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The idea that in order to get clear about the meaning of a general term one had to find the common element in all its applications, has shackled philosophical investigation; for it has not only led to no result, but also made the philosopher dismiss as irrelevant the concrete cases, which alone could have helped him to understand the usage of the general term. When Socrates asks the question, “what is knowledge?” he does not even regard it as a preliminary answer to enumerate cases of knowledge. If I wished to find out what sort of thing arithmetic is, I should be very content indeed to have investigated the case of a finite cardinal
The idea that in order to get clear about the meaning of a general term one had to find the common element in all its applications, has shackled philosophical investigation; for it has not only led to no result, but also made the philosopher dismiss as irrelevant the concrete cases, which alone could have helped him to understand the usage of the general term. When Socrates asks the question, “what is knowledge?” he does not even regard it as a preliminary answer to enumerate cases of knowledge. If I wished to find out what sort of thing arithmetic is, I should be very content indeed to have investigated the case of a finite cardinal {{MS reference|Ts-309,31}} arithmetic. For
 
Ts-309,31
 
arithmetic. For
 
(a) this would lead me on to all the more complicated cases,
 
(b) a finite cardinal arithmetic is not incomplete, it has no gaps which are then filled in by the rest of arithmetic.
 


:(a) this would lead me on to all the more complicated cases,
:(b) a finite cardinal arithmetic is not incomplete, it has no gaps which are then filled in by the rest of arithmetic.


What happens if from 4 till 4.30 A expects B to come to his room? In one sense in which the phrase “to expect something from 4 to 4.30” is used it certainly does not refer to one process or state of mind going on throughout that interval, but is a great many different activities, and states of mind. If for instance I expect B to come to tea, what happens may be this: At four o'clock I look at my diary and see the name ‘B’ against today's date; I prepare tea for two; I think for a moment “does B smoke?” and put out cigarettes; towards 4.30 I begin to feel impatient; I imagine B as he will look when he comes into my room. All this is called “expecting B from 4 to 4.30”. And there are endless variations to this process which we all describe by the same expression. If one asks what the different processes of expecting someone to tea have in common, the answer is that there is no single feature in common to all of them, though there are many common features overlapping. These cases of expectation form a family; they have family likenesses which are not clearly defined.
What happens if from 4 till 4.30 A expects B to come to his room? In one sense in which the phrase “to expect something from 4 to 4.30” is used it certainly does not refer to one process or state of mind going on throughout that interval, but is a great many different activities, and states of mind. If for instance I expect B to come to tea, what happens may be this: At four o'clock I look at my diary and see the name ‘B’ against today's date; I prepare tea for two; I think for a moment “does B smoke?” and put out cigarettes; towards 4.30 I begin to feel impatient; I imagine B as he will look when he comes into my room. All this is called “expecting B from 4 to 4.30”. And there are endless variations to this process which we all describe by the same expression. If one asks what the different processes of expecting someone to tea have in common, the answer is that there is no single feature in common to all of them, though there are many common features overlapping. These cases of expectation form a family; they have family likenesses which are not clearly defined.


 
There is a totally different use of the word “expectation” if we use it to mean a particular sensation. This use of the words like “wish”, “expectation”, etc., readily suggests itself. There is an obvious connection between this use and the one described above. There is no doubt that in many cases if we expect some one, in the first sense, some, or all, of the activities described are accompanied by a peculiar feeling, a tension; and it is natural {{MS reference|Ts-309,32}} to use the word “expectation” to mean this experience of tension.
 
There is a totally different use of the word “expectation” if we use it to mean a particular sensation. This use of the words like “wish”, “expectation”, etc., readily suggests itself. There is an obvious connection between this use and the one described above. There is no doubt that in many cases if we expect some one, in the first sense, some, or all, of the activities described are accompanied by a peculiar feeling, a tension; and it is natural
 
Ts-309,32
 
to use the word “expectation” to mean this experience of tension.
 
 


There arises now the question: is this sensation to be called “the sensation of expectation”, or “the sensation of expectation that B will come?” In the first case to say that you are in a state of expectation admittedly does not fully describe the situation of expecting that so-and-so will happen. The second case is often rashly suggