Tarski, in his important book Der Wahrheitsbegriff in den formalisierten Sprachen, has shown that the words 'true' and 'false', as applied to the sentences of a given language, always require another language, of higher order, for their adequate definition. The conception of a hierarchy of languages is involved in the theory of types, which, in some form, is necessary for the solution of the paradoxes; it plays an important part in Carnap's work as well as in Tarski's. I suggested it in my introduction to Wittgenstein's Tractatus, as an escape from his theory that syntax can only be 'shown', not expressed in words. The arguments for the necessity of a hierarchy of languages are overwhelming, and I shall henceforth assume their validity. [These arguments are derived from the paradoxes; their applicability to the words 'true' and 'false' is derived from the paradox of the liar.

My inference from the paradox of the liar was, in outline, as follows; A man says 'I am lying', i.e. 'there is a propositions such that I assert p and p is false'. We may, if we like, make the matter more precise by supposing that, at 5.30, he says 'between 5.29 and 5.31 I make a false statement', but that throughout the rest of the two minutes concerned he says nothing. Let us call this statement 'q'. If q is true, he makes a false statement during the crucial two minutes; but q is his only statement in this period: therefore q must be false. But if q is false, then every statement that he makes during the two minutes must be true, and therefore q must be true, since he makes it during the two minutes. Thus if q is true it is false, and if it is false it is true.

Let 'A(p)' mean' I assert p between 5.29 and 5.31'. Then q is 'there is a proposition p such that A(p) and p is false'. The contradiction emerges from the supposition that q is the proposition p in question. But if there is a hierarchy of meanings of the word 'false' corresponding to a hierarchy of propositions, we shall have to substitute for q something more definite, i.e.' there is a proposition p of order n, such that A(p) and p has falsehood of order n'. Here n may be any integer: but whatever integer it is, q will be of order n + 1, and will not be capable of truth or falsehood of order n. Since I make no assertion of order n, q is false, and, since q is not a possible value of p, the argument that q is also true collapses. The man who says 'I am telling a lie of order n' is telling a lie, but of order n + 1. Other ways of evading the paradox have been suggested, e.g. by Ramsey, Foundations of Mathematics, p. 48.]

The hierarchy must extend upwards indefinitely, but not downwards, since, if it did, language could never get started. There must, therefore, be a language of lowest type. I shall [60] define one such language, not the only possible one. [My hierarchy of languages is not identical with Carnap's or Tarski's.] I shall call this sometimes the 'object-language', sometimes the 'primary language'. My purpose, in the present chapter, is to define and describe this basic language. The languages which follow in the hierarchy I shall call secondary, tertiary, and so on; it is to be understood that each language contains all its predecessors.

The primary language, we shall find, can be defined both logically and psychologically; but before attempting formal definitions it will be well to make a preliminary informal exploration.

It is clear, from Tarski's argument, that the words 'true' and 'false' cannot occur in the primary language; for these words, as applied to sentences in the n^th language, belong to the (n + 1)^th language. This does not mean that sentences in the primary language are neither true nor false, but that, if 'p' is a sentence in this language, the two sentences 'p is true' and 'p is false' belong to the secondary language. This is, indeed, obvious apart from Tarksi's argument. For, if there is a primary language, its words must not be such as presuppose the existence of a language. Now 'true' and 'false' are words applicable to sentences, and thus presuppose the existence of language. (I do not mean to deny that a memory consisting of images, not words, may be 'true' or 'false'; but this is in a somewhat different sense, which need not concern us at present.) In the primary language, therefore, though we can make assertions, we cannot say that our own assertions or those of others are either true or false.

When I say that we make assertions in the primary language, I must guard against a misunderstanding, for the word 'assertion' is ambiguous. It is used, sometimes, as the antithesis of denial, and in this sense it cannot occur in the primary language. Denial presupposes a form of words, and proceeds to state that this form of words is false. The word 'not' is only significant when attached to a sentence, and therefore presupposes language. Consequently, if 'p' is a sentence of the primary language, 'not-p' is a sentence of the secondary language. It is easy to fall into confusion, since 'p', without verbal alteration, may [61] express a sentence only possible in the secondary language. Suppose, for example, you have taken salt by mistake instead of sugar, and you exclaim 'this is not sugar'. This is a denial, and belongs to the secondary language. You now use a different sprinkler, and say with relief 'this is sugar'. Psychologically, you are answering affirmatively the question 'is this sugar?' You are in fact saying, as unpedantically as you can: 'the sentence "this is sugar" is true'. Therefore what you mean is something which cannot be said in the primary language, although the same form of words can express a sentence in the primary language. The assertion which is the antithesis of denial belongs to the secondary language; the assertion which belongs to the primary language has no antithesis.

Just the same kind of considerations as apply to 'not' apply to 'or' and 'but' and conjunctions generally. Conjunctions, as their name implies, join words, and have no meaning in isolation; they therefore presuppose the existence of a language. The same applies to 'all' and 'some'; you can only have all of 'swe'i you can only have all of something, or some of something, and in the absence of other words 'all' and 'some' are meaningless. This argument also applies to 'the'.

Thus logical words, without exception, are absent from the primary language. All of them, in fact, presuppose propositional form: 'not' and conjunctions presuppose propositions, while 'all' and 'some' and 'the' presuppose propositional functions.

Ordinary language contains a number of purely syntactical words, such as 'is' and 'than', which must obviously be excluded from the primary language. Such words, unlike those that we have hitherto considered, are in fact wholly unnecessary, and do not appear in symbolic logical languages. Instead of 'A is earlier than B' we say 'A precedes B'; instead of 'A is yellow' a logical language will say 'yellow(A)'; instead of 'there are smiling villains' we say: it is false that all values of 'either x does not smile or x is not a villain' are false. 'Existence' and 'Being', as they occur in traditional metaphysics, are hypostatized forms of certain meanings of 'is'. Since 'is' does, not belong to the primary language, 'existence' and 'being', if they are to mean [62] anything, must be linguistic concepts not directly applicable to objects.

There is another very important class of words that must be at least provisionally excluded, namely such words as 'believe', 'desire', 'doubt', all of which, when they occur in a sentence, must be followed by a subordinate sentence telling what it is that is believed or desired or doubted. Such words, so far as I have been able to discover, are always psychological, and involve what I call 'propositional attitudes'. For the present, I will merely point out that they differ from such words as 'or' in an important respect, namely that they are necessary for the description of observable phenomena. If I want to see the paper, that is a fact which I can easily observe, and yet 'want' is a word which has to be followed by a subordinate sentence if anything significant is to result. Such words raise problems, and are perhaps capable of being analysed in such a way as to make them able to take their place in the primary language. But as this is not prima facie possible, I shall for the present assume that they are to be excluded. I shall devote a later chapter to the discussion of this subject.

We can now partially define the primary or object-language as a language consisting wholly of 'obiect-words', [There must be syntax. but it need not be rendered explicit by the use of syntactical words, such as 'is'.] where 'object-words' are defined, logically, as words having meaning in isolation, and, psychologically, as words which have been learnt without its being necessary to have previously learnt any other words. These two definitions are not strictly equivalent, and where they conflict the logical definition is to be preferred. They would become equivalent if we were allowed to suppose an indefinite extension of our perceptive faculties. We could not, in fact, recognize a chiligon by merely looking at it, but we can easily imagine beings capable of this feat. On the other hand, it is clearly impossible that any being's knowledge of language should begin with an understanding of the word 'or', although the meaning of this word is not learnt from a formal definition. Thus in addition to the class of actual object-words, there is a class of possible object-words. For many purposes the class of [63] actual and possible object-words is more important than the class of actual object-words.

In later life, when we learn the meaning of a new word, we usually do so through the dictionary, that is to say, by a definition in terms of words of which we already know the meaning. But since the dictionary defines words by means of other words, there must be some words of which we know the meaning without a verbal definition. Of these words, a certain small number do not belong to the primary language; such are the words 'or' and 'not'. But the immense majority are words in the primary language, and we have now to consider the process of learning what these words mean. Dictionary words may be ignored, since they are theoretically superfluous; for wherever they occur they can be replaced by their definitions.

In the learning of an object-word, there are four things to be considered: the understanding of the heard sound in the presence of the object, the understanding of it in the absence of the object, the speaking of the word in the presence of the object, and the speaking of it in the absence of the object. Roughly speaking, this is the order in which a child acquires these four capacities.

Understanding a heard word may be defined behaviouristically or in terms of individual psychology. When we say that a dog understands a word, all that we have a right to mean is that he behaves in an appropriate manner when he hears it; what he 'thinks' we cannot know. Consider, for example, the process of teaching a dog to know his name. The process consists of calling him, rewarding him when he comes, and punishing him when he does not. We may imagine that, to the dog, his name means: 'either I shall be rewarded because I approach my master, or I shall be punished because I do not'. Which alternative is considered the more probable is shown by the tail. The association, in this case, is a pleasure-pain association, and therefore imperatives are what the dog understands most easily. But he can understand a sentence in the indicative, provided its content has sufficient emotional importance; for instance, the sentence 'dinner!' which means, and is understood to mean: 'you are now about to receive the nourishment that you desire.' When I [64] say that this is understood, I mean that, when the dog hears the word, he behaves very much as he would if you had a plate of food in your hand. We say the dog 'knows' the word, but what we ought to say is that the word produces behaviour similar to that which the sight or smell of a dinner out of reach would produce.

The meaning of an object-word can only be learnt by hearing it frequently pronounced in the presence of the object. The association between word and object is just like any other habitual association, e.g. that between sight and touch. When the association has been established, the object suggests the word, and the word suggests the object, just as an object seen suggests sensations of touch, and an object touched in the dark suggests sensations of sight. Association and habit are not specially connected with language; they are characteristics of psychology and physiology generally. How they are to be interpreted is, of course, a difficult and controversial question, but it is not a question which specially concerns the theory of language.

As soon as the association between an object-word and what it means has been established, the word is 'understood' in the absence of the object, that is to say, it 'suggests' the object in exactly the same sense in which sight and touch suggest one another.

Suppose you are with a man who suddenly says 'fox' because he sees a fox, and suppose that, though you hear him, you do not see the fox. What actually happens to you as a result of your understanding the word 'fox'? You look about you, but this you would have done if he had said 'wolf' or 'zebra'. You may have an image of a fox. But what, from the observer's standpoint, shows your understanding of the word, is that you behave (within limits) as you would have done if you had seen the fox.

Generally, when you hear an object-word which you understand, your behaviour is, up to a point, that which the object itself would have caused. This may occur without any 'mental' intermediary, by the ordinary rules of conditioned reflexes, since the word has become associated with the object. In the morning you may be told 'breakfast is ready', or you may smell the bacon. Either may have the same effect upon your actions. [65] The association between the smell and the bacon is 'natural', that is to say it is not a result of any human behaviour. But the association between the word 'breakfast' and breakfast is a social matter, which exists only for English-speaking people. This, however, is only relevant when we are thinking of the community as a whole. Each child learns the language of its parents as it learns to walk. Certain associations between words and things are produced in it by daily experience, and have as much the appearance of natural laws as have the properties of eggs or matches; indeed they are exactly on the same level so long as the child is not taken to a foreign country.

It is only some words that are learnt in this way. No one learns the word 'procrastination' by hearing it frequently pronounced on occasions when some one is dilatory. We learn, by direct association with what the word means, not only proper names of the people we know, class-names such as 'man' and 'dog', names of sensible qualities such as 'yellow', 'hard', 'sweet', and names of actions such as 'walk', 'run', 'eat', 'drink', but also such words as 'up' and 'down', 'in' and 'out', 'before' and 'after', and even 'quick' and 'slow'. But we do not learn in this way either complicated words such as 'dodecahedron' or logical words such as 'not', 'or', 'the', 'all', 'some'. Logical words, as we have seen, presuppose language; in fact, they presuppose what, in an earlier chapter, we spoke of as 'atomic forms'. Such words belong to a stage of language that is no longer primitive, and should be carefully excluded from a consideration of those ways of speaking which are most intimately related to non-linguistic occurrences.

What kind of simplicity makes the understanding of a word into an example of understanding an object-language? For it is to be observed that a sentence may be spoken in the object-language and understood in a language of higher order, or vice versa. If you excite a dog by saying 'rats!' when there are no rats, your speech belongs to a language of higher order, since it is not caused by rats, but the dog's understanding of it belongs to the object-language. A heard word belongs to the object-language when it causes a reaction appropriate to what the word means. If some one says 'hark, hark, the lark', you may listen, [66] or you may say 'at heaven's gate sings'; in the former case, what you have heard belongs to the object-language, in the latter case, not. Whenever you doubt or reject what you are told, your hearing does not belong to the object-language; for in such a case you are lingering on the words, whereas in the object-language the words are transparent, i.e. their effects upon your behaviour depend only upon what they mean, and are, up to a point, identical with the effects that would result from the sensible presence of what they designate.

In learning to speak, there are two elements, first, the muscular dexterity, and second, the habit of using a word on appropriate occasions. We may ignore the muscular dexterity, which can be acquired by parrots. Children, make many articulate sounds spontaneously, and have also an impulse to imitate the sounds made by adults. When they make a sound which the adults consider appropriate to the environment, they find the results pleasant. Thus, by the usual pleasure-pain mechanism which is employed in training performing animals, children learn, in time, to utter noises appropriate to objects that are sensibly present, and then, almost immediately, they learn to use the same noises when they desire the objects. As soon as this has happened, they possess an object-language: objects suggest their names, their names suggest them, and their names may be suggested, not only by the presence of the objects, but by the thought of them.

I pass now from the learning of an object-language to its characteristics ewhen learnt.

We may, as we have seen, divide words into three classes:

1. object-words, of which we learn the meaning by directly acquiring an association between the word and the thing;
2. propositional words, which do not belong to the object-language;
3. dictionary words, of which we learn the meaning through a verbal definition.

Let us now consider how much, in the way of language, can be done by object-words alone. I shall assume, for this purpose, that the person considered has had every possible opportunity of acquiring object-words: he has seen Mount Everest and Popocatepetl, the anaconda, and the axolotl, he is acquainted with Chiang Kai-shek and Stalin, he has tasted birds' nests and shark's fins, and altogether has a wide experience of the sensible world. But he has been too busy seeing the world to acquire the use of such words as 'not', 'or', 'some', etc. If you say to him 'is there any country that you have not visited?' he will not know what you mean. The question is: what will such a person know, and what will he not know?

Can we say: 'he will know everything that can be known by observation alone, but nothing that needs inference'? Let us first alter our question, and ask, not what can he know, but what can he express in words?

To begin with: if he can put every observable fact into words, he must have as many words as facts; now some-words are among facts; therefore the number of his words must be infinite. This is impossible; consequently there are facts he leaves unexpressed. The case is analogous to Royce's bottle with a label on which there was a picture of the bottle, including, of course, a picture on the label.

But although he must leave out some observable facts, there is not any one observable fact of which we can say 'he must leave this one out.' He is in the position of a man who wishes to pack three suits into a suit-case that will only hold two; he must leave one out, but there is not one that he must leave out. So our travelled friend, we will suppose, sees a man called Tom, and without difficulty he says: 'I see Tom'. This remark is itself an observable fact, so he says: 'I say that I see Tom'. This again is an observable fact, so he says: 'I say that I say that I see Tom'. There is no one definite point at which he must break off this series, but he must break it off somewhere, and at that point there is an observable fact which he does not express in words. It seems, therefore, that it is impossible for a mortal [68] to give verbal expression to every observable fact, but that, nevertheless, every observable fact is such that a mortal could give verbal expression to it. This is not a contradiction.

We have thus two different totals to consider: first, the total of the man's actual statements, and secondly the total of possible statements out of which his actual statements must be chosen. But what is a 'possible' statement? Statements are physical occurrences, like thundersyorms or railway accidents; but at least a novelist or poet can describe a thunderstorm that never took place. But it is difficult to describe a statement without making it. In describing a political speech, you may remark: 'what Sir Somebody So-and-So did not say was . . . ' and then follows a statement; that is to say, in order to say that a statement was not made, we have to make it, except in the rare instances of statements that have names, such as the Coronation Oath.

There are, however, ways of avoiding this difficulty, the best of which is due to Gödel. We assume a completely formalized laqguage, with an entirely explicit vocabulary and syntax. We assign numbers to the words of the vocabulary, and hence, by arithmetical rules, to all possible sentences in the language. If, as we are assuming, the initial vocabulary is finite, but there is no limit to the length of sentences (except that they must be finite), the number of possible sentences will be the same as the number of finite integers. Consequently, if n is any finite integer, there is one definite sentence which is the n^th, and our rules will enable us to construct it, given n. We can now make all sorts of statements about Mr A's statements, without having actually to make his statements. We might say 'Mr A never makes a statement of which the number is divisible by 13', or 'all Mr A's statements have numbers which are prime'.

