, and when the human mind first invented writing it consisted of little pictures (hieroglyphics, Chinese characters). Gradually it was seen that similarity between object and symbol is quite superfluous and that convenience and practical utility are the only things which matter. If in order to denote a certain shade of green we use a little patch of colour together with our written words we use the same method as those ancient writings: we avail ourselves of the similarity of colour in the same way as they did of the similarity of shape.

It would be a mistake to think that by using samples as symbols in the way just described we had succeeded in communicating content and had avoided the indirect method of expression. This can be seen by referring to the arguments of section 8, and if you agree with them you will admit that we have no possibility of saying that the reader of the "sample writing" will have "the same content" in his mind as the writer of it. Although the "sample symbolism" is very useful for certain purposes, it cannot be said to be in every respect the most perfect language, it does not fulfill its function any more correctly than a verbal language can. There can be no doubt, for instance, that a scientific description of a colour in terms of wave lengths and other physical data (perhaps including the physiological state of the percipient) must be regarded as ever so much safer and more accurate than the presentation of a sample or the coloured object itself, for the latter may have undergone all kinds of changes when we were not looking (or, for that matter, even while we were looking), and the physiological condition of the percipient may not be at all what we expected it to be. The colour sample language can be understood only by people with normal eyesight, it will produce a certain colour perception in their minds, but it will not "communicate" any "colour content" to them.

Thus we may say in conclusion that we need Language for communication, there is no escape from it and consequently no possibility of "communicating content". We can introduce samples into our language, i. e. speak with colours about colours, with sounds about sounds etc. but Content refuses to enter into it. In so far as a sample can communicate anything it does not do so by its content, but because it is used as a symbol (i. e. as something whose signification must be indicated) and it functions in the same way as all symbols do. Signs remain signs, no matter how we fix their meaning. We can relate the symbol to the object we want it to symbolise by pointing at both of them simultaneously, or by agreeing that the sign shall exhibit a. well defined similarity to its object (as in the case of "samples"), or in some other way: in all cases it is entirely a matter of arbitrary agreement.

No fact can be an "expression" except by agreement. Nothing expresses anything by itself. No series of signs, whether consisting of human sounds, or marks on paper, or any other natural or artificial elements, is a "proposition" simply by its own nature, if by this word we denote something which "says" anything or has a "meaning". A series of marks can become a proposition only by virtue of some agreement which assigns a signification to the single signs and a grammar to the way in which they are combined.

12. On "Sameness of quality".

Several times during the course of the foregoing considerations I had to warn the reader that I was not expressing myself correctly, and had to ask his pardon for it. We shall now examine one of the most important cases in which our language was imperfect, and then see in general how we can guard ourselves against falling into error on account of such imperfections. We have continually been speaking of "Content" (although often with some hesitation) and we have discussed the possibility of two separate minds experiencing "the same" content. It is usually admitted — on the strength of arguments like those presented in section 8 — that it is forever impossible to find out whether or not two people have the same "data of consciousness" in their minds; at the same time it is generally believed that two data in different minds must either be alike or not alike, and that the question concerning their sameness has a definite meaning, although, unfortunately, it cannot be answered with absolute certainty. Usually it is added that only a high degree of probability is attainable for the answer, because sameness or diversity of mental states of different individuals 'cannot be observed directly but must be inferred by analogy'.

What are we to think of these current opinions? They seem to me to by very ambiguously expressed, and it is necessary to become perfectly clear about the meaning which the phrase "sameness of quality" can possibly have in these assertions. I think it is perfectly legimitate to say that two individuals experience "the same" or "different" feelings or qualities of sensation as long as the truth or falsity of such statements can actually be tested. Such tests are carried out by the physiologist who can examine and compare the perceptive powers of different individuals. He discovers, for instance, that most people exhibit a difference in their responses (e.g. their verbal utterances) when confronted with two different shades of colour, but that a certain percentage of individuals cannot be made to react differently in the two cases. These latter persons are called "colour blind" by the physiologist; he says that the quality of their sense perception is not the same as that of people with normal eyesight. He is perfectly right in maintaining this, and his statement is by no means based on an inference by analogy, it is an empirical judgment of the same kind of validity as any proposition in chemistry or physics. It asserts the existence of certain structures in the personality of the individuals in question: there is a difference in the multiplicity of reactions between a colour blind person and a normal one, there is a greater variety in the perceptions of a normal individual, and this is, of course, a purely formal property. This is all that can be said, and nothing else is said by the proposition 'the qualities of the sensations in the two cases differ in such and such a way'. The system of colours is more complicated in a normal person than in a colour blind one, the internal relations are less simple, and this is a difference of structure.

Thus the assertions of the physiologist are ordinary statements of fact and contain everything that can be said about the qualities. If the statements cannot be made with absolute certainty but only with a lesser or greater degree of probability this is not because the qualities "cannot be observed directly but must be inferred by analogy", but it is because those statements share the fate of all empirical assertions: the observations on which they are based are never complete and always subject to error, they may be corrected by subsequent and perhaps more careful investigations of reactions of the same individuals.

These reactions reveal the structure of the sense perceptions, and everything that can possibly be said about their qualities can be said in terms of those responses. As soon as you try to say anything more, as soon as you think that there is anything more to be said, namely about the "content" of the qualities, your assertions will not become less probable or more hypothetical, but they will cease to be assertions at all, the word "quality" will simply have become meaningless, you will not be making an intelligible use of it. The reason for this lies in the fact that no series of words will actually form a proposition, will have actual meaning, unless we can indicate a way of testing its truth, at least in principle. This will be explained later (section 14); at present we confine ourselves to saying that statements about the Sameness or Diversity of Qualities must by no means be interpreted as dealing with Content. Like all other propositions, they express the facts they communicate by showing forth their structures; Content is not touched upon in any way.

This is not because content were too difficult to get at, or because the right method of investigating it had not yet been found, but simply because there is no sense in asking any questions about it. There is no proposition about content, there cannot be any. In other words: it would be best not to use the word 'content' at all, there is no need for it, and my only excuse for using the word (even in the title of these lectures) is that this forbidden road seemed to me to be the easiest way of taking the reader to a point which will allow him to get a first view of the land before him. He will now be able to turn back and find the right road which will actually take him to the promised land. I shall continue to use the term 'content' now and then for the sake of convenience, but the reader will understand that a sentence in which this word occurs must not be regarded as a proposition about something called 'content', but as a sort of abbreviation of a more complicated sentence in which the word does not occur.

13. Communication with one's self.

I do not flatter myself to have removed all doubts concerning the justice of our dealings with 'Content'. I can imagine that you may admit the validity of my arguments and still hold the opinion that there are cases in which "sameness of quality" must mean "sameness of content". You will ask: How about the comparison of qualities perceived by one and the same person? Our former considerations do not seem to apply here. If I declare that the leaf I see to-day has the same colour as one I saw yesterday, or perhaps even the same colour as one lying next to it at this moment: am I then not dealing with quality in a deeper, more intimate sense than that of "mere" structure?

I answer that undoubtedly there is a great difference in the meaning of the word "same" when it is used in regard to "data in two minds" and when it is used in regard to "data in one mind", but that this difference cannot be described by saying that the word denotes equality of structure in the first case and equality of content in the second case. The propositions are verified in a different way in the two cases, they express different kinds of facts, but the second one is just as far from expressing "content" as the first one — indeed, infinitely far.

This grows clear as soon as we realise that the main point of our reasoning (which consisted in regarding incommunicability as the criterion of inexpressibility) remains applicable even when we restrict ourselves to the consideration of a single mind.

It would be wrong to suppose that one could not speak of communication at all unless there were at least two individuals involved, and between them some kind of causal connection by means of which a message could be transmitted. If this were so our whole argument would presuppose certain empirical facts, as the existence of different persons and particular relations between them; but actually we make no assumptions of any kind, our reasoning does not rest on any presuppositions about the real world. All genuine philosophy (as I shall have to point out later on) moves entirely in the realm of possibilities — possibilities which will, of course, always be suggested by realities, but may be considered quite apart from their realisation.

In our case what we said about the possibility of expression remains perfectly valid in a universe which contains no living being beside myself (we will not discuss the question whether such a universe would be the ideal of a "solipsistic" philosopher); I can express facts to myself and communicate with myself — in fact, I do so every time when I take down something in my note book or commit something to my memory. In reading my note or recalling the remembered fact my present self receives a communication from my former self. My note book and my "memory" are vehicles carrying through time the description of a fact; the description consists of a series of marks whose meaning must be understood, and there is a possibility of misunderstanding and of faulty transmission. The note in my book may have been changed, my memory may deceive me.

You observe that for the essence of communication it makes no difference whether the note book is what the metaphysician would call "a mere dream", or possesses what he might call "objective reality". The marks in it, whether "real" or "imagined" (whatever that may mean) do express something, either correctly or incorrectly.

As soon as we try to ascertain whether a proposition which has thus been transmitted from an earlier self to a later self is true or false we find that the methods We use for this purpose consist in comparing structures and that there can be no mention of content. When I keep in mind the colour of a green object, and to-morrow I am shown another object and am asked whether it has the "same" colour as the first one, my memory will give a more or less definite answer to the question. The question has a good meaning, of course, but can it be said to refer to "sameness of content"? Most certainly not! This follows from the way in which the answer given by memory is tested. For in a certain sense we must admit that our memory may "deceive" us. When do we say that it has done so? If there are methods of testing its judgment, and if all these methods fail to verify it. Such methods are: 1) looking again at the object in question and taking into account, on empirical grounds, the probability of its colour having changed in the meantime; 2) comparing my present judgment with a description. I wrote down during the first observation; 3) comparing it with the descriptions given by other people.

The criterion of the truth of the judgment is the agreement of all these different propositions; and if we say that the colour is truly the same, that my memory has not deceived me, we mean nothing but that there is this formal agreement between the descriptions based on memory and on observation. This is entirely a matter of structures; we cannot speak of a repetition or comparison of "content".

If we knew of a case in which there were nothing else with which the judgment of our memory could be compared, we should, in this case, have to declare it impossible to distinguish between a trustworthy and a deceptive memory; we therefore could not even raise the question whether it was deceptive or not: there would be no sense in speaking of an "error" of our memory. It follows that a philosopher would be uttering a meaningless question if he were to ask: "Is it not possible that the colour I am seeing now seems to me to be green, while actually it is red?" The sentence "I am seeing green" means nothing but "there is a colour which I remember has always been called green". This recollection, this datum of my memory, is the one and only criterion of the truth of my statement. I recall it so, and that is final; in our supposed case I cannot go on asking: do I remember correctly ? for I could not possibly explain what I meant by such a question.

Thus we see that the question "is the green I see to-day the same colour as the green I saw yesterday?" refers only to the structure of our expressions and not to some content "green" which is supposed to be beyond. Sameness, equality cannot be predicated of content any more than anything else can be predicated of it; and the case of "two data of consciousness in the same mind at different times" forms no exception.

14. Meaning and verification.

In the preceding arguments we have often made use of the principle that the meaning of a statement can be given only by indicating the way in which the truth of the statement is tested. What is the justification of this principle? There has been a great deal of dispute about this question in modern philosophy, and certainly it deserves our full attention, for if I am not mistaken it is the fundamental principle of philosophizing, and neglect of it is the cause of all serious troubles in metaphysics.

The object of every proposition is to express a fact. It seems, then, that in order to state the meaning of the proposition we have to indicate the fact which it expresses. But how strange ! Is not the fact in question already indicated by the proposition itself? In fact, we have convinced ourselves long ago (see above p. 6 f) that a proposition expresses its own meaning, it does not stand in need of an explanation. An explanation which said more than the proposition itself would not be a correct explanation of it, and if it said the same thing as the proposition it would be superfluous. As a matter of fact, when we hear somebody make a statement and ask him "What do you mean by it?" we usually get and expect as an answer a mere repetition of the first statement, only in different words, and very often we are actually satisfied by this procedure which is nothing but a translation from one language into another one. Why are we satisfied? Evidently because we did not understand the first expression, but do understand the second one.

This last remark gives us the clue to solve the paradox. We can ask for a meaning only as long as we have not understood a statement. And as long as we have not understood a sentence it is actually nothing but a series of words; it would be misleading to call it a proposition at all. A series of words (or other signs) should be regarded as a proposition only when it is understood, when its meaning is comprehended. If we agree to use our terms in this way there will be no sense in asking for the meaning of a proposition, but we may very well inquire (and that was our actual problem) after the meaning of a sentence or any complex of signs which we suppose to express something.

Now there is not the slightest mystery about the process by which a sentence is given meaning or turned into a proposition: it consists in defining the use of the symbols which occur in the sentence. And this is always done by indicating the exact circumstances in which the words, according to the rules of the particular language, should be used. These rules must be taught by actually applying them in definite situations, that is to say, the circumstances to which they fit must actually be shown. It is of course possible to give a verbal description of any situation, but it is impossible to understand the description unless some kind of connection between the words and the rest of the world has been established beforehand. And this can be done only by certain acts, as for instance gestures, by which our words and expressions are correlated to certain experiences.

Thus, if I utter a sentence, and you ask me what I mean by it (perhaps by shrugging your shoulders or by looking at me with a vacant stare) I shall have to answer you by translating the sentence into a language you understand, or, if you do not understand any language yet, I shall have to teach you one; and this involves certain acts on our part, I have to make you undergo certain experiences. All your future understanding will be by virtue of these experiences. In this way all meaning is essentially referred to experience.

It must be clear by this time that there is only one way of giving meaning to a sentence, of making it a proposition: we must indicate the rules how it shall be used, in other words : we must describe the facts which will make the proposition "true", and we must be able to distinguish them from the facts which will make it "false". Still in other words: The Meaning of a Proposition is the Method of its Verification. The question "What does this sentence mean?" is identical with (has the same answer as) the question: "how is this proposition verified?"

It is one of the most serious errors in philosophy to think of a proposition as possessing meaning independently of the possible ways of its verification. People have fallen into hopeless confusion because they believed they knew the meaning of a phrase, and yet had to declare themselves unable in principle to define any circumstances in which it would be true. As long as it is logically impossible for me to indicate a method of ascertaining the truth or falsity of a proposition, I must confess I do not know what is actually asserted by the proposition.

After you have once seen this clearly you will no longer understand even the possibility of a different opinion : you will recognize that no opinion can even be formulated without admitting the truth of the preceding remarks. The view contained in these remarks has, it is true, found many opponents, but the very name by which it is usually called shows that it has not been properly understood. It is known as the "experimental theory of meaning". But it is not a theory; there can be no "theory" of meaning. A theory is a set of hypotheses which may be either true or false and have to be tested by experience. It is not necessary to make hypotheses about meaning, and they would come too late, because we must presuppose meaning in order to formulate any hypothesis. We have not made any assumptions, we have done nothing but formulate the rules which everybody always follows whenever he tries to explain his own meaning and whenever he wants to understand other people's meaning, and which he never actually violates — except when he begins to philosophize.

In establishing the identity of meaning and manner of verification we are not making any wonderful discovery, but are pointing to a mere truism. We are simply maintaining that a proposition has meaning for us only if it makes some kind of difference to us whether it is true or false, and that its meaning lies entirely in this difference. Nobody has ever explained the meaning of sentence in any other way than by explaining what would be different in the world if the proposition were false instead of true (or vice versa).

This, I am sure, cannot be denied. But the great objection usually raised against the view I have been defending consists in maintaining that the "difference in the world" expressed by the proposition may not be observable or in any way discoverable. In other words: if a sentence is to have meaning for us we must, of course, know which fact it expresses, but it may be absolutely impossible for us to find out whether the fact actually exists. In this case the proposition could never be verified, but it would not be meaningless. Therefore, our adversaries conclude, meaning is distinct from verifiability, and not dependent upon it.

This argument is faulty on account of an ambiguity of the word "verifiability". In the first place, one might call a proposition verifiable, if the actual facts are such as to permit our finding out its truth or falsity whenever we feel like it. In this sense it would be impossible for me to verify the statement: "there is gold to be found in the earth 300 feet below my house", for there are many empirical circumstances which absolutely prevent me from discovering its truth; and yet the assertion was certainly not nonsensical. Or take the statement: "On the back side of the moon there are mountains 10.000 feet high". It is not improbable that no human being will ever be able to verify or falsify it, but what philosopher would be bold enough to declare the sentence to be devoid of meaning! — I think it must be clear that we have nothing to do with this use of the term "verifiability", and that we must have had something else in mind when we said that the Meaning of a Proposition was its Method of Verification.

As a matter of fact, we call a proposition verifiable if we are able to describe a way of verifying it, no matter whether the verification can actually be carried out or not. It suffices if we are able to say what must be done, even if nobody will ever be in a position to do it.

II. The Nature of Knowledge.

What is the nature of knowledge? In asking this question we use the word "knowledge" in that particular sense in which it signifies the object and aim of all scientific endeavours. (What is it, really, that we are seeking in disinterested scientific research?)

Scientific thinking is not essentially different from thinking in every day life, it is only a higher stage of it. Scientific knowledge is a continuation of practical knowledge, such as human beings need in order to exist and to live well. They cannot live without knowledge and thinking, because they lack the sure guidance of instincts by which animals are led comparatively safely through life's troubles. Nature has instead endowed man with reason, and reason is a much better tool and guide than instinct, because it is infinitely more adaptable and flexible. An instinct is rigid, it is adjusted only to a particular kind of situation whereas reason does the adjusting itself and is therefore able to prescribe the proper (i. e. most useful) actions for any situation. (The possibility of this is seen immediately when the nature of knowledge is analysed.)

What is required to get the best possible adaptation of a living being to its surroundings? (Obviously it is necessary to have all its activities adjusted to continually changing circumstances.) Each situation will be a little different from all previous situations, and sometimes it will happen that the organism is confronted with entirely new circumstances which seem to have no resemblance with former experiences. (A perfectly well adapted organism must be prepared for everything, but instinct can prepare it only for a limited number of typical cases because it is formed by circumstances that recur continually for many generations.)

How does human reason manage to prepare man for the unforeseen? How can it foresee what has to be done in a case with which it has never been acquainted before? Certainly not by means of some miraculous power of deviation, but there is only one possibility = the use of former experiences.

But what good can old experiences do in a new situation, which is quite different? (It is true if there were absolutely no resemblance between the old and the new, reason would be staggered and surprised and unable to give any advice: but this never happens except in earliest youth. It is the function of reason to detect similarities between the new and the old, between one object and another. However different two things or events may be: analysis will usually discover that both are composed of similar elements, only in different combinations.)

(Suppose a man were suddenly brought to a foreign country with a climate and plants and animals quite different from his own: he need not perish, as an animal might, but by comparing the new circumstances with the old ones would find means of sustaining and protecting himself, would discern between friend and enemy, useful and harmful plants, and would not be defeated by the cold of winter even he has never experienced it with the same intensity before.)

Reason enables man to find his way about in the world, firstly by preventing him from ever being taken completely by surprise and being baffled: he will know how new things behave because he will recognise them as combinations of known things; and secondly by helping him to make inventions, i. e. intentionally creating new combinations of old elements in order to produce effects which would otherwise be unattainable.

In every case the practical aim of knowledge is prediction, and we have good reasons to regard as the defining characteristics of knowledge those properties of it which make prediction possible. „Savoir pour prévoir." Prediction requires mental anticipation of future events, a survey of possible combinations of given elements. This cannot be accomplished by taking the real elements and arranging them in various orders — that would be trying out, and not predicting: we want to judge about possible combinations before they have actually come into existence. It is necessary, therefore, to replace the real objects by something else that can represent them in the game of combinations, i. e. by symbols which can easily be handled. The role of these signes is played either by so — called mental pictures, which we can arrange and rearrange in our imagination (and this mainly is the psychological process of thinking) or — in more complicated cases — we use written signs = figures and numbers in drawings and calculations or perhaps even little models (especially in the case of technical inventions). As nearly everywhere else, words play a great part here, they are helpful signs both in gaining knowledge, and in communicating it. So what happens when we acquire knowledge or cognition of a fact is this: we reduce it mentally to some other thing or things with which we are already acquainted, and this "reduction" is simply a description of the new object by means of the same signs that described the old objects. In this way the "unknown" is made "known".

Whatever other case we may examine — in all genuine knowledge we find as a common feature an act of recognition which enables us to describe the object of it by means of signs that are used also on other occasions.

Now this activity of finding similarities between things which at first sight do not seem to have anything in common has gradually become a pleasure in itself. The process of acquiring knowledge, at first nothing but an indispensable means of mastering things and situations for the purposes of life, has had the same fate as other useful activities: as walking developed into dancing, speaking into singing, so the pursuit of knowledge developed into science. The human mind takes a delight in reducing things to one another, man enjoys this game, no matter whether he can derive any practical advantage from it or not.

Every progress in scientific knowledge is the discovery of a new description of a thing or process, a description in terms of something else. The chemist describes water as a particular compound of oxygen and hydrogen, he does not need the word "water" any more and can always write the combination of signs H₂O instead. The physicist discovers similarities between all the different chemical "elements" which enable him to describe them as combinations of "protons" and "electrons", thereby reducing the number of necessary symbols from 92 to 2; he describes all the properties of light, of radiating heat, of Roentgen rays and of radio waves in terms of the electromagnetic properties of "photons".

It must not be supposed that this scheme is restricted to sciences in the narrower sense of the word; the historian, the linguist, the worker in the field of social science — they all follow the same method in their own domains.

The historian who discovers by whom Caesar was killed finds out that the new description "murderer of Caesar" can be applied to Brutus (and a few others) ; the linguist who follows up the etymology of a certain term discovers that a certain other word may be described as the "root of that term" and so forth.

Wherever there is a real progress of knowledge it always has the same character : it consists in giving a description of something in terms of something else, i. e. a description which is formed by a new combination of old signs.

Now it is time to remember what we had to say about language and Expression: it embodied the possibility of representing and communicating a fact by a new combination of old symbols. So we conclude: all genuine knowledge is Expression. This is, of course, not a mere coincidence, not just an interesting fact, but it constitutes the very essence of scientific as well as everyday knowledge.

This is of the utmost importance. I think we may say — and I hope you will be convinced of it at the end of the lecture — that all the misery of metaphysics is caused by the failure to see this point clearly. Knowledge is Expression; there is, consequently, no inexpressible knowledge. You cannot tell us: "Ah, I have discovered what this thing is, but it is impossible for me to say what it is". Real knowledge is recognition, so if you tell us that you really know a thing, you must be able to answer the question "Well, as what have you recognised it?"

Before drawing further conclusions from this insight we should find out whether there is a complete identity between knowledge and Expression by asking: if every knowledge is expression, is it also true that every expression is eo ipso knowledge ? In order to answer the question it is sufficient to consider expressions in our ordinary verbal language, in which everything else can be translated, that is to say, we restride ourselves to propositions in the usual form. Does every proposition convey knowledge?

We must immediately exclude mere tautological propositions which do not say anything and should perhaps not be regarded as propositions at all; we shall have to speak of them on a later occasion. After leaving them out there remain what in Kant's terminology would be called synthetic judgments, and there can be no doubt that all of these do convey some kind of knowledge.

When I listen to a proposition which is not tautological I am actually told something which will be new to me (unless I happened to know it before), and the proposition will save my finding it out myself. (We assume the proposition to be true ; if it is false it will express not knowledge, but error.) The simple sentence "the ring is lying on the book" certainly communicates some kind of knowledge just as well as the scientific proposition "the neutral helium atom contains two free electrons".

Yet obviously there is an essential difference between these last two cases. The first one is a statement of one single fact which does not simplify our picture of the world, the second one has the character of an explanation. For some particular purpose it may be of the utmost importance to know that the ring was lying on the book, and certainly it is knowledge, for it presupposes at least three acts of recognition: 1) of one object as a ring; 2) of another object as a book; and 3) of the spatial relation between the two as the first object being on top of the second one. Yet we feel that this knowledge remains, as it were, on the lowest possible level, whereas the statement about the helium atom belongs to a very high region of thinking.

The second statement is of a very much higher order of "interest" than the first one. You will think immediately that this is due to the different levels of generality: the proposition about the ring deals with one small insignificant fact, that about the helium is applicable to all the countless helium atoms in the world. There is some truth in this, but it is not the whole story. In the first place, it is possible for single never reoccuring facts to have a high degree of importance — when this is the case they are called "historical facts". But in the case of history of mankind it will be seen that the interest is not scientific, but human (it appeals to feeling rather than intellect). In the second place, knowledge of a single object or event may sometimes be counted as a great advance of science, as the discovery of a star or the explanation of a volcanic eruption in geology. So the difference in generality (generalness?) is not sufficient to account for the distinction between knowledge as knowledge of a fact, and knowledge as explanation. The answer may be a description or an explanation. The real difference seems to be this: we have to do with a mere statement of fact if the acts of knowledge on which the proposition is based consists in recognising some directly given entity as something with which I am already familiar and to which I can, therefore apply a name or description. I see a round thing — or feel of it — and say: "This is a ring"; I see a flat thing and say: "this is a leaf"; I see an object of which I do not know the name or use but I say: "this is something I have seen in Central Africa". Or I may say: "this is above that" "this is darker than that", and so on. The common feature of all these propositions is, that they contain the words "this" or "that". In all such instances the acts of recognition lead only to the result that an entity, at first indicated only by the word "this" is now denoted by the word which is always used for it (or for each one of a class of similar things). In order to get the proposition "the ring is lying on the book" we just have to call everything by its ordinary simple name and put the words in the right order = such a proposition will merely express the existence of a fact in the world without explaining it.

In the case of explanatory knowledge, as we may call it, the situation is different. Here the proposition speaks of the thing or event by means of the ordinary name, i. e. the simple word always used as a symbol for it, and then gives it a new name which is a new combination of other symbols.(In the future, if it were convenient, one could always use the new combination, thereby eliminating the simple symbol altogether.) Thus explanation leads to a reduction of the number of symbols necessary for the description of the world and that is the very nature and essence of explanation. Some of the greatest steps in the explanation of the universe are marked by the discoveries which enabled physicists to do away entirely with special symbols for the phenomena of heat and sound and light and describe everything by electrodynamic and mechanical symbols only.

The two kinds of knowledge, although they finally rest on the same base of acts of recognition, are so different in their importance that it would be better not to call them by the same name.

Once I thought that perhaps the term "cognition" could be used for explanatory knowledge, but this would hardly be advisable, as it would make cognition dependent on preceding recognition. There is the term "explanation" of course, but again it is not customary to use the word in this connection ; to most people it would sound strange to speak of epistemology as the "theory of explanation" instead of "Theory of knowledge". But after having made the distinction I think there is no danger of confusion for us; and wherever we want to emphasise that we are not speaking of mere factual knowledge we can always use the term "explanation".

But unfortunately there is another very common use of the word "knowledge" which we shall be very careful to avoid, for in my opinion it has given rise to the most terrible mistakes — I should even say, to the most fundamental mistake of the philosophy of all times. The misuse I am speaking of occurs when the word "knowledge" is applied to what is often called — immediate awareness" or — and this is the most famous technical term "intuition". When I hear a sound or see a colour we often say that by these very acts of hearing or seeing I come to "know" what a sound is or what a colour is, — or it would be more cautious to say; I get knowledge of that particular sound I happen to be hearing, or the particular colour I am seeing, for as you probably know, a great deal of meditation has been devoted to the question concerning the transition from these particulars to the universal "colour" and "sound".

The particular colour or sound or feeling that is present "in my mind" at a particular time is exactly what we called "content" in the first lecture, and you can easily guess the bearing of our present question to our main issue. — When we look at our leaf, we get an immediate acquaintance with a particular quality of "green". Is there any reason or justification to speak of this acquaintance as a kind of "knowledge"? The use of our words, i.e. our definitions, should be determined entirely from the practical point of view, and we ought not to employ the same word for two things which have nothing in common in their nature and purpose. Mr. Bertrand Russell distinguishes between "knowledge by acquaintance" and "knowledge by description" but why should the first be called "knowledge" at all? The word "acquaintance" alone seems to me sufficient, and then we can emphasize the distinction between acquaintance and knowledge. There is no similarity of meaning between the two.

Since acquaintance has to do with content we are bound to blunder whenever we try to speak of it. In saying that we "know" content by acquaintance or by intuition we treat content as the object of an activity, as something which is "grasped" by the "mind", is drawn into it, is made to form part of it, or, worst of all, "perceived" by it. Here the impression is given as if mind gained "knowledge" of content by appropriating it in some way. This is extremely misleading. Content is content; nothing can be done to it, it is simply there (and even this cannot be "expressed") that is all. I can perceive a green leaf; I say that I perceive it if (among other things) the content "green" is there, but it would be nonsense to say that I perceive this content. And I must not say, of course, that the content is "in the mind", for, apart from other serious difficulties involved in the use of the term "mind", this would make sense only if content could also not be in the mind (perhaps before being "grasped" by it), for a proposition has no meaning unless it is possible for it to be false as well true (although only one of the two possibilities is actuality, of course). But if there is no sense in the question "can the same content be in two minds?" — as we saw in the first lecture — there is certainly no meaning in the question: can a content be as well in the mind as outside of it?"

By "knowledge" we always mean an act or rather the result of an act (of comparing, recognising, naming) but content is simply present, no act of intuition, of getting acquainted is required to bring it before the mind or into the mind, all these phrases are nothing but futile attempts to express its simply being there; we should not say that content is ever "known" or could be known. If we insist in using a verb which takes "content" as its object and the "ego", or "mind" as its subject, the word "enjoying" presents itself. It is the nearest equivalent to the German "erleben", but has certain disadvantages; we shall have to say, for instance, that the mind "enjoys pain". But as we know, there is no way of speaking correctly here, we must be satisfied to banish the word "knowledge" from these phrases.

The word "intuition" is a very good term to denote certain mental acts, namely those of guessing true propositions before they can be proved to be true, and these are really acts of acquiring knowledge — but there is no justification for using it the way Mr. Bergson does, for he speaks of it, as if it were an act by which content is grasped.

Bergsonian intuition has nothing whatever to do with knowledge in the sense which this word has in science as well as in daily life. Nevertheless Bergson's "intuitive knowledge" is nothing but a particularly emphatic formulation of a very old idea which pervades nearly all the traditional systems of philosophy. It is the idea that there are different degrees of knowledge (which is quite true) and that the degree of knowledge depends upon the intimacy of contact between the knower and the thing known (which is altogether false). It was believed that all explanatory knowledge, ordinary and scientific, which describes the known thing in terms of something else must for this very reason remain superficial, merely descriptive, and would never attain the highest degree, for it seemed as if what we really wanted to know was the thing itself, not merely a description of it. Scientific knowledge, therefore, seemed to be only a preface to, or a substitute for, the highest kind of knowledge, which consisted in the immediate awareness of the object itself.

From what has been said already it must be clear what a frightful confusion is committed, in this reasoning. It is nonsense to contrast with each other the knowledge of the thing and the knowledge of its description. We have seen that genuine knowledge of things consists in their description (in terms of other things) consequently, the highest degree of knowledge of a thing is the most complete, most perfect description of it, and not the thing itself (The thing is not the most perfect of its own descriptions, but something entirely different). He who wants to know an object as completely as possible, wants an explanation of it, he does not want the object itself. He cannot possibly want it, because he has it already; for if he did not have it, if he were not acquainted with it (in the sense in which intuition is supposed to furnish acquaintance) — how could he wish for an explanation? (If you have the desire to know something, you certainly must be aware of it before the desire can arise.) Thus Bergsonian intuition, so far from being the end and highest aim of all knowledge, is not even the beginning of it, it must precede all attempts to know anything. Content must be there before its structure can be studied.

(I hope nobody will object here that the wish to "know" a thing is often stimulated by a description and satisfied only by its actual presence; if, for example, we have heard a great deal about the Egyptian pyramids a vivid desire may be kindled in us to get acquainted with them personally, and we may not rest until we have travelled to Egypt and actually set eyes on them. But in a case of this kind it is obvious that what we are seeking is not knowledge at all (although we describe the result of our experience with the words "Now at last I know the pyramids!") but it is enjoyment. We want a certain thrill which is quite different from genuine explanatory knowledge. Real knowledge about the pyramids consists of propositions about their nature and history, and in order to get these (which would also give us a thrill but of a different kind) we do not have to see the pyramids at all, we can read about them, or, if we want to find out facts about them which are not described in any books we can send another person to Egypt and have him make the necessary observations and communicate them to us. But the enjoyment we have when looking at the pyramids cannot be communicated and there is no substitute for it. And it remains true that it is neither the highest degree of knowledge nor even its lowest degree, but simply the indescribable datum that precedes everything else.

(If intuition were the most perfect sort of knowledge we should not need — and indeed there could not be — any science of Psychology, at least if the object of psychology is supposed to be the knowledge of "data or processes of consciousness". For whatever this phrase may signify, it is surely meant to stand for everything with which we are most intimately acquainted: the données immédiates de la conscience, which according to Bergson, are the only things given to us by intuition. If these things are what is best and most completely "known" — what would be the use of psychology? Psychological intuitive cognition would be the ideal of all knowledge, its scientific development and systematisation would be impossible and entirely superfluous, Socrates' "know Thyself" would be a ridiculous advice as it would be impossible not to know one's self completely. In reality there is a science of psychology and a very necessary one if we really want to know about the working of "consciousness", but it is also one of the most imperfect sciences, for it appears to be very difficult to know one's self and the laws of consciousness. It seems to require the scientific methods of experiment, observation and comparison, while mere intuition, if it does anything, just furnishes the data which are to be known, but not their knowledge.

The chief reason why it was so generally believed that all real knowledge must in some way culminate in immediate acquaintance or intuition lies in the fact that they seem to indicate the point where we must look for the ultimate meaning of all our words and symbols. A definition gives the meaning of a term by means of other words, these can again be defined by means of still other words, and so on until we arrive at terms that no longer admit of a verbal definition — the meaning of these must be given by direct acquaintance: one can learn the meaning of the words "joy" or "green" only by being joyful or by seeing green. Thus the final understanding and interpretation of a proposition seems to be reached only in those acts of intuition — is it not through them, therefore, that the real knowledge which the proposition expresses is ultimately attained?

The considerations in our first lecture have taught us already to what extent these remarks are true. We saw that our ordinary verbal language must be supplemented by pointing to objects and presenting them in order to make our words and sentences a useful means of communication, but we saw at the same time that in this way we were only explaining our language of words by a language of gestures, and that it would be a mistake to think that by this method our words were really linked to the content which intuition is supposed to provide for us. We showed that the meaning of our words was contained entirely in the structure of the intuitive content. So it is not true that the latter (the inexpressible greenness of the green), which only intuition can furnish, actually enters into the understanding of knowledge. It cannot possibly do so.

Besides, — and this remark settles the question independently of all other considerations — the fact that intuition, immediate awareness, or as we should rather say, the mere presence of content, is indispensable for all knowledge, this fact has no significance whatsoever, for it is indispensable for everything; it is the ineffable ever present fundament of all else, also of knowledge, but this does not mean that it is itself knowledge — on the contrary, it makes it impossible to apply to it the word knowledge, which is reserved for something utterly different.

(When I look at the blue sky and lose myself in the contemplation of it without thinking that I am enjoying the blue, I am in a state of pure intuition, the blue fills my mind completely, they have become one, it is the kind of union of which the mystic dreams. Bergsonian intuition is the mystical conception of knowledge. Shall we not say that through the state of pure awareness which I just described we come to know what "blue" really is? By no means! In order to give a name to the colour I am seeing I have to go beyond the immediacy of pure intuition, I have to think, be it ever so little. I have to recognise the colour as that particular one I was taught to call "blue". This involves an act of comparison, or association; to call a thing by its proper name is an intellectual act — the very simplest act of the intellect, to be sure — and its result is real knowledge in the proper sense in which we use the word. The sentence "this is blue" expresses real knowledge, not explanatory but factual knowledge.

The simple descriptive knowledge "this is blue" gives rise to an explanation replacing the term "blue" by a complex of other terms: a rather difficult task, which is undertaken by physics (or physiology) and leads to a proposition of the form: "this blue is light of the intensity so — and — so, the wave — length so — and — so!", and so on (or "this blue corresponds to such — and — such a process of such — and — such a nervous system"). All this confirms our statement that knowledge does not require a real intimacy between the knower and the known and that the most perfect knowledge does not consist in a union of both. On the contrary, all knowledge seems to become more and more complete the farther we move away from the object. Think of how perfect our knowledge of the nature of matter is at the present time — at least compared with former times — and how utterly remote it is from what people thought they knew about matter by intuition ! If we ask the scientist about the nature of water he tells us that it consists of molecules composed of two atoms of hydrogen and one atom of oxygen, and that these atoms consist of protons and electrons in very definite numbers and arrangements, and that protons and electrons are nothing but a certain way of speaking of frequencies of vibrations, probabilities, and so on, thus substituting for the word "water" other terms with extremely strange meanings far, far away from anything with which we are directly acquainted and showing no similarity with the intuitions that arise when we are on intimate terms with water (e.g. when drinking it or bathing in it). The scientist arrives at his results in an exceedingly roundabout way, and we accept them as the true answer to our question concerning the real nature of water. Could we also accept the answer of the metaphysician? He tells us that the result of the scientist does not satisfy him, because it gives a description of water in terms of something else, contemplating it merely from the outside and in this way falsifying our knowledge, whereas the only true method of discovering what water really is consisted in identifying one's self with it. Schopenhauer believed that if he did this he would find out that water was nothing but Will, and Bergson assures us that it would disclose itself as élan vital. Can we accept such statements? If we really turned into water, we should be water, but it seems to me that this does not mean we should know what water is. Does gold know the nature of gold? does light know the nature of light?

Intuition, identification of mind with an object is not knowledge of the object and does not help towards it, because it does not fulfil the purpose by which knowledge is defined: this purpose is to find our way among the objects, to predict their behaviour, and that is done by discovering their order, by assigning to every object its proper place within the structure of the world. Identification with a thing does not help us to find its order, but prevents us from it. Intuition is enjoyment, enjoyment is life, not knowledge. If you say that it is ever so much more important than knowledge I shall not contradict you, but it is perhaps all the more reason not to confuse it with knowledge (which has an importance of its own).

We found the most essential feature of knowledge in the fact that it requires two terms: one that is known, and one as which it is known. But in intuition we have only one term: when we lose ourselves in the enjoyment of the blue sky, there is "blue" and nothing else. This is the reason, too, why the content of intuition cannot be expressed, whereas expressibility is an essential not an accidental property of knowledge.

The mystic who maintains that intuition is the highest form of knowing is condemned to absolute silence; he cannot communicate his vision, he would commit a self-contradiction if in his books or sermons he tried to describe his "knowledge", although he could, of course, explain in what condition and circumstances he was when the intuition came to him, and what he did in order to get into this condition.

If we recapitulate in the shortest possible manner the chief points of contrast between intuition and real knowledge we get the following table.

Intuition

only one term
enjoyable
living
presentation
acquaintance
inexpressible
that which is ordered
content

Knowledge

two terms
useful
thinking
explanation
description
expression
order
form

The main result of this discussion is, that it clears the air of all prejudices against scientific knowledge and its method. We can no longer believe that philosophy is in possession of a higher kind of knowledge giving us a profound and ultimate insight into the nature of things that science is always approaching without ever being able to attains it, because it has to stop short at certain points which mark the final boundary of all discursive scientific knowledge. There is no such boundary, there is no intuitive knowledge which philosophy can claim as her own special method.

It is only in recent times that scientific and philosophical knowledge have been confronted in this confusing way. It has been most decidedly done by Schopenhauer and Bergson who both declare that science looks at the world from the outside only, whereas philosophy, by means of intuition, looks at it from the inside.

The thought which shines through the words of these two thinkers is the fundamental idea not only of their own philosophy, but of the metaphysics of all times. Metaphysics, in the stricter sense of the word, has always been aiming at the "inmost nature of things in themselves", and what was really meant by this or some similar phrase is nothing but content, although this term may never have been used; and its conception of knowledge, although this was often not stated explicitly, has always been the mystical one of intuition, of intimate acquaintance. All metaphysicians have tried to tell us what the content of the world was like: they sought to express the inexpressible. That is why they failed.

A careful survey of the history of philosophy would easily show that all metaphysics really consisted of desperate attempts to express content; here we must be satisfied to consider one or two examples that will elucidate the situation for us.

The greatest systems of metaphysics and those that have had the largest number of supporters are "idealistic" systems. What is the doctrine of metaphysical idealism, and why has it such a great fascination for philosophers ? It asserts that the real essence of all things is of the same kind as that which we experience in our own consciousness; and since the data of consciousness have the character of "ideas" their view is called idealism. I think it is very plain how these phrases have to be interpreted. They reveal the philosopher's desire to become as intimately acquainted with all things as he is with the contents of his own consciousness. It is the one place where the self coincides with reality, where the knower is identical with the known. And, so he goes on to argue, if in this one place I discover reality to be "mental" (i.e. to consist of the stuff ideas are made of) I am justified to infer by analogy that the same will be true also of all other parts of reality with which I do not happen to be so intimately acquainted.

After everything we have said about the nature of knowledge the pitiful logic of this reasoning must be clear. It is not, of course, that we would find fault with the inference by analogy, if there were any inference, but actually there is none, as all these sentences are devoid of meaning. We notice the desperate efforts to say something about content: that with which we are immediately acquainted is declared to be "mental". What does this mean? It does not mean anything, for evidently "contents of consciousness", "that with which we are immediately acquainted" and "mental" are, in this context, absolutely equivalent terms, and we are not saying anything, when we predicate one of the other. And we are not saying anything, either, when we predicate one of them of the "real essence" or the "inmost nature" of a thing. For by these latter phrases the metaphysician wishes to indicate the thing as it would be given to us in intuition if we could penetrate into it, if our mind or consciousness could become identical with it; so, by substituting this meaning into the statement of the metaphysician we find him asserting that all things, if they could completely enter into our consciousness, would be mental i.e. contents of our own mind — which would again be nothing but a pitiful tautology, even if the hypothetical part of the sentence had any meaning. But it has no sense at all, for it is nonsense to speak of things "entering into the mind" and yet remaining what they were before they entered it. (It is really too primitive a picture to compare consciousness to a box into which objects could be put and taken out. And we had already convinced ourselves a few minutes ago that one can never say that the same content is here and there; "in" the mind and "outside" of it, for whatever we say will express structure only. By the way, the words "consciousness" and "mind" are so treacherous that practically all philosophical sentences in which they occur are devoid of sense. I should like to go so far as to say that these terms have a good, honest, definable meaning only in the common use of ordinary language, as when I say "he has an acute mind" or "she lost consciousness").

But however this may be, I think it has become clear now, why idealism is the preferred form of metaphysics: the metaphysician is hunting for content (calling the "real essence of being" or the "intrinsic nature of things" etc.) he finds it only in his own perceptions, feelings, ideas (calling them mental), and so he triumphantly pronounces the fundamental principle of idealism: "the inner nature of everything is mental" — which we have just seen to be a meaningless chain of words.

It is hardly necessary to add that other metaphysical systems, such as dualism, or materialism are no better. It is easy to see from the arguments pro and contra these views (which fill our philosophical test books) that both materialists and dualists (and whatever other varieties of metaphysicians there may be) believe they are telling us something about content. It is not quite easy to see in which way the word "matter" (signifying physical substance) could be regarded as denoting content — and that is why materialistic metaphysics has in general stood in smaller favour than idealism — but there is no doubt that it was meant this way from the time of Democritus on. The essential characteristic of his material atoms was that they occupied space, and since in earlier times the distinction between physical space and the intuitive spaces could, of course, not be made, the filling of space was regarded as content with which we were directly acquainted.

But we need not here carry the criticism of metaphysical systems and the attempt to understand their mistakes any further; it is time to draw the important positive conclusions from our result that all knowledge is expression, and that all expression is a rendering of structure, not of content. In the development of science during the last two or three decades the possibility and necessity of a sharp distinction between form and content has become clearer and clearer, and the all-importance of structure has been more fully recognised. The gradual dawning of this truth — which has not grown into full daylight yet — seems to me to be the greatest achievement of modern epistemology.

The separation of Form and Content has a history of many centuries: at first it took a metaphysical shape in the philosophy of Aristotle; since that time the border-line between Structure and Matter has continually shifted in one direction until in our present day, the last traces of content, as it were, have been removed, and pure Form has revealed itself as the purely Logical.

Science is not a collection of factual knowledge (statements of facts), but a system of explanatory knowledge (description by Laws). The more perfect it grows, i.e. the more its propositions become logically connected, the more clearly the formal character of knowledge becomes evident even to the untrained eye: science clothes itself in mathematical garments. Although this attire is sometimes looked upon with a mixture of awe and scorn even by philosophers, the really great thinkers of all times, from Plato and Democritos to Leibniz and Kant, have always been well aware that there is no hope for philosophical analysis unless it starts from an understanding of knowledge in its strictest, i.e. in the mathematical shape.

Knowledge has reached its most advanced stage in theoretical physics, and to it we have to adress ourselves in order to understand science. (Later on we shall cast a glance at other realms of knowledge and shall see that everything remains true for them. We cannot adress ourselves to pure mathematics because — this may seem strange but is a necessary consequence of the terminology we adopted — it does not contain any genuine knowledge. It is not a science, but an instrument of science which is used to formulate scientific truths and represent properly the connections between them. It does not express anything itself, but is the purely analytical method or technique of transforming equivalent expressions into each other).

Theoretical physics, if we do not consider it in the making (although, of course, it is always in the making) but as a completed system, consists of an indefinite number of propositions called Laws of Nature: They are logically interconnected, i. e. every single one of them can be deduced from (= is logically contained in) certain others.

It is possible to select a group of propositions such that all other propositions of the system can be derived from them the laws of nature which form this group are called axioms. The choice of axioms is arbitrary within certain definite limits, which is to say that there are many ways of singling out a set of axioms from which all the other propositions can be deduced; there are consequently, many different forms in which the system can be represented; a law of nature which plays the role of an axiom in one of these forms appears as a derivative proposition in another one. These different forms differ only in their outward appearance, not in their essential nature, for all of them are expressions of the same facts in the world. It is a matter of convenience, economy and — last, not least — beauty to make the set of axioms as small and as simple as possible — which means that ordinarily of all the possibilities of choice that one is preferred which makes the set of axioms consist of a minimum of simple propositions. (The two postulates of simplicity and of the smallest number are not always compatible, by the way, but we are not concerned with these questions here, which are sometimes considered to form the subject of a special logical discipline called "axiomatics". But it is important to keep in mind that the word "axiom" is used in a relative, not in an absolute way. In the old systems of philosophy, that of Spinoza for example, "axiom" meant a self-evident principle forming the natural and necessary formulation of all other propositions, but we do not attach this philosophical dignity to the word any longer, it is, in principle, a matter of arbitrary selection wether a certain law of nature plays the part of an axiom or is regarded as derived from a set of axioms. The only thing that counts in the mutual logical relation between the propositions of the system, the possibility of deriving each one from a set of others.)

Outwardly the propositions appear as sentences composed of certain words or as formulae composed of figures and letters representing measured quantities. Now, all the work of the theoretical physicist is done entirely on his paper, all his calculations are done by jotting down long rows of symbols and shifting them about, according to the rules of mathematics. As long as he is really only calculating, i.e. considering the logical relations between the propositions within the system, it is obvions that he does not have to think of the meaning of his symbols at all; it does not make the slightest difference to his calculations what they signify, he is concerned with them only in so far as they satisfy the axioms of the system, or, in his mathematical language, that certain equations hold between them. This is absolutely everything he has to know, and nothing else can possibly enter into the system of theoretical physics, as it appears in any scientific paper or test book.

This state of affairs has first been clearly recognized with respect to Geometry, if by this word we mean the science of Space, expressing certain truths about points, plains, straight lines etc. in physical space, is not a branch of pure mathematics, but forms part of physics.

This was already seen by Newton, who declared it to be "the most general part of mechanics". The first representation of geometry as a coherent system is due to Euclid who already gave to it the classical form of a set of axioms from which all other geometrical propositions are derived. The derivation of a proposition from the axioms is called the proof of the proposition. Closer inspection of Euclid's proofs soon reveals the fact that they are by no means purely logical derivations, but consist of a mixture of logical deductions and appeals to drawings or the observation of the behaviour of rules and compasses. Drawings, rules, and compasses are physical objects, and an appeal to their observation is really an appeal to experience. Philosophers who did not wish geometrical truths to be based on brute facts of experience have denied this and have maintained that drawings etc. are not really the source of geometrical knowledge, but only artificial representations of some original "pure intuition" that precedes all experience and is independant of it. This doctrine (most vigorously advanced by Kant) encounters insuperable difficulties, but this is not the place to criticize it, in any case, it just tried to secure and indicate a situation which to Euclid, if he had been fully aware of it, would have seemed very deplorable and needing correction: namely, that the proofs of his propositions were not of a purely logical nature. The mathematicians (who have always been the most ardent and most scrupulous logicians in the world) were very much troubled and dissatisfied and set to work in order to purge all geometrical proofs from everything that was not purely logical, i.e. from all appeals to the meaning of the words occurring in the propositions, no matter whether this meaning was provided by experience or by Kant's mysterious "pure intuition". A proof is purely logical if it is valid by virtue of its form only, independently of the meaning of its terms (As the simplest example you can take the old modus barbara: if all M's are P. and if all S's are M's, then all S are P, whatever the meaning of the terms M, S, P, may be).

Now, what has become of geometry after the purification of all non-logical elements? Since all its deductions or proofs can now be carried out by some one who is not at all acquainted with the meaning of the symbols, the whole system can be considered as such, with regard only to its interior coherence and without regard to its signification. It will then no longer be a physical science — (for in a physical science all symbols must stand for physical things, or events, they must mean something) — it has become "pure" geometry, something that is of interest to the pure mathematician only, who enjoys transforming expressions into one another without caring what they express; it does not tell us anything about space any more, even if the word "space" should occur in it continually; it has lost all contact with reality; it is a frame, that frames nothing; it is mere structure without content. If no interest is taken in the application of the structure, the particular set of axioms of the systems becomes unimportant, and the mathematician can amuse himself by introducing arbitrary changes of it. This led to the invention of "non-Euclidean" geometries, which would, at first, be regarded as empty creations of the human mind, until physical applications happened to be found for some of them, for instance in connection with the theory of Relativity.

It was this pure geometry, obviously, that Bertrand Russell was thinking about when he gave his famous definition of Mathematics as the Science in which we don't know what we are talking about nor whether what we say is true. As a matter of fact, if the meaning of our symbols is disregarded, we are evidently not speaking of anything particular, and before a meaning is given to them, the question whether we are speaking truly or falsely cannot be asked. I do not think Mr. Russell would stick to his definition now; he would hardly be able to make it fit arithmetic as he himself conceives it, and it gives the wrong impression as if mathematics were really a science consisting of propositions which could actually be true — only we did not care whether they were or not. But this is not correct of our "pure geometry".

Sentences or formulae in which the words or symbols have no definite meaning are, of course, no propositions at all; they are "propositional functions", i.e. empty forms which will become propositions as soon as certain definite significations are assigned to the symbols of which they are composed. As long as no signification is assigned the symbols are really nothing but simple marks to indicate empty places which must be filled with meaning in order to get a proposition. There is, of course, the condition that wherever the same sign occurs, it must be given the same meaning. Such signs indicating empty places for significant symbols, are called variables, and the significant symbols by which they are replaced are called concepts.

What has been done in the case of geometry can be done for any other science in so far as it is really scientific, i.e. consists of logically connected propositions: by disregarding the meaning of the symbols we can change the concepts into variables, and the result is a system of propositional functions which represents the pure structure of science, leaving out its content, separating it altogether from reality. When we speak of science, we shall, for the reasons given above, always have in mind theoretical physics, at least for the time being.

A purely deductive system of the kind described has been called (the term was first used by Pieri, I think) a hypothetical-deductive system. It is called "hypothetical" with respect to its possible use in science. It will, evidently, be useful in all cases where we find entities in nature, which, when substituted for the variables of the system, will change all its propositional functions into true propositions. (Perhaps I ought not to say that the entities themselves could be substituted for the variables; I mean of course that the variables are replaced by symbols signifying those entities.) We may express this by saying: If the symbols of our system stand for entities for which the axioms hold, then all the propositions of the system will be true of those entities. Or, in other words: If entities can be found which satisfy the axioms of the system, then the system will be science of these entities. It is on account of the "if" at the beginning of these sentences that the deductive system is called "hypothetical". (One and the same system may possibly find many applications to reality. Many sets of entities may be discovered so that the axioms, and consequently the whole system, will be true for each set. All these sets will have those properties in common that are expressed by the axioms, but in all their other properties they may, of course, be entirely different from each other — so different that they may belong to entirely different realms of being (if I am permitted to use this old fashioned philosophical phrase): one may be a set of colours, another one a set of points in space, another one a set of economic values, and so forth, and yet each set may fit into the same frame, the purely formal relations between the elements may be the same within each set, so that they will all be interpretations of the same hypothetical deductive system).

All this is well known to anyone who has studied the subject, and it is generally recognised that science in its logical aspects has the character I have been trying to describe. But for our present purpose we must concentrate our whole interest on the question, "how is the empty structure of a hypothetical-deductive system actually filled with meaning?"

What is the stuff which must be added to the empty frame, in order to make a science of it ? — There seems to be only one possible answer to this question, namely, "the purely formal structure must be filled with content — it could not be anything else, because there is nothing else". (Indeed, did we not say ourselves, that all structure must be the structure of some content, and that content was nothing but that which had a certain structure? If we are to have concepts instead of mere variables, if we are to have real propositions instead of mere empty forms, if we are to have a science of some domain of reality instead of a mere hypothetical-deductive system, then our symbols must stand for real content, for if they stood for mere structure, we should again in the end, be left without meaning, for again there would, be the possibility of many different interpretations. But actual science deals with reality, which is unique, and not with possibilities only, of which there are many.

If this is the right answer it must appear difficult to reconcile it with our former insight that content never enters into our propositions and that all expression is done solely by means of pure structure. Nevertheless it is the right answer and it can be reconciled, if it is only properly understood. We must take great care, for misunderstanding at this point is very easy and very dangerous.

It cannot be doubted or denied that in a certain sense our symbols must point to content, for our propositions speak of the real world, and content is reality. (It must be remembered that my sentences do not have the ambition to be propositions themselves, their purpose is to give a certain direction to the reader's attention). But this cannot mean that our propositions really say anything about content, for the reasons we gave for the impossibility of this are perfectly valid and cannot be overthrown by an analysis of the nature of science. And the same reasons must in the end show us the way to the solution of the problem.

Let us start by considering an example in physics in which the same structure is used to describe many essentially different physical processes. There is a certain differential equation, the so-called wave equation, which applies to the propagation of waves of any kind, e.g. sound, radio waves, Röntgen rays. What is the difference between these various things which obey the same formal law? In the case of sound the waves are formed by mechanical vibrations of material particles, air molecules, for instance —, in the case of radio waves and Röntgen rays we have to do with oscillations of "electric and magnetic forces" (if we use the language of Maxwell's theory, leaving aside the most recent development). Now air molecules and electric forces are utterly different in their physical nature; although both of them may exhibit a certain behaviour that is expressed by the same wave equation, there are innumerable other formulae which are true for the one but not for the other, which means that they differ completely in their structures. So we see that at this point we do not have to have recourse to content at all; the signs substituted for the variables occurring in the wave equation stand for various structures, not for content.

But you will say: as long as this is the case the new signs will be nothing but variables either; the word "electric force", for instance, will have no definite meaning, but will signify any entity that fulfils certain axioms (these axioms, in the classical theory, will be Maxwell's fundamental equations), and there may be innumerable such entities; which of these is really meant? Before this question is answered our formal system will not be connected with reality, it will not be a science, but only a possible, frame for one.

This is perfectly true, and it is clear that by introducing symbols for structures instead of the original variables, we have not given a definite meaning to the symbols but have postponed the decision about the meaning. It would be absurd to suppose that we can give a signification to our system by the introduction of new and more complicated signs, especially as everybody knows perfectly well the way in which an interpretation of a formal system is actually given by the scientist: it is done by observation.

In the case of the physicist, observation always takes the strict form which is called measurement. The relationships between what is actually observed or measured and the quantities which finally appear in the equations expressing the laws of nature are extremely complicated, but we do not have to concern ourselves with them. It is sufficient to remark that the whole process leads to the establishment of a one — one — relation between a particular value of a certain physical quantity and a particular fact of observation. In other words: it is stipulated — lastly by arbitrary agreement — that the proposition "Under such and such circumstances (here the apparatus and the whole procedure have to be exactly described) such and such a fact is observed" shall be equivalent to the proposition: "The quantity so-and-so has the value so-and-so". This is simply the definition of the quantity: it is the way in which the sign denoting the quantity is connected with reality.

Observation involves content ("data of consciousness" in the ordinary questionable way of speaking), and just because it does this can it link our symbols to the (real) world — or I should rather say: the two phrases "involving content" and "linking to reality" are equivalent in their use.

Now, at last, we are prepared to see with perfect clarity the part which is played by content when we seek to determine the meaning of our symbols and propositions and, as we knew beforehand, this part proves to be such that content is left entirely outside of our language and expressions.

For let us consider what happens in an "observation". We suppose it to be done visually, for instance by looking through a telescope and watching a blue spectral line coincide with a black mark in the field of vision. If the contents "blue" and "black" together with their intuitive spatial qualities were not there, there would of course be no observation; so content does play an absolutely essential role. But now the observer formulates the observed fact by enunciating (or writing down) the proposition "the blue line coincides with the black mark". He may think of the words "blue", "black", "coincides" etc. as standing for the contents in his visual field, but after all that has been said in the first lecture we know that his words and the proposition express nothing of it. The statement expresses the structure of the observed fact in the way which we described formerly in regard to some other example, but it does not convey the content blue or any other. Another scientist who hears or reads the statement must immediately fill the communicated structure with some content of his own, or rather, the communication of the structure is even effected only by arousing in his mind some content which has that structure. Contents will rise in his imagination which he will call "a blue line" etc.; but, as we convinced ourselves long ago, we cannot assert that his content is at all similar to that of the first observer — such an assertion would not be false, it would be meaningless. (If the second scientist happens to be blind and deaf, he will nevertheless be able to understand the statement of the first observer, provided he has received a proper training [Helen Keller], for he will be able to imagine some tactual content of the required structure. If the statement of our observer should induce another scientist to repeat the experiment for himself, use the same apparatus, look through the same telescope under the same circumstances; if he then would confirm the statement by saying: "Yes, the blue line coincides with the black mark" — even then it would be nonsense to say that he had the same content as the first observer, although we should most certainly maintain that they are both in possession of the same structure.)

I hope the whole matter has now become completely clear: the empty frame of a hypothetical-deductive system does have to be filled with content in order to become a science containing real knowledge, and this is done by observation (experience). But every observer fills in his own content. We cannot say that all the observers have the same content, and we cannot say that they have not — not because we are ignorant, but because there would be no sense in either assertion. All the different individuals communicate to each other the structural forms, the patterns, and they can all agree about these; but each one has to find out for himself their applicability to the world, each one has to consult his own experience, thereby giving the symbols a unique meaning, and filling the structures with content as a child may colour drawings of which only the outlines are given. And about this ineffable content they can neither agree nor disagree.

Content does not enter into science. Not on account of some imperfection of scientific knowledge, not on account of some weakness of our cognitive capacity, but simply on account of the nature of all knowledge : it is essentially a matter of structure ; he who is hungry for content is hungry for something that is utterly different from knowledge — that is all. Science is a logical structure common to all who are able to study it.

Each individual must interpret it for himself; they all agree in everything that can be expressed and tested, but we cannot even ask the question whether they agree in regard to their interpretation also, contents are essentially private and cannot be compared. But we can ask the question whether our fellow — beings always find in their own experience some content that exhibits the same structure as the one we experience in our own world. If the question has to be answered in the affirmative it simply means that we all live in one and the same world. Even a colourblind person can understand all assertions about colours and study optics just as well as any one else, although his colour perceptions have a different multiplicity from that of other people with normal eye sight. He will, for instance, imagine a sort of frame in one of his intuitive spaces so that every place in the frame will represent to him a shade of colour, and the multiplicity of all these places will correspond exactly to the multiplicity of the colour system.

By these means he will be able to find meaning in every proposition about colours and deal with it intelligently. (This method is actually in use in psychology in order to arrange all possible shades of colours in a well ordered system.)

We can never understand science and knowledge if we do not realise that the question concerning the real nature of a thing is completely and exhaustively answered by giving the structure of the thing, and there is nothing left which ought to be expressed. If you inquire into the nature of gravitations, for instance, Einstein's equations (supposing them to be correct) will give you the answer to any question you can possibly ask about gravitation - you certainly cannot expect more than this, you cannot expect answers to impossible, senseless questions. And a question aiming at the "internal" nature of gravitation, as opposed to its properties as they reveal themselves in the equations (which purely formal, of course) would be senseless.

There is no meaning in any distinction between the "inner" and the "outward" nature of things. The best expression of the "nature of electricity" are the equations of the theoretical physicist: it would be ridiculous to think of replacing them by some immediate intuition; no one can seriously believe that a person experiencing an electric shock had really a better knowledge of the essence of electricity than Maxwell and his modern followers.

This point must be especially insisted upon, as there seems to be a certain lack of clarity in this respect even in the writings of some of the most enlightened thinkers who are otherwise perfectly well aware of the all—importance of form and structure for scientific knowledge. Bertrand Russell, certainly one of the greatest living authorities on the nature of science has written in his "Introduction to mathematical Philosophy" (2nd ed. p. 55) : "We know that certain scientific propositions [...] are more or less true of the world, but we are very much at sea as to the interpretation to be put upon the terms which occur in these propositions. We know much more (to use, for a moment, an old-fashioned pair of terms) about the form of nature than about the matter." The word "matter" seems to be used here in the same sense in which we have used the word "content"; and if this is so, Russell's statement surely stands in need of correction. It will not do to say that we know very little about the content of nature and to speak as if this were a regrettable but perhaps not altogether hopeless state of affairs: no, it is self-contradictory to speak of "knowledge of the content of nature"; such a phrase is devoid of meaning. A few pages further on, where Russell is concerned with different possibilities of interpretation for one and the same formal structure, he seems to be on the right track when he writes (p. 61): "[...] the only difference must be in just that essence of individuality which always eludes words and baffles description, but which, for that very reason, is irrelevant to science." Can this mean that science is not interested in content, but that it is very important in all other respects, for instance for poetry and life? I do not wish to reject such a formulation altogether, especially after having myself contrasted knowledge and form on one side with life and content on the other — but we have to be extremely careful not to fall into a severe misunderstanding here. In the first place, we must regard the statement as a mere hint, not as a real proposition — for otherwise it would say something about content, which we know to be impossible; secondly, it would be a frightful blunder to infer that because content, in a way, is life, it might be a wonderful advantage if it were possible to express content, and that it was a great pity for life that it is impossible. And a worse error is committed by those who think that inexpressibility of content is restricted to the methods of theoretical science only, and that the miracle might perhaps be achieved in some other way.

Among those who have seen with unusual clarity that knowledge deals with nothing but structural patterns is Prof. C.I. Lewis. When considering the possibility of two persons experiencing identically the same content, he writes (Mind and the World Order, p. 76): "For the rest, the question of such identity is, in the end, merely idle speculation because we have no possible means of investigating it." But here the phrase "idle speculation" seems much too weak for something in which there is no sense at all. In fact Prof. Lewis does not seem to think it altogether meaningless, for he says in another place (ibid., p. 112, note) : "The only reason that the possibility of such ineffable individual difference of immediacy is not altogether meaningless, is that we have interests which pass beyond those of cognition. Interests such as those of appreciation, sympathy, love, concern the absolute identity and quality as immediate of other experience than our own. Esthetics, ethics and religion are concerned with such interests which transcend those of action and knowledge [...]." In view of statements as these we must protest that aesthetics, ethics and religion can express the inexpressible no better than science can, whatever their methods of expression may be. For our arguments are based on the analysis of expression in general, without any restrictions, and must be valid for religion and poetry just as well as for theoretical physics.