But there are still difficulties, of the kind emphasized by the finitists. We are used to thinking of the whole series of natural numbers as in some sense 'given', and we have utilized this idea to give definiteness to the theory of possible statements. But how about numbers which no one has ever mentioned or thought of? What is a number except something that occurs in a statement? And, if so, a number that has never been mentioned [69] involves a possible statement, which cannot, without circularity be defined by means of such a number.

This subject cannot be pursued at present, since it would take us too deep into the subject of logical language. Let us see whether, ignoring such logical points, we can be a little more definite about the possibilities of a language which contains only obiect-words.

Among object-words, as we saw, are included a certain number of verbs, such as 'run', 'eat', 'shout', and even some propositions such as 'in' and 'above' and 'before'. All that is essential to an object-word is some similarity among a set of phenomena, which is sufficiently striking for an association to be established between instances of the set and instances of the word for the set, the method of establishing the association being that, for some time, the word is frequently heard when a member of the set is seen. It is obvious that what can be learnt in this way depends upon psychological capacity and interest. The similarity between different instances of eating is likely to strike a child, because eating is interesting; but in order to learn in this way the meaning of the word 'dodecagon' a child would need a precocity of geometrical interest surpassing Pascal's and a superhuman capacity for perceiving Gestalt. Such gifts are, however, not logically impossible. But how about 'or'? You cannot show a child examples of it in the sensible world. You can say: 'will you have pudding or pie?' but if the child says yes, you cannot find a nutriment which is 'pudding-or-pie'. And yet 'or' has a relation to experience; it is related to the experience of choice. But in choice we have before us two possible courses of action, that is to say, two actual thoughts as to courses of action. These thoughts may not involve explicit sentences, but no change is made in what is essential if we supposed them to be explicit. Thus 'or', as an element of experience, presupposes sentences, or something mental related in a similar manner to some other fact. When we say 'this or that' we are not saying something directly applicable to an object, but are stating a relation between saying 'this' and saying 'that'. Our statement is about statements, and only indirectly about objects.

Let us consider, in like manner, negative propositions which [70] seem to have an immediate relation to experience. Suppose you are told 'there is butter in the larder, but no cheese'. Although they seem equally based upon sensible experience in the larder, the two statements 'there is butter' and 'there is not cheese' are really on a very different level. There was a definite occurrence which was seeing butter, and which might have put the word 'butter' into your mind even if you had not been thinking of butter. But there was no occurrence which could be described as 'not seeing cheese' or as 'seeing the absence of cheese'. [This subject will be discussed again in a later chapter, and what is said above will be at once amplified and guarded against a too literal interpretation.] You must have looked at everything in the larder, and judged, in each case, 'this is not cheese'. You judged this, you did not see it; you saw what each thing was, not what it was not. To judge 'this is not cheese', you must have the word 'cheese', or some equivalent, in your mind already. There is a clash between what you see and the associations of the word 'cheese', and so you judge 'this is not cheese'. Of course, the same sort of thing may happen with an affirmative judgement, if it answers a previous question; you then say 'yes, this is cheese'. Here you really mean 'the statement "this is cheese" is true'; and when you say 'this is not cheese' you mean 'the statement "this is cheese" is false'. In either case, you are speaking about a statement, which you are not doing in a direct judgement of perception. The man, therefore, who understands only object-words, will be able to tell you everything that is in the larder, but will be unable to infer that there is no cheese. He will, moreover, have no conception of truth or falsehood; he can say 'this is butter' but not 'it is true that this is butter'.

The same sort of considerations apply to 'all' and 'some'. Suppose our unphilosophical observer goes to a small Welsh village in which everyone is called Williams. He will discover that A is called Williams, B is called Williams, and so on. He may, in fact, have discovered this about everybody in the village, but he cannot know that he has done so. To know it, he would have to know 'A, B, C, . . . are all the people in this village'. But this is like knowing that there is no cheese in the larder; it involves knowing 'nobody in this village is neither A nor B nor C [71] nor . . .'. And this is plainly not to be known by perception alone.

The case of'some' is a little less obvious. [This topic, again, will be resumed in a later chapter.] In the above case, will not our friend know that 'some people in this village are called Williams'? I think not. This is like 'pudding-or-pie'. From the standpoint of perception, none of them are 'some people'; they are the people they are. It is only by a detour through language that we can understand 'some people'. Whenever we make a statement about some of a collection, there are alternative possibilities in our minds; in each particular case, the statement may be true or false, and we assert that it is true in certain cases but perhaps not in all. We cannot express alternatives without introducing truth and falsehood, and truth and falsehood, as we have seen, are linguistic terms. A pure object-language, therefore, cannot contain the word 'some' any more than the word 'all'.

We have seen that the object-language, unlike languages of higher orders, does not contain the words 'true' and 'false' in any sense whatever. The next stage, in language is that in which we can not only speak the object-language, but can speak about it. In this second-type language, we can define what is meant by saying, of a sentence in the first-type language, that it is true. What is meant is that the sentence must mean something that can be noticed in a datum of perception. If you see a dog and say 'dog', you make a true statement. If you see a dog in a kennel and say 'dog in kennel', you make a true statement. There is no need of verbs for such sentences, and they may consist of single words.

One of the things that have seemed puzzling about language is that, in ordinary speech, sentences are true or false, but single words are neither. In the object-language this distinction does not exist. Every single word of this language is capable of standing alone, and, when it stands alone, means that it is applicable to the present datum of perception. In this language, when you say 'dog', your statement is false if it is a wolf that you are looking at. In ordinary speech, which is not sorted out into languages of different types, it is impossible to know, when the word 'dog' occurs by itself, whether it is being used as a word in the object-language [72] or in a linguistic manner, as when we say 'that is not a dog'. Obviously, when the word 'dog' can be used to deny the presence of a dog as well as to affirm it, the single word loses all assertive power. But in the object-language, upon which all others are based, every single word is an assertion.

Let us now restate the whole matter ot the object-language.

An object-word is a class of similar noises or utterances such that, from habit, they have become associated with a class of mutually similar occurrences frequently experienced at the same time as one of the noises or utterances in question. That is to say, let A₁, A₂, A₃ . . . be a set of similar occurrences, and let a₁, a₂, a₃ . . . be a set of similar noises or utterances; and suppose that when A₁ occurred you heard the noise at, when A₂ occurred you heard the noise a₂, and so on. After this has happened a great many times, you notice an occurrence A_n which is like A₁, A₂, A₃ . . ., and it causes you, by association, to utter or imagine a noise an which is like a₁, a₂, a₃ . . . If, now, A is a class of mutually similar occurrences of which A₁, A₂, A₃ . . . A_n are members, and a is a class of mutually similar noises or utterances of which a₁, a₂, a₃ . . . a_n are members, we may say that a is a word which is the name of the class A, or ' means' the class A. This is more or less vague, since there may be several classes which satisfy the above conditions for A and a. A child learning the object-language applies Mill's Canons of Induction, and gradually corrects his mistakes. If he knows a dog called 'Caesar', he may think this word applies to all dogs. On the other hand, if he knows a dog whom he calls 'dog', he may not apply this word to any other dog. Fortunately many occurrences fit into natural kind; in the lives of most children, anything that looks like a cat is a cat, and anything that looks like one's mother is one's mother. But for this piece of luck, learning to speak would be very difficult. It would be practically impossible if the temperature were such that most substances were gaseous.

If now, in a certain situation, you are impelled to say 'cat', that will be (so long as you are confined to the object-language) because some feature of the environment is associated with the word 'cat', which necessarily implies that this feature resembles the previous cats that caused the association. It may not resemble [73] them sufficiently to satisfy a zoologist; the beast may be a lynx or a young leopard. The association between the word and the object is not likely to be 'right' until you have seen many animals that were not cats but looked rather as if they were, and many other animals that were cats but looked rather as if they were not. But the word 'right', here, is a social word, denoting correct behaviour. As soon as certain beasts suggest the word 'cat' to you and others do not, you possess a language, though it may not be correct English.

Theoretically, given sufficient capacity, we could express in the object-language every non-linguistic occurrence. We can in fact observe fairly complicated occurrences, such as 'while John was putting the horse in the cart, the bull rushed out and I ran away', or 'as the curtain was falling, there were cries of "fire" and a stampede'. This sort of thing can be said in the object-language, though it would have to be translated into a sort of pidgin English. Whether it is possible to express in the object-language such observable facts as desires, beliefs, and doubts is a difficult question, which I shall discuss at length in a later chapter. What is certain is that the object-language does not contain the words 'true' and 'false', or logical words such as 'not', 'or', 'some', and 'all'. Logical words will be the subject of my next chapter.