Let us consider the case of the poet. Most people believe that he has the gift of expressing things that can be expressed by no other power — except perhaps by music, painting or sculpture, but certainly not by science or ordinary language and that the realm, of art certainly must be content, joy and sorrow as such, colour and sound in itself. No one can feel more strongly than I do that the greatest miracles on earth are wrought by the poet and that no revelations and values can compare with those given to us by art, and I have the greatest admiration for the expressive power of poetry, but at the same time I know that the poet cannot express anything that could not be expressed by science, and that most certainly a volume of poetry does not communicate content any more than a scientific book. We must acknowledge the great magic of art, but we must not attribute it to the wrong causes. The merit of poetry does not lie in its wonderful capacity of expression, it is to be found in the great effects it produces in our souls by that which it expresses. While the ultimate purpose of science is knowledge, perfect expression of real facts the purpose of art is to evoke in us certain emotions, and expression is but a means to this end. Emotions are content (possessing, of course, a certain structure), they are not communicated by poetry, but produced by it. We have had occasion to speak of this distinction before. You will say: "but the poet knows what kind of emotion he wants to produce, and does it — is not this a kind of communication of his feelings from his soul to mine ? You are right, but if you speak this way you deal with the structure of emotions and feelings, not with their content. It is true, the poet introduces Falstaff to make you gay, and you laugh when you see Falstaff; the poet makes Lear suffer to arouse your sympathy for him, and the tears come to your eyes when you see Lear. The poet is satisfied to see you laugh and cry and he knows that you really feel the way he wants you to feel. How does he know it? He sees your laughter and your tears that is all.

You say he concludes that you are gay or sad because gaity causes laughter, and sadness causes tears. Perhaps you are right, but this means simply: he infers that something is going on "in your mind" which has a similar structure as the joy or sadness with which he is acquainted from his own experience. William James may have been wrong when he taught that the emotions are identical with the corresponding physiological processes in the body, but it is certain that the structure of laughter has something in common with the structure of hilarity, and the structure of crying with that of grief.

Thus we see that in the case of poetry and art — just as well as in all other cases of human interest and action — we deal only with structure. Ineffable content remains beyond forever. We must not make the mistake (which is really the source of all difficulties here) to think that art would be more wonderful or more perfect if it could express content, and that its inexpressibility must always remain a matter of regret. No such thing! These misunderstandings must be radically overcome. It is perfectly true that Poetry — one of the great realities in life - is a matter of content, but content is important because of its formal properties. What is joy? If I want to describe it (not only to some one else, but also to myself) I must say: it is that emotion which makes me smile, makes me dance, makes me be kind to my fellow creatures, makes you forget sorrows — and so forth; I may mention a hundred other things, they will be all formal properties, nothing else can be said, nothing else is expressed in poetry.

Can anyone still think that when the poet speaks of a green meadow, the word "green" stands for the content while when the scientist speaks of a green leaf the same word will stand for the structure of green? I think we must be convinced by this time that the word, wherever it occurs in a sentence can never express content, no matter who utters the sentence and for what purpose. The sound of the word "green" may of course produce a certain content in the listener, which is not done by the words "light of wave-length so-and-so" although the meaning is the same.

What is true for art is a fortiori true for aesthetics; which tries to speak about art, and it is hardly necessary to add that propositions in Ethics certainly will not have a power which they have nowhere else. As regards psychology, it may be noted that its method, whether "introspective" or "experimental", is in its last principles not different from the method of physical science: its propositions express psychological facts by repeating their structure. Old-fashioned psychologists used to think that we can "know" more about our own minds than about other people's, because only our own mind can be investigated by introspection. But this view rests again on a confusion of intuition and knowledge in the legitimate sense of the word. What we really know by introspection, can be expressed in our propositions and if this is the case we can learn just as much from the propositions in which other persons describe their own mental life, and from other manifestations in which that life expresses itself. As all bodily manifestations, including speech, form part of a person's behaviour, we may maintain that all possible psychological truths rest on behaviour as their only and absolutely sufficient basis.

If it is this, and nothing else what is implied by the doctrine of "behaviourism" (of which I am not sure) the behaviouristic view seems to me absolutely unassailable.

Just one word about the so-called moral sciences, especially history. History has often been contrasted with the natural sciences, and the view has been advocated, especially by a very influential school of thought in modern Germany, that historical knowledge was of an essentially different kind from that afforded by the natural sciences, it was deeper, of greater intrinsic value, revealing more of the inner nature of things; it gave us real understanding, whereas it was the business of natural science to give explanation.

This view seems to me entirely errorious. After all we have said there cannot be the slightest doubt but that all the genuine knowledge contained in history (of political events, of art, civilisation etc.) is of exactly the same nature as we found it to be in all other cases. As a matter of fact, it is very easy to see that it consists of an immense amount of factual or descriptive knowledge and a rather small and disconnected body of explanatory knowledge in just that sense in which we have introduced these terms.

But it is not difficult to discover the reason why the doctrine I have just criticised was advanced. It lies in the fact that history is akin to art in that the ultimate purpose of those who study it is, in most cases, enjoyment rather than knowledge. For the historian proper the main end of his endeavours may often be a casual explanation of events, and in so far they will be scientific, but there will be another purpose in his mind also — and this will be the chief purpose of historical studies for most people and for many historians, namely: to enjoy within themselves the emotions and thoughts which they believe to have been the emotions and thoughts of the heroes of history and to visualise in their own imagination the great events of the past, as the contemporaries would have seen them; they want to live the past over again.

It is this awakening of certain emotions and pictures of the imagination which is called "understanding" by those modern philosophers and is mistaken by them for a special kind of knowledge. In reality it is a result of historical knowledge, but quite distinct from it, it is an enjoyment of the past, not an understanding of it, which could be achieved only by causal structures. Scientific knowledge has often been reproached for being one-sided, for unjustly preferring one particular kind of knowledge and proudly but blindly neglecting other kinds which are just as good and even more profound. We have convinced ourselves, I think, that these reproaches are utterly unfounded, and the result of grave misunderstandings. The main cause of these misunderstandings is the erroneous opinion that knowledge could be anything but formal, that in some way or other it must be possible to grasp and express content. We know this to be nonsense, and therefore impossible for the language of every day life, art, religion just as well as for science. So science is not inferior to anything else in this respect; on the contrary, it avails itself to the fullest extent of all the possibilities of the one kind of knowledge which is the only kind. Life and art are centered around "enjoyment" of content, for them expression is not the ultimate end, but only a means, and is, accordingly, valued only in so far as it leads to the production (not communication) of certain contents.

Expression itself is incomparably less perfect in all other fields than in science, and science has never pretended to replace art or life.

It is often said that science in its most perfect form, as mathematical physics, takes into account the quantitative aspects of experience only, and neglects altogether its qualitative sides. We recognise in this complaint a form of the same confusion and prejudice against which we had to fight all the time: "quality" may be regarded as the popular word for Content. (I have avoided the use of the word quality in this sense, because the word may stand, and often does stand, for properties which are not Content at all, according to our way of speaking.) This charge against science has no more justification than all the others. The quantitative method, characterised by the use of numbers in the representation of logical structure, is for practical as well as theoretical reasons, the very best instrument of knowledge, and science should be praised for using it as much as possible. The theoretical reasons, if I may just hint at them, lie in the fact that counting and numbering is made possible by the repeated occurence of similar or equal events in experience; and, as we stated at the beginning, it is exactly this repetition of similarity in the world, which forms the basis of all possible knowledge. There are no "quantitative aspects" in the world, besides these similarities; the adjective "quantitative" can be applied to the method only, not to nature itself; science does not "pick out" the quantitative sides of things, and it does not think of overlooking qualities as if they did not exist.

The semblance as if scientists simply disregarded qualities is caused by the fact that they usually succeed in discovering space-time structures which exactly correspond to the qualitative (now metrical) relations they are investigating, and space-time structures always lend themselves easily to quantification, i.e. description by means of numbers. The most typical example is the substitution of waves or vibrations for "colours". The reason why such a substitution of space-time structures for qualitative relations is possible lies in certain very general facts of experience which have something to do with what used to be called "psychophysical parallelism"; but we are not concerned with these matters here.

Thus the last argument in which the opposition of quantity and quality represents the opposition of form and content, is shown to be no better than all the others, which were directed against the view that all knowledge is purely formal. For us there can be no doubt that this view is right. But you will have missed the most important point of all if you do not see quite clearly that this view implies no resignation of any kind, that it does not restrict the field of knowledge in any way. If I have myself used the phrase that knowledge deals only with form, the "only" must not be understood as having a restrictive meaning, it is just meant to indicate a contrast with certain other current views. Not for one moment must we allow ourselves to think, or even to speak as if there were two realms in the world, a realm of form and a realm of content and that only the former could be known, whereas unfortunately our powers of knowledge were too weak to penetrate into the realm of content, so that we were forever condemned to stand longingly at its gate.

And it would be a still greater misunderstanding to believe that the gate was not irrevocably closed to the human mind, but that life and art and religion and metaphysics each were in possession of a key that would open the door for those who were able to find it, and that only poor science must always remain locked out because the unfortunate method it had adopted might be excellent for the discovery of outward structures, but utterly inadequate and helpless in any attempt to express the interior content of things. In reality of course, there are no two such fields of form and content, there is no wall between them, and there is no gate. There is just the one old world which we are "enjoying" all the time; but which we know only in so far as we express its structure or order (be it for its own sake, as in pure science, or for practical or aesthetic purposes as in ordinary life), because what we call knowing is the expression of this order.

III. The Validity of Knowledge

After having gained the insight which I hope we have gained in the first two lectures it will be profitable and perhaps enjoyable to view some of the great issues of traditional philosophy from the standpoint to which our simple considerations have taken us. We shall be surprised to notice how elevated this point of view is considering the shortness of the climb, and the easiness of the steps by which we have reached it.

We have raised ourselves to such a height, or at least to such a favourable standpoint that for us the traditional problems have lost their formidable aspect entirely, and can be overcome without difficulty, although, perhaps, in an unexpected way.

The so-called philosophical problems are usually believed to be interconnected in such a way, that if you solve a single one completely, you have at the same time shown the way to the solution of all the rest. In other words: it is believed that what you need in philosophy is one fundamental idea which will serve as a key to all the important issues as well as all the minor questions. This belief caused the great thinkers of the past to build up their philosophies in the form of a system, which means a coherent whole in which all the single truths are based on and held together by, one fundamental principle. I cannot share this belief because I cannot adopt (for reasons which will become apparent very soon) the definition of philosophy on which it rests; nevertheless it remains true that as soon as you really see through one of the so-called philosophical problems with perfect clarity, you have done with all of them. Thus in order to see how these problems are disposed of from our point of view, it will be sufficient to concentrate our attention on one of the great questions, and I propose to select the problem of the Validity of Knowledge.

This issue forms the centre of Kant's philosophy, and it is here, where he believed he had found the key to the ultimate understanding of the world of experience.

He regarded as real, genuine knowledge only such propositions as possessed absolute validity, i.e. were known to be true anywhere and at any time. These propositions must be valid a priori i.e. they cannot be based on experience, because a proposition which expresses a fact of experience is, on account of its very definition, valid for this particular fact only, and we cannot know whether it will be true also for facts at other times or in other places as long as we have no experience of them. Kant did well to insist that the term a priori must not be understood psychologically, but logically: that is to say, a judgment a priori is not one that is produced in the mind without any previous experience (this, evidently never happens, and if it did happen, the judgment might not be valid at all) but it is one, whose truth is not based on experience; it would not come into existence without experience, but does not derive its validity from it. A judgment a posteriori, on the contrary, owes its validity to experience, simply because it is nothing but the expression of a fact of experience. This distinction between the psychological and the logical a priori, between the genesis and the validity of a proposition, had not been made with sufficient clarity by Kant's predecessors, especially Locke and Hume, but it is very helpful to avoid confusion. In any discussion of the validity of propositions it is convenient to use Kant's terminology, because with its help it is easy to express the various possible opinions and to state one's own case.

I need only mention the well known distinction between synthetic and analytic judgments. The former are propositions, which, if they are true, actually contain and convey some knowledge about the world; the latter are, what we have called tautologies mere empty forms which do not impart any information about reality; (Kant saw clearly, of course, that) all analytic propositions must be a priori: the validity of tautology is quite independent of experience, as it rests on nothing but the definitions of the concepts occurring in it; if I have defined a planet, for instance, as a celestial body moving around the sun, the validity of the proposition "all planets move around the sun" is certain, it need not and cannot be established by experience, experience cannot disprove it, for if I find that a certain celestial body does not move around the sun, I cannot call it a planet, because by definition I have agreed not to do so, that is all. Kant recognised that most synthetic propositions were a posteriori but these were of no interest to him; he believed that there were also synthetic propositions that were necessarily and generally true, that is to say, a priori, and he thought that the most fundamental truths of natural science and all mathematical propositions were of this kind.

He saw plainly the extreme importance of this issue (if you believe a synthetic judgment a priori you are a rationalist, although Kant did not confess to this name); if you do not, you are an empiricist, and these two philosophies are diametrically opposed to each other, and no reconcilation between them is possible. (Kant's own view does not reconcile them, as he believed it did, but is an essentially rationalistic solution.)

The results of our first two lectures make it absolutely impossible for us to accept any view except the empiristic one. Knowledge, we saw is the expression of a new fact by means of old terms, it is based on a recognition of the constituents of the fact. Without this recognition there is no knowledge, and it does not only precede knowledge, but forms the logical basis of it, it provides the ground for its validity. But this process evidently is what is commonly called "experience". What else could we mean wherever we use the the word "experience" if not this first work (and its result), of recognizing the primary material which presents itself and giving it its proper names? The material is prior to everything we can say about it — how could it be otherwise? The statement that all knowledge is empirical is itself a mere tautology — this remark will save us from being too proud of our empiricism. Rationalism, on the other hand, is not a possible point of view which just happens to be false and is discovered to be wrong after a careful examination of human reason and its relation to the world — no, it is simply self-contradictory.

A synthetic judgment a priori would be a proposition which expresses a fact without being dependent of the fact — contradictory to the essence of expression. It is well known how Kant tried to avoid this nonsense: he maintained that the facts were dependent on the propositions (at least that is what his doctrine amounts to) — a paradox which could be made to seem plausible only after the whole situation had been obscured by a great deal of confusion. It is very instructive to follow the round-about paths of Kant's thought, but we have no time to indulge in criticism. It suffices to point out, that, according to Kant himself, the existence of synthetic judgments a priori must seem utterly incredible to the unprejudiced mind. Nevertheless he believed that the actual existence of such judgments in science and in mathematics could not be denied; these disciplines seemed to be full of propositions — such as the principle of causality, and the Euclidean axioms — whose absolute validity could not seriously be doubted: so Kant believed himself confronted with the question: "These incredible propositions actually occur in the strictest of the sciences — how on earth are they possible?"

How is it to be explained, that we have knowledge, necessarily and absolutely valid knowledge — about facts of which we have not had any experience ? How can we be sure, that an event, which happens to-morrow or a hundred years from now, will have a cause ? or that seven objects and five objects, when counted on some distant, unknown star, will together be twelve objects ? — You know that the whole of the Critique of Pure Reason is devoted to the solution of this Problem. But alas ! there is no such problem, for there are no synthetic judgments a priori in natural science or in mathematics, or any where else. Kant must be excused for not recognizing the true nature of geometry, for in his time it was almost impossible to perceive that geometry, in so far as it dealt with the properties of space, is a physical science whose propositions are empirical, not a priori; and that in so far as it is a priori it is nothing but a hypothetical deductive system, consisting of propositional functions only, and consequently not asserting anything about any facts at all. Kant must perhaps also be pardoned for believing, even after Hume's criticism, in the absolute validity in the principle of causality, although the attitude of modern physics towards the principle proves that this belief is very far from being even a psychological necessity; but it is extremely difficult to justify Kant's opinion concerning the nature of arithmetical formular. His attempt to prove that 7+5 = 12 is a synthetic judgment seems very superficial and weak, especially if one considers Leibniz's treatment of the subject, and is one of the poorest passages in his whole work. Although there is at present still considerable disagreement about the ultimate foundation of mathematics nobady can nowadays hold the opinion any more that "arithmetical propositions" communicate any knowledge about the real world. They are certainly a priori, but their validity is that of mere tautologies, they are true, because they assert nothing of any fact, they are purely analytic. If a man tells me that he owns 7+5 acres of land, and I say to him: "ah! — you own 12 acres!" I have not told him anything new (even he should not happen to be able to add 5 to 7). I have simply repeated his own statement in different words. "5 + 7 = 12" is no proposition at all, it is a rule, which permits us to transform a proposition in which the signs 5+7 occur into an equivalent one in which the sign 12 occurs. It is a rule about the use of signs and therefore does not depend on any experience, but only on the arbitrary definitions of the signs. An arithmetical formula never expresses a real fact, but it is always applicable to real facts in the sense that it is applicable to propositions which express real facts by means of numbers, as is shown in the above example. (Another example : the arithmetical rule 1+1+1=3 teaches me that the proposition "he called me once, and once more, and once more" has the same meaning as the proposition "he called me three times".)

I repeat: arithmetical rules have tautological character; they do not express any knowledge in the sense in which we used this term. The same is true of all logical rules (no matter wether arithmetic is just a part of logic — as Bertrand Russell will have it — or not); it really would have been quite consistent of Kant if he had declared the logical principles (e.g. the Law of Contradiction) to be synthetic and a priori propositions; but it is evidently due to his sound instinct that such a nonsensical idea never occurred to him. In reality the logical principles are no propositions either, they do not express any knowledge, but are rules for the transformation of propositions into one another. A deductive inferinference is nothing but such a purely analytical transformation.

The application of logic to reality consists in its application to propositions about reality — but in applying the logical rules in this way we are not asserting anything about reality. I may, for instance, consider it an application of the Law of the Excluded Middle when I say, "to-morrow it will either rain or not rain"; here I have made a statement which is, undoubtedly absolutely true, and it appears to be a statement about a future fact. It does speak of the future, beyond doubt, but it does not assert anything about it, for evidently I know absolutely no more about to-morrow if I am told that it will either be raining or not raining, than if I had not been told anything at all. I believe that one has taken the most important step in philosophy if one has gained a perfect understanding of the nature of logic and its relation to reality or experience. In the first lecture I spoke of that particular misunderstanding of logic which has been called psychologism and consists in the belief that the logical principles are psychological laws of the working of human minds. The same error may take a more general form. Often the logical rules are treated as if they were laws of nature or of "Being".

This error is committed by many "rationalistic" schools of philosophy from the time of the Eleatic Thinkers down to Hegel and some recent writers. It is committed by those who assert an "identity of thought and reality" as well as by those who believe that the "correspondence of thought and reality" which is exhibited in knowledge is due to some special property of reality, commonly expressed by the phrase that "reality is rational". It is even committed by those who like to speak of an "irrational element" in reality, because this phrase implies that reality could partly lend itself, partly oppose itself to the rule of logic.

Just as psychologism must lead to the meaningless questions: "May not other beings have a logic which is different from our human logic? May not even human minds differ in their logic? Should we not try to construct some non-Aristotelian logic?" — in the same way the general error concerning the relation of logic to experience must lead to senseless questions like these: "May there not be some region in the world where the Law of Contradiction does not hold ? Might not (say) some astronomical observation, by being contrary to the predictions of our mathematicians, show, that our calculations, and consequently our logic, were not valid for the behaviour of our heavenly bodies?" But no fact can prove or disprove the validity of logical principles, simply because they do not assert any fact, and are, therefore, compatible with any observation.

Usually our astronomical predictions are very accurately confirmed by observations, and we may justly be proud of this mastery of the human mind over nature — but we shall be speaking nonsense if we try to express our joy and our wonder by saying : "how marvellously logical is the universe! how astonishing is the corresspondence between our reasoning and the ways of nature! There must be a preëstablished harmony between them!" And yet a great many philosophers have indulged in thoughts of this kind. They failed to perceive that what is really confirmed or corroborated by observation is not the validity of our logical deductions (which we suppose to be correct in the ordinary sense), but the validity of the assumptions from which our calculations started. If some day an astronomer should not find a planet at the place which he had calculated for its position, he would not think that the mistake lay in his using ordinary logic in his deductions, but he would know, that something was wrong with the hypotheses from which he deduced the position of the planet. (These hypotheses would concern the laws of motion, the initial position of the planets, the absence of disturbing influences etc.) A sceptic might object that in principle the failure of the astronomer could be explained in two ways: (1) by inadequate hypotheses, (2) by inadequate logic. But the second explanation is impossible. It is based on the fundamental error that the calculation, as it were, adds something to the hypothesis, and that the result of the calculation is the product of two factors: initial assumptions and logical deduction. But this is not so. On the contrary, it is clear that the initial hypotheses alone determine the position of the planet, the deduction or computation cannot be regarded as introducing as a new hypothesis the validity of ordinary logic, which may or may not be fulfilled. No, the assumption that the motion of the planet follows certain laws, etc. is the assumption that the planet will have a certain position at a given time, and (of course) certain other positions at other times; the law of motion is nothing but a short way of saying that the planet will occupy a certain series of positions at definite times — it must not be misunderstood as a kind of imperative order given by nature that the planet must and shall move in a prescribed orbit. A natural "law" is a formula which describes, it does not prescribe. The mathematical calculation by which the present position of the planet is "deduced" from the general law does not do anything but show that the proposition about the particular place of the planet is already contained in the law; that is to say: that proposition is not a result of the Law plus Logic, but the Law is an abbreviated way of asserting an indefinite number of propositions. One of these is picked out — that is all. Thus, if such a proposition is found to be false by observation, this proves that the law is false, it has nothing to do with logic.

It must be clear by this time that the validity of logic (and mathematics) for the world does not presuppose anything about the world, not any "rationality" of it, or whatever it may be called. It has nothing to do with any properties of the universe; it is concerned with the expression of facts by propositions (i. e. by other facts), and more particularly with the equivalence of different expressions. There an no conditions for the validity of logic.

Perhaps I should remark, in passing, that there are certain conditions for the possibility of speaking about the world at all — but that is quite a different matter. In order to use language there must be occasion for employing words (or the equivalent of words), and this occasion does not exist unless there are similarities in the world, for if every object or event occured just once, there would be no sense in giving a name to it, for the name could never be used. There would not be one world, in fact, however changing, but there would be continually new worlds having nothing to do with each other. There would be no possibility and no need of expressing anything, and we could not ask any questions. But as soon as we are able to ask questions there is the possibility of expression, and there is logic. It is even misleading, although I have done it myself for the sake of argument, to speak of the "validity of logic", for an invalid logic would not be logic, it would be nonsense.

Once more : the world cannot be logical or irrational — such phrases are nothing but excuses for bad philosophy. Whatever the universe is like — we can describe it by true propositions. The world consists of facts, the facts have a structure, and our propositions will picture the facts correctly — they will be true if they have the same structure.

In this simple way we must give account of the notion of truth; there is not much more to be said about it. The older philosophers were quite right when they declared that truth was a kind of correspondence between the judgment and that which is judged, although it was impossible for them to recognize the nature of the correspondence, which is simply identity of structure.

The phrase "identity of structure" must not be misinterpreted. When there is a ring lying on a book, for instance, this is an extremely complicated fact in nature, in which an indefinite number of details could be discerned: there are innumerable different ways in which a ring can lie on a book ; both objects may have innumerable different shapes and may be in innumerable different physical conditions. No heed is taken of all these possibilities in the simple statement that the ring is lying on the book : the structure which is represented in the proposition is just one feature of the fact. All facts (and there is an infinity of them) which have this feature in common would make the proposition true. The range of facts described by a certain proposition is larger or smaller according to the nature of the proposition. If I say, "the ring is lying in the middle of the top-cover of the book" the range is smaller; if I say "the ring is lying on the book or on the table" it becomes still larger. The proposition "the ring is lying on the book or somewhere else" would describe still a great many more possibilities, and, finally, the proposition "there is a ring and there is no ring" embraces all possible facts, it is always true. If it is always true whatever the facts may be, it must be a priori, and, as a matter of fact, if we look at it a little more closely, we recognize it as a tautology. We see: a tautology or an analytic proposition is a boundary case of a proposition when the range of facts with which it is compatible embraces all possibilities, or, we may say, the whole world (Wittgenstein). In this case the proposition ceases to express anything; it is true, not because the structure corresponds to a particular range of facts in the world, but because it does not point to any particular fact at all. It is true by virtue of its own structure, or, in the language of old-fashioned logic, it possesses "formal truth" only, where as a synthetic propositions has "material truth", it expresses an actual fact.

Tautologies (or analytic judgments) are the only propositions a priori, they have absolute validity, but they own it to their own form, not to a correspondence to facts, they tell us nothing about the world, they represent simply structures.

Kant had seen correctly, although rather vaguely, that if a proposition is valid a priori it must own its validity to the form of knowledge, not to its material, because our understanding cannot possibly know beforehand what material will present itself to the mind in experience, while it might very well impress its own form on any material. Thus he concluded that the synthetic judgments a priori, in which he believed, had the ground of their validity in the forms of our reason (the categories) and of our intuition (space and time). But alas! he failed to see that even the whole complicated apparatus of cognition which he invented could not explain the possibility of synthetic propositions a priori; and he was unable to realise this because his "forms" are not purely formal at all, but, if I may use the expression, simply loaded with content. This is clear immediately when we think of what I had to say, for instance, about intuitive space in the first two lectures. Space, time and the categories are spoken of as "pure forms" in Kant's philosophy, but they are used as if they were a strange mixture of form and content. There is no such mixture, of course, and as soon as one realises that only the Logical deserves to be called pure Form, one will easily get rid of the confusion which seems to give some plausibility to Kant's explanation of the supposed possibilities of synthetic judgments a priori.

Kant drew the line between the a priori and the a posteriori in the wrong place, and consequently the line between form and content — which he rightly felt, must coincide with the former line — was drawn in the same wrong place. In this way he obtained a region between this line and the line separating the synthetic propositions from the analytic ones — it was the region of his synthetic judgments a priori. But as a matter of fact there is no place for them, as the two borders of that region coincide and leave no space between them: there is no a priori except in tautology, and there is nothing synthetic, no real knowledge, except on the side of the a posteriori.

All knowledge is a posteriori, is beset on experience. It can be known to be true only for that experience on which it is based. A proposition about a future fact, or even about a past fact, or about "all" facts of a certain kind (so-called "grand complications"), must in a way, be regarded as hypotheses. The transition from true propositions to new propositions which are not known to be true but are expected to be so, is called induction. All I want to say about it here, is, that an induction is certainly not a logical process. No validity cannot be proved. It cannot even be proved that a proposition informed by induction will be probably true, whatever the degree of probability may be supposed to be. Logical inference as we have seen, is a transformation of an expression into an equivalent one of a different form, but the new proposition, since it really expresses something new, is surely not just a different form of the old proposition from which it is derived by induction. Therefore it is forever impossible to justify induction logically.

The old dispute between the "correspondence theory" and the "coherence theory" of truth (they should not be called "theories" of course) is simply settled in this way that the "formal" truth, which is the truth of tautological propositions, and is to be found in the realm of logic and mathematics, must be explained on coherence, but the truth of all propositions expressing real knowledge (which, in a sense is the only important kind) must be regarded as a correspondence between a fact and the sentence which expresses it.

The chief argument against the correspondence view asserts that it is impossible to compare our propositions with reality, because reality is not known to us except through our propositions, so that in the end the mutual coherence of the latter remains the only criterion. But this argument rests on the strange assumption of a metaphysical dualism, as if there were a realm of propositions apart and mysteriously separated from the realm of reality.

As a matter of fact there is no difficulty in carrying out the required comparison. Every proposition is given empirically as a spoken or written sentence, a complex of physical signs, which is itself a fact in the real world: comparing a proposition with the state of affairs it expresses is, therefore, nothing but a comparison of two facts. It is something we do a hundred times every day of our lives, and nobody can very well deny the possibility of it.

A proposition will be verified, the truth will be established if the structure is the same as the structure of the fact it tries to express. Certainly the two facts (the sentence and the state of affairs it communicates) are always very different from each other — how can they have the same logical structure? We must remember that the sentence has been given a logical structure and a meaning only by assigning definite significations to its parts; it is only through this interpretation that it has become a proposition at all (instead of remaining a simple ordinary dead fact) and has become coordinated to the expressed fact. The logical structure of the proposition has of course, very little to do with the linguistic grammatical structure of the sentence and is ever so much more complicated. In order to get at it we must imagine all the words of the sentence to be replaced by their definitions, the terms occurring in the definitions must be replaced by sub-definitions, and so on until we reach the boundary of ordinary verbal language where it ends in gestures or prescriptions to perform certain acts. In some cases where no explicit definition of a term is possible, the whole sentence will have to be transformed into a new shape, and the actual procedure of finding its meaning might become inextricably complicated, if in psychological reality it were not shortened and simplified by habit and instinct. But after the meaning has been grasped, and the necessary steps towards the verification of the proposition have been taken, there is, in principle no difficulty in ascertaining, whether the structures of the propositions and the fact are the same or not.

I can see with one glance that the ring is lying on the book and not on a plate and that the book is not lying on the ring. In the case of real knowledge or material truth, which we have just been considering, it is necessary to find the meaning of the proposition first (which is the same as finding the way of its verification) and then we can look to see wether it is true or not. But when we have to do with analytic judgments, or tautologies, which is the case of formal truth, the matter is much simpler. In this case the grasping of the meaning and the verification are not two processes which follow each other; there is only one process which yields meaning as well as truth. For if I know the meaning of the proposition I know also that it is tautological and therefore know that it is true.

This disposes of certain sceptical arguments which have sometimes been brought forward against analytic judgments. It has been said that the human mind is so weak that it cannot be sure of the truth of tautologies even. For however short the process may be by which I convince myself of the truth of a tautological statement — do I not have to keep in mind the exact signification of the terms occuring in it, and the connection between them? Do I not have to remember all the definitions involved? and is it not just possible that my memory has just failed me during these few seconds since it does happen that we sometimes forget a fact from one minute to the next? So how can I be sure of anything ?

These difficulties have occasionally been emphasised to such an extent that the analytic judgment has declared to be the most difficult problem of epistemology.

In reality there is no problem that would raise any difficulties for Logic. Our answer to those sceptical doubts is simply this: If during the short process of thinking we should forget the signification of the words (perhaps without knowing it) the consequence would be that we are unable to understand the meaning of the sentence. We have no proposition at all, but just an empty series of falsity. There is a proposition only after we have understood the sentence, and if we have understood it we have understood it as a tautology and know that it is true. For recognising something as tautological and recognising it to be true (by virtue of its form) are only two modes of expressing one and the same thing. The result is that perhaps some philosopher like Heraclitus' disciple Kratylus may doubt that we can ever be in possession of meaningful sentences, but he cannot even indicate by a motion of his sceptical finger that a person might understand a tautological proposition and not be convinced of its truth.

It is the fate of many post-Kantian systems of philosophy that in their endeavour to correct Kant by out-doing him they contradict him most decidedly in those particular places where he happened to be on the right track. Thus it is one of the basic doctrines of the most influential school of philosophy in contemporary Germany that Kant's opinion concerning the formal character of all a priori propositions was a mere prejudice. It is the so-called "phaenomenological" philosophy, founded by Husserl, that claims to be in possession of a great deal of a priori knowledge dealing with the very material or content of cognition, and not being due to any formal properties of the cognitive process. The followers of Husserl maintain with him that the source and justification of these indubitably and absolutely valid synthetic propositions is to be found in some kind of intuition called "Wesensschau", which is supposed to be the intuition not of an individual, singular thing, or event, but of the general nature, the "essence" of an entity or a class of entities.

They say, for instance, that such material, a priori synthetic knowledge is expressed by propositions like the following: "every musical tone must have a pitch and an intensity"; the surface of a physical body (or a patch on the visual field) cannot be both red and green at the same place and at the same time"; "orange as a colour quality ranges between red and yellow" and so forth. Husserl and his disciples believe that propositions of this sort form an unlimited field of important necessary truths which constitutes the proper domain of philosophy. Here at last, according to their opinion, it has become a strict science, as rich and as reliable mathematics.

The sober critic will have very grave doubts when he reads these statements, and two important points will force themselves upon his attention from the very beginning. In the first place, he will be astonished to see that the question as to the possibility of those synthetic propositions a priori is not answered. It is not even seriously asked. We are just told that they are "evident "and that, therefore, their validity cannot be doubted. Well — Kant maintained that his synthetic judgments a priori were evidently beyond all doubt, but that was just what puzzled him and made it necessary for him to write the whole Critique of Pure Reason. Kant's arguments have no validity for the phaenomenologist, for, even if they were correct, they could account for a formal a priori only. Thus the material synthetic a priori judgments remain entirely unjustified, Husserl makes no attempt to explain the incredible "fact" that synthetic knowledge can be valid a priori. Certainly we should entertain serious suspicions as to the existence of this "fact". Are the phaenomenologists right in assuming that the above mentioned propositions (or similar ones) express real synthetic knowledge ?

If this were the case it could form a second reason for great astonishment. If it is a synthetic proposition, a relevant truth, that e. g. every colour must have some extension, why does it appear to us as a simple truism? why is it our first impulse to say; "why, yes, naturally" what of it ? why don't we feel inclined to exclaim "ah, how interesting! this matter deserves to be investigated!" as we should when confronted with Euclid's fifth postulate or with the principle of causality? Real synthetic propositions always give rise to a sequence of new discoveries, because they must have some foundation which we are anxious to find (that is, since in reality all "synthetic propositions are empirical statements of fact, we simply inquire into the causes or laws of that fact) ; but the great truths of "phaenomenology" appear to be final, incapable of explanation, and therefore — in spite of Husserl's assertions to the contrary — do not form the base of any progressive science. This is another reason why we feel convinced that those propositions cannot possibly have the character of a "material a priori".

After what has been said before it is easy for us to discover the fundamental error of this philosophy (I have just been criticising). It is, of course, perfectly true, that there is no colour without an extension, that every tone must have a pitch, that orange necessarily ranges between yellow and red, that the same place in our visual field cannot be both red and green at the same time and so on. These truths are certainly a priori, no possible experience can contradict them — what is there about them that made people think they were synthetic and expressed real "knowledge"? I think it was the same error which made them believe that they had to do with a "material" a priori: they felt sure that their assertions expressed the very nature or essence of the Content of the colours or sounds they were speaking about. The proposition "a surface cannot be red and green at the same time and place" does not say anything about the content of "red" or "green", for all the reasons which were given in the first lecture and need not be repeated here, because they were entirely general — the proposition is nothing but a tautology which reveals the way (or form) in which the terms "red" and "green" are used. The incompatibility of the two is due not to some mysterious antagonism between two real essences, two kinds of content but to the internal structure of the two concepts "red" and "green". A surface cannot be red and green for exactly the same reason which makes it impossible for a tall man to be a short man at the same time. No one can seriously think that he has uttered anything but the merest tautology, when he tells us that a man who is 6 feet is not also 4½ feet. We know this a priori i.e. without consulting experience and we do not consider it to be a statement conveying knowledge about the essence of "man" or even about "length"!

We know its truth to be purely formal. It follows from the definition of measurement that if the result of it is indicated by one number all other numbers are excluded (provided we use the same unit), in the same way it follows from the way we use our colour names that if we attribute a certain colour to anything, we, at the same time exclude other colours. It is, as in all cases of internal structure, a matter of grammatical rules. In this case it is revealed by the use of the definite article: we have to say: The height of the Empire State Building is 1270 feet, we cannot say that this number indicates a height of the building. In the same way we can speak only of the colour of a definite place of a coloured patch. (If a patch has several colours they must be in different places, just as a building may have several towers, but not in the same place.)

The word "six" denotes a certain place in the structure of internal relations, called the system of numbers; in the same way the word "red" wherever it occurs in a sentence, stands for a place within a structure called the system of colours. We find the same situation in all other cases, and we conclude that the statements which have been mistaken for material a priori propositions are purely tautological, they convey no knowledge and their a priori validity is due, as it always must be, to their form. There is no genuine knowledge a priori.

Hume has seen this very clearly, as everybody knows; and all attempts to avoid his result in a round about way are in vain. (There is no logic of induction, there are rules of induction of course, but they are practical prescriptions which guide our expectations and actions, they have absolutely no logical character.)

I see no reason why the philosopher should regret this. Induction is necessary and important in the domain of actions, which belongs to life, not to theory and science (although it belongs to the pursuit of science, which is part of life) and for life and action the important thing is belief an expectation, not reasoning and absolute truth. Modern science, at any rate, is perfectly reconciled with the idea that all its general statements, all ist formulations of natural laws, must be considered as hypothecal and may have to be revised one day. The progress of scientific knowledge is none the worse for this attitude, it helps the scientific not to be dogmatic and keep his mind open to new ideas, and the impossibility of a logical proof of the general validity of his laws need not, and does not, shake in the least his practical belief that his description and explanation of the world is continually growing more accurate and more complete, that his knowledge is forever becoming more and more unified by continually diminishing the number of symbols requiered for the description, thereby showing the world to be a real universe. (Those who really know the spirit of science have always protested against the popular accusation of science as being fickle and unstable, giving up her old theories and replacing them by new ones. The truth is that no theory which has at all been verified by experience was ever entirely overthrown; on the contrary, its essential framework by which the structure of nature is expressed has always been absorbed by the new theories, and the only changes consist in the addition of new details affording better approximation, and the abandonment of misleading intuitive illustrations which do not form part of the theory but just serve to facilitate the understanding and the use of the theory. It is natural that these inessential illustrations seem to be most important to the unscientific mind; and this explains the unjust reproaches directed against science.

Only the scientific mind has the right to criticise the validity of knowledge. And whatever may be said against the validity of general scientific propositions, such as the laws of physics: it may be said with much greater right against all assertions in any other field of human occupation and life. The fundamental propositions rest on a much broader basis of experiment than any of the beliefs which are held most strongly in every day life. Under these circumstances nobody should speak disparagingly of the validity of scientific knowledge — not even the scientist himself.

If any philosopher should be disappointed by an analysis because we had to deny the possibility of real a priori knowledge, he will find enough compensation when we go on to examine the scope of knowledge instead of the validity. Most philosophers have stated with regret that human understanding, however efficiant it may be in some fields, is entirely incompetent in other fields, that the scope of knowledge is restricted to certain parts and aspects of the world, while other parts and aspects must forever remain beyond its reach. There are certain limits which it cannot possibly transcend. Beyond these limits there is the Unknowable into which our reason and our senses can never penetrate.

This view is held by schools of various descriptions: we find it among empiricists like Herbert Spencer, who believes in the existence of the Unknown beyond the realm of experience, this realm of experience is just a corner or section of the world to which all our knowledge is definitely confined. We find it also among rationalists who have the greatest faith in reason, like Spinoza — God in Nature, he says has an infinite number of attributes — but only two of these can be known to man, he has no conception of the infinite rest. We find it in the "critical" philosophy of Kant, who declares that human knowledge is restricted to phaenomena, appearances, while the things in themselves, of which they are the appearances are absolutely unapproachable, our reason as well as our senses live within unsurmoutable walls.

Now. I believe we shall all agree most heartily that we cannot know everything. I cannot tell you what the back side of the moon looks like, and it is even possible that no human being will ever know it. No historian knows, as far as I am aware, at what hour of the day Socrates was born and it is quite likely that this will never be found out by any one. So there certainly are limits to human knowledge.

But you notice immediately that such limits as I have just mentioned, are of a different kind from those which play the important role in the systems of philosophy. They are — as it were, less serious and do not interest the philosopher, although he must admit their existence.

It is necessary, in fact, to make a very important distinction here. There are two entirely different kinds of impossibility of knowing: a logical one, and an accidental or factual impossibility. In Kant's philosophy, for instance, it is logically and absolutely impossible for any human understanding to acquire knowledge of "things in themselves" — this means, it is unthinkable, we cannot describe what should have to be done in order to get such metaphysical knowledge, and we cannot imagine any beings that could be capable of it (although Kant believed he could describe such beings by saying they would have to be endowed with "intellectual intuition" — which is a contradiction, for intellect — if I may use our own terminology — has to do with form, and intuition with content). In this case knowledge of things in themselves would be impossible in principle. In the case of the far side of the moon, or the birth hour of Socrates, however, the impossibility of knowing them, has quite a different character.

It is not due to a principle, but to accidental circumstances, it is of a practical or technical, not of a logical nature. We know exactly what would have to happen if we wanted to know about the birth of Socrates: we would have to find some old papyrus or inscription in which a reliable and accurate account of the event was given, and it is just an unfortunate chance that such a document, as far as we know, does not exist. But it might exist; we can easily imagine it, and that means that our knowledge of the fact just happens to be impossible, the impossibility is a consequence of accidental circumstances, not of the nature of knowledge itself. Similarly there is no difficulty in describing the circumstances which would enable us to know the back part of the moon: we should simply devise some means of going around the moon and look at it. This happens to be technically impossible at present, but may not be so in the future; and even if we were certain that human beings will never succeed in going around the moon, still it would not be unthinkable, and this is sufficiant for us to declare that our knowledge of the hidden parts is only practically, not absolutely impossible. This would remain true if there were a law of nature which would forever prevent a journey from our planet to its satellite; for the laws of nature might be different, and we can imagine them changed in such a way that we could say what would have to be done and what our physical and mental faculties would have to be if we wanted to enjoy the sight of the moon's averted surface.

It must be admitted: the majority of questions one might ask about the world, can actually, not be answered, our knowledge is limited. But although it may even be definitely limited: if the limitations are of the sort I have just been describing, they are not "absolute" — they may be actually unsurmountable, but they do not worry the philosopher: when he pronounces his ignorabimus he means to assert an absolute impossibility of knowing, he means to say that there are certain domains of knowledge which are in principle unaccessible to human understanding.

The view I have been advocating is strictly opposed to all philosophies which believe in an essential limitation of knowledge, in a realm of Being which is unknowable in principle. There are a great many things concealed from us, but none that might not be revealed. Whatever we do not actually know may at least be known in principle ; there is no absolute ignorabimus although there are innumerable cases of ignoramus, the skope of possible knowledge has no boundary, no question is necessarily unanswerable for the human mind.

No elaborate reasoning is required to prove this statement; like everything else I have been saying it is a simple consequence of the definition of knowledge; in other words, it is tautological, in still other words the assertion that there are unsurmountable borders which necessarily restrict all human knowledge is not false, it is a nonsensical contradiction. We can easily convince ourselves of this, by viewing once more the whole situation from which the agnostic doctrine of eternally hidden truths has sprung.

If we ask the agnostic why he believes in the existence of a reality which can never be known and is, in so far "Transcendent", he will answer that he infers it from his experience. He says that in order to understand the world of experience (either on account of a priori elements it seems to contain, or on account of its fragmentary, unsatisfactory character) he must assume the existence of metaphysical entities "behind" the empirical facts. These facts point to something beyond experience; we know that they point to it, but we cannot know what they are pointing to. In short, we are confronted with the old dualism of phaenomena or appearances on one side, and things in themselves, or reality on the other, and the agnostic doctrine is, that the latter must forever remain hidden from our minds.

It is easy to disclose the fallacies of this views. In the first place it rests on that confusion of knowledge and intuition which is the cause of the most typical failures in philosophy. For the chief characteristic of what is called "appearance" or "phaenomenon" is its immediacy, it is given intuitively, it is content, and as long as one believes that knowledge consists in the presence or expression of content one must maintain that only "phaenomena" can be known.

We need not lose a word about this fundamental mistake: for us there can be no doubt that the presence of content is not the slightest reason why the "phaenomenon" should be better known than the thing in itself of which the content is not given. The knowledge of a phaenomenon is something entirely different from the intuition of its content.

In the second place, it is contradictory to say that the data of experience allow us to infer the existence but not the nature of things beyond experience. For, as I said before, it is nonsense to assert the existence of something without knowing what we assert the existence of. The same reasons which lead us to think that there are certain things there, must be sufficient to ascribe certain propositions to those things. If it seems necessary to assume the existence of unperceived entities it can be only because they are needed to fill certain places or functions. To assert therefore, that they exist, is to assert that they fill their places and have their functions. And this means that we can predicate of them just as much as we can of anything else, we have knowledge of them, our propositions reveal their structure just as they do in the case of "appearances", the content of the latter does not enter into our propositions either, and thus there is no difference between the two cases as far as knowledge is concerned.

The same reasoning can be expressed in this way: If the "phaenomena" are appearances of something else, then the mere fact that this "something else" is that particular reality of which that particular phaenomenon is the appearance — this fact enables us to describe the reality just as completely as the appearance of it. The description of the appearance is at the same time, a description of that which appears.

The phaenomenon can be called an appearance of some reality only in so far as there is some correspondence between them, they must have the same multiplicity; to every diversity in the phaenomenon there must be a corresponding diversity in the appearing things, otherwise the particular diversity would not form part of the phaenomenon qua phaenomenon, nothing would "appear" in it. But if this is so, it means that the "appearance" and the "appearing reality" have identically the same structure (this was pointed out with perfect clarity by Bertrand Russell-Introduction to Mathematical Philosophy, p. 61 sq.). These two could be different only in content, and as content cannot possibly occur in any description we conclude that everything which can be asserted of the one, must be true for the other also. The distinction between appearance and reality collapses, there is no sense in it.

To repeat the same argument in a little different form: either a certain complex is called a phaenomenon of something else — in this case they must have the same structure; or they differ in their structure — in that case the diversities of the one do not point to diversities of the other and we have no right to say that the relation of appearance and reality holds between them. We might assume all kinds of relation between them, simultaneity, causality, and what not, but evidently this is not what we mean when we speak of phaenomenon or appearances.

These considerations would suffice to show — even if it were not obvious for a simpler and more fundamental reason — that the distinction between reality and appearance with all its philosophical implications is altogether unjustified. There are no phaenomena or appearances in the metaphysical sense of these words; there are no different degrees of reality — a genuine kind — and a "merely" phaenomenal kind, a metaphysical and empirical reality: there is just one sort of reality, and all our propositions deal with nothing else. Every proposition is either true or false, it either does or does not communicate the structure of a real fact; it is nonsense to say that it is "partly" true, or true "only for phaenomena and not for reality". It would be best to banish the words "phaenomenon" and, "appearance" from philosophy altogether, there are very few thinkers who have not been led astray by them.

If there is anything in the world of our experience that "points to" anything else — that is, if the truth of our propositions makes us believe in the truth of another one without there being any logical connection between the two-then the inferred reality must be of the same kind as the one from which it is inferred, we must be able to experience it, or, in short, to perceive it in some way or other.

Suppose I have a closed box and hear a rattling noise every time I shake it: I infer that when the box is opened I shall "see stones" or, when I put my hand into it, shall "touch certain hard objects". These inferences can easily be verified and no objections can be raised if I call the rattling noise a "phaenomenon" and the stones the "reality" which is responsible for the appearance of the noise. But evidently the rattling is just as real as the sight or touch of the stones; they are, all of them physical processes correlated in a certain way, and whatever inferences may be drawn concerning the box and its contents — they will always lead to physical processes, empirical facts, and cannot lead to anything "beyond", to metaphysical things.

It is worth noticing that the arguments which prove the existence of physical entities like atoms or electrons are of exactly the same nature as those which make us believe that there are stones in our rattling box. Even when there are no stones in a box, the physicist observes certain symptoms which make him declare that it is not empty, but full of air, and that the air consists of molecules, and so on. It is true, we do not say that we "perceive" the molecules in the same way as we do the stones: nevertheless the verification of the existence of atoms or other physical entities is not essentially different from the case of visible and tangible objects, it would not even be correct to say that the chain of reasoning is longer in one case, shorter in the other. Atoms, therefore, are empirical entities just like stones, and just as real. In fact the physicist has a right to say that "stone" in nothing but a name for a complex of atoms, and that we have just as much knowledge of stones (and no more) than we have of the atoms of which they are composed.

This illustrations show that the supposed transition from a known appearance to an unknown reality is nothing but the transition from one empirical fact to another, both of which can be known equally well. And what is evident from these examples is a special case of a most general insight: just as in this case there would be no sense in speaking of atoms at all unless they were empirical facts about which we can make any number of verifiable assertions, so there is no meaning in a sentence that speaks of anything in the world as absolutely unknowable, i.e. as beyond the reach of every possible experience.

Every proposition is essentially verifiable. This is the short fundamental principle of philosophizing; we shall do well to devote the rest of our time to its elucidation.

Wherever we assert anything we must, at least in principle, be able to say how the truth of our assertion can be tested, otherwise we do not know what we are talking about; our words do not form a real proposition at all, they are mere noises without meaning. (This must be admitted by every one who ask himself sincerely and carefully how he becomes aware of the meaning of a proposition.) What criterion have we to find out whether the meaning of a sentence has been grasped? How can I assure myself, for instance, that a pupil has properly understood the sense of a proposition which I try to explain to him?

There is only one answer, and it is this: a person knows the meaning of a proposition if he is able to indicate exactly the circumstances under which it would be true (and distinguish them from the circumstances which would make it false). This is the way in which Truth and Meaning are connected (it is clear that they must be connected in some way). To indicate the meaning of a proposition and to indicate the way in which it is verified are identical procedures.

Every proposition may be regarded as an answer to a question, or (if the question is difficult) as the solution of a problem. A sentence which has the grammatical form of a question (with an interrogation mark at the end) will have meaning only if we can indicate a method of answering it. It may be technically impossible for us to do what the method prescribes, but we must be able to point out some way in which the answer could be found. If we are, in principle, unable to do this, then our sentence is no genuine question at all. And where there is no question there can be no answer; we are confronted with an "insolvable problem". This is the only case of an "absolutely unanswerable" question: it is unanswerable, because it is no question. It may look like one, because outwardly it has the grammatical form of a question, but in reality it is a meaningless series of words, followed by a question mark.

Now we understand the nature of the so-called insolvable problem about which philosophers have worried so much: they are insolvable not because their solution lies in a region forever inaccessible to the knowing mind, not because they pass the power of our understanding, but simply because they are no problems.

Unfortunately — no, fortunately — all genuine "metaphysical questions" turn out to be of this kind. Metaphysics, as we stated before, consists essentially in the attempt to express content, i.e. in a self-contradictory enterprise, but it is by no means easy to see that a question inquiring into the nature of content is nothing but a meaningless arrangement of words. The difficulty of perceiving this is the real cause of all the troubles from which philosophical speculation has been suffering for about twenty-five centuries. If the nonsense in the typical metaphysical issues had been as easy to detect as the lack of meaning (say) in the question, "Is time more logical than space?" most of the futile discussions of our great thinkers could have been avoided.

The situation is made more complex by the fact, that in many cases the verbal formulation of the doubtful issues admits of two interpretations: one in which the words (or at least one of them) stand for content — and in this case the sentence expresses nothing — and another one in which the whole can be regarded as a structure complying with the rules of logical grammar: in this case the issue is changed into a real scientific question which must be answered by observation and experiment, the ordinary methods of experience (only the second interpretation, of course, is really an interpretation, the first one gives a semblance of meaning only).

An instructive example of the situation is afforded by the formulations which are supposed to express the metaphysical positions of idealism and materialism. In my last lecture I have treated the sentence "The internal nature of everything is Mind (or Matter)" as a metaphysical assertion in which the word Mind (or Matter) was supposed to signify content, and I have tried to show that this deprives the assertion of its meaning. But there is also a legitimate use of the words mind and matter, or soul and body or mental and physical. There is for, instance, perfectly good sense in my words when I say: "I am suffering from mental and from physical pain" although it may not be an easy task to get a perfectly satisfactory insight into the meaning of such a sentence. Without going into details, for which we have no room here, we know beforehand that the words Mind and Body, when used legitimately must in some way indicate different logical structures, and we may hold that the difference between these structures must reveal itself somehow — or rather, is nothing but — the difference between the logical form of propositions belonging to psychology and of propositions belonging to physical science. (In other words: there are two languages differing in the rules of logical grammar which for the sake of convenience, we prescribe for them, words of which they are formed. The difficulties of the so-called psychological problem arise from a careless confusion of the two languages. You cannot use different rules of grammar incompatible with each other, in one and the same sentence without speaking nonsense.)

Thus, if we use the word Mind in its nonmetaphysical meaning and substitute this in the idealistic phrase, the assertion that everything in the world is essentially mental becomes: "All real facts can be expressed in psychological language". This is a very vague statement because the language of psychology, owing to the primitive state of this science, is exceedingly fragmentary, and the rules of its grammar are rather ill-defined; nevertheless it is a statement from which special verifiable propositions can be derived, empirical propositions which can be tested by observation. Experience, as far as I am aware, does not afford us any reasons to believe that the structure of all physical laws is the same as that of psychological laws, so that the language of the latter could conveniently be used for the expression of the first. On the other hand a great deal of empirical evidence seems to support the statement resulting from the transformation of the "materialistic" thesis that there are no limits to the applicability of the language of physics. It does seem to be true that all facts and events without exception have a logical form which lends itself to an expression by means of physical concepts. Experience seems to show that any process which we usually represent by psychological phrases employing terms like: feeling, perception, volition etc., can also be expressed in terms of physical concepts such as: stimulus, response, brain process, nervous discharge, and so forth. If this is correct, it may be regarded as a justification of certain ideas from which the metaphysical views of Democritus and his followers have sprung, but Materialism itself, as a metaphysic, remains as nonsensical as before. The question of metaphysics is so important that I may perhaps be permitted to give another illustration of the way in which it disappears from our philosophy.

Descartes, as is well known, maintained the view that only human beings were endowed with "consciousness" and that we must look upon animals as mere automata behaving exactly "as if" they were "conscious" creatures, but in reality being condemned to a "soulless" existence. One may easily and justly point out that Descartes' argument might be extended to our human fellow-beings. How can I ever be sure that my human brothers and sisters are more than mechanical automata and possess a consciousness similar to my own?

Most philosophers, I believe, are inclined to regard the question as a genuine question, and to answer it in this way: the behaviour of all human beings, and also the behaviour of all animals, down to insects and worms, is, in the most important respects so similar to my own behaviour, that I must infer the existence of consciousness "within" them; it is an inference by analogy, it is true, but based on such striking correspondence that it must be regarded as valid with a degree of probability which can hardly be distinguished from certainty. Nevertheless these philosophers admit that the probability is not exactly equal to 1. That it is not absolute certainty, and that here we are confronted with a case where absolute certainty can never be gained. According to their opinion the existence of consciousness in beings other than myself is a typical unsolvable problem. There is no imaginable way of deciding it. — What are we to think of it ? Our verdict is simple: if the question is really definitely unanswerable it can be only because there is no meaning in it. And if this is so, if there is no problem at all, there can be no probable answer either, it must be nonsense to assert that animals and human beings "very likely" possess consciousness. We can speak of probability only where there is at least a theorical possibility of discovering the truth. The fact is that our question is actually meaningless because it is interpreted in a metaphysical way: the word "consciousness" (one of the most dangerous terms in modern philosophy) is supposed to stand for content, and this is the reason why it was declared that we could not be absolutely sure of its existence except in our own ego, for did not content require intuition and was not intuition restricted to our own consciousness ? I know that most people find it very difficult to admit that there is no sense in their reasoning, but I must insist that without admitting it we cannot even take the first step in philosophy.

Our "problem" is meaningless, because the word "consciousness" occurs in it in such a way that we cannot possibly express what we mean by it. It is used in such a way that it makes it no discoverable difference in the world whether my fellow creatures are "conscious" beings or not. Whether the answer is "yes" or "no": it cannot be verified and this means that we did not know what we were talking about when we put the question.

It is one of the most important tasks of philosophy to analyse how the word "consciousness" must be interpreted in order make sense in different contents. We know, of course, that some structures must be indicated by it. Keeping this in mind we can easily give a non-metaphysical interpretation to our question: "are animals conscious beings?" If it is to be a real legitimate question it can mean nothing but: "does the behaviour of animals show a certain structure?" Now it has become a genuine problem and can receive a definite answer. The answer is, of course, not given by the philosopher but by the biologist. It is his business to define carefully the kind of structure which comes into question (he will probably describe it in terms of "stimuli" and "responses"), and to state by observation in each case whether a particular animal or human being under particular circumstances exhibits this particular structure. This is an entirely empirical statement to which truth or probability may be ascribed in the same way as to any other expression of a fact. It must be noted that wherever the phrase "a person is conscious (or unconscious)" is used in every day life it has a perfectly good meaning and is verifiable because it expresses nothing but observable facts (which a physician, for instance may enumerate).

It is only on the lips of the metaphysician that the word is employed in a different way, in a "philosophic" way, which he believes to be a consistent interpretation, but which actually is a metaphysical abuse.

Our discussion of the "problem" of other people's "consciousness" or "soul" has shown that the confusion is due not only to a careless use or lack of analysis of the terms "consciousness" or "self" but that a misunderstanding of "existence" has also something to do with it. For clearly our question could have been formulated by asking: "Does consciousness or 'a soul' or 'a mind' exist in other living being?" The same misunderstanding is the cause of the nonsensical problem concerning the "Existence of an External World". In order to get rid of such meaningless questions we need only remember, once for all, that, since every proposition expresses a fact by picturing its structure, this must also be true for propositions asserting the "existence" of something or other. The only meaning such a proposition can have is that it pictures a certain structure of our experience.

This was seen quite clearly even by Kant. He expressed it in his own way by saying that the "reality" was a "category", but from his explanation of his own thought we can infer that what he had in mind practically coincides with the interpretation we have to give to the term "existence".

According to this interpretation such questions as: "Does the inside of the sun exist?", "Did the earth exist before it was perceived by any human beings?" etc. have a perfectly good sense, and must, of course, be answered in the affirmative. There are certain ways of verifying these positive answers, certain scientific reasons for believing them to be true, and they assure us of the reality of mountains and oceans, stars, clouds, trees and fellow men by the same methods of observation or experience by which we learn the truth of every proposition. If by "external world" we mean their empirical reality, its existence as a problem, and if the philosopher means something else, if he is not satisfied with empirical reality, he must tell us what he does mean. He says he is concerned with "transcendent" reality. We do not understand this word and ask him for an explanation, which he may give by saying that "transcendent" refers to genuine metaphysical being, not to merely empirical reality. If we ask him what is meant by this distinction and how a proposition asserting transcendental existence of anything can be verified, he must answer that there is no way of ever testing the truth of such a proposition definitely. We must inform him that, if this is the case there is no meaning in his propositions about a metaphysical external world and that we must continue to use this phrase in the good old innocent sense in which it stands for stars, mountains, and trees, as contrasted with dreams, feelings and wishes which form the "internal" world. We must inform the philosopher that it is not his business to tell us what is real and what is unreal — this must be left to experience and science — but it is his business to tell us what we mean when we judge of a certain thing or event that it is "real". And in every case he can answer the question concerning the sense of such a judgment only by pointing to the operations by which we should actually verify its truth. If I know exactly what I have to do in order to find out whether the shilling in my pocket is real or imagined, then I know also what I mean by declaring that the shilling is a real part of the external world and there is no other meaning of the words "real" or "external world".

For, let us repeat it once more: the complete and only way of giving the meaning of a proposition consists in indicating what would have to be done in order to find out if the proposition is true or false (no matter whether we are actually able to do it). This insight is often called "the experimental (or operational) theory of meaning" but I should like to point out that it would be unjust to call it by such an imposing name. A "theory" consists of a set of propositions which you may believe or deny, but our principle is a simple triviality about which there can be no dispute. It is not even an "opinion", since it indicates a condition without which no opinion can be formulated. It is not a theory, for its acknowledgement must precede the building of any theory. A proposition has no meaning unless it makes a discoverable difference whether it is true or false; a proposition whose truth or falsity would leave the world unchanged, does not say anything about the world, it is an empty sentence without meaning. "Understanding" a proposition means: being able to indicate the circumstances which would make it true. But we could not describe these circumstances if we were not able to recognise them, and if they are recognisable it means that the proposition is in "principle" verifiable. Thus understanding a statement and knowing the way of its verification is one and the same thing.

This principle is nothing surprising or new or wonderful: on the contrary, it has always been followed and used by science as a matter of course, at least unconsciously, and in the same way it has always been acknowledged by common sense in everyday life; the only place where it has been neglected is in philosophical discussions. Science could not possibly act otherwise, because its whole business consists in testing the truth of propositions, and they cannot be tested except on the strength of our principle.

Now and then it happens in the development of science that a concept is used in a vague manner so that there is no absolute clarity about the verification of the propositions in which the concept occurs. Within certain limits of accuracy the ordinary tests of their truth may suffice for years or centuries and then suddenly some contradiction will show itself and force the scientist to inquire carefully into the signification of his symbols. He will have to stop and think. He will pause in his scientific investigation and turn to philosophic meditations until the meaning of his propositions has become perfectly clear to him.

The most famous instance of this kind, and one which will forever be memorable, is Einstein's analysis of the concept of time. His great achievement, which is the basis of the Restricted Theory of Relativity, consisted simply in stating the meaning of assertions that physicists used to make about the simultaneity of events in different places. He showed that physics had never been quite clear about the signification of the term "simultaneity", and that the only way of becoming clear was to answer the question, "how is the proposition (two distant events happen at the same time) actually verified?" If we show how this verification is done we have shown the complete sense of the proposition and of the term, and it has no meaning besides. All those philosophers who have condemned Einstein's ideas and theory (and some are condemning it even to this day) do it on the ground that there is a simultaneity the signification of which is understood without verification. They call it "absolute simultaneity". This sounds very well, but unfortunately those philosophers have failed to tell us how their simultaneity can actually be distinguished from that of Einstein; they have not been able to give us the slightest hint how anyone can ever find out whether two distant events occur "absolutely simultaneously" or not. Considering this I think we must take the liberty of regarding their assertion as meaningless.

I have just alluded to the difference between the scientific attitude and the philosophical attitude. We can formulate it by saying. Science is the pursuit of Thruth, and Philosophy is the Pursuit of Meaning.

Of course the two cannot actually be separated. It is impossible to discover the truth of a proposition without being acquainted with its meaning. No one can essentially contribute to the progress of science without having before his mind the genuine and final sense of the Truths he is investigating. That is why all great scientists have also been Philosophers. They have been inspired by the philosophic spirit. Nevertheless the distinction must be made, and it has the advantage of giving a satisfactory answer to the endless questions concerning the nature and task of philosophy. Our definition of philosophy gives a clear and full account of its relationship to science and makes it easy to understand the historical development of their relationship.

Philosophy is most certainly not a science not even the Science of the sciences, and it has been one of its greatest misfortunes that it has been mistaken for one, and that philosophers have, in outward appearance adopted scientific methods and language. It often makes them a little ridiculous, and there is a good deal of truth in the way in which Schopenhauer describes the contrast between the genuine philosopher and the academic scholar who regards philosophy as a sort of scientific pursuit.

A Science is a connected system of propositions which form the result of patient observation and clever combination. But Philosophy, as Wittgenstein has put out "is not a theory, but an activity. The result of philosophy- is not a number of "philosophical propositions", but to make propositions: "clear". It is a matter of fact, the result of the pursuit of meaning cannot be formulated in ordinary propositions, for if we ask for an explanation of a meaning, and the answer is given in a sentence, we should have to ask again "but what is the meaning of this sentence?" and so on. If we are to arrive at any sense at all this series of questions and definitions cannot go on forever, and the only way in which it can end is by some prescription that will tell us what to do in order to get the final meaning. You want to know what this particular note here signifies? Well, strike this particular key of this piano! That puts an end to your questions.

Thus a teacher of philosophy cannot provide us with certain true propositions which will represent the solution of the "philosophical problem": he can only teach us the activity or art of thinking which will enable us for ourselves to analyse or discover the meaning of all questions. And then we shall see that the so-called philosophical problems are either meaningless combinations of symbols, or can be interpreted as perfectly sound questions. But in the latter case they have ceased to be philosophical and must be handed over to the scientist who will try to answer them by his methods of observation and experiment.

Kant, who in spite of his complicated philosophy had many bright moments of profound insight, has said that he could teach philosophizing, but not philosophy. That was a very wise statement, and it implies that philosophy is nothing but an art or activity, that there are no philosophical propositions, and consequently no system of philosophy (another great thinker who seems to have been well aware of the nature and place of philosophy was Leibniz. When he founded the Prussian Academy of Science in Berlin and sketched out the plans for its constitution, he assigned a place in it to all the sciences, but philosophy was not one of them. He must have felt somehow that it could not be regarded as the pursuit of a particular kind of truth, but that the determination of meaning must pervade every search for truth).

When we look for the most typical example of a philosophical mind we must direct our eyes towards Socrates. All the efforts of his acute mind and his fervent heart were devoted to the pursuit of meaning. He tried all his life to discover what it really was that men had in their minds when they discussed about virtue and the Good, about Justice and Piety; and his famous irony consisted in showing his disciples that even in their strongest assertions they did not know what they were talking about and that in their most ardent beliefs they hardly knew what they were believing.

As long as people speak and write so much more than they think, using their words in a mechanical conventional manner, disagreeing about the Good (in ethics) the Beautiful (in Aesthetics) and the Useful (in Economies and Politics), we shall stand in great need of men with Socratic minds in all our human pursuits. And since also in science the great discoveries are made only by those superior minds who in the routine of their experimental and theoretical research keep wondering what it is all about and therefore remain engaged in the pursuit of meaning, the philosophical attitude will be recognised more than ever as the most powerful force and the best part of scientific attitude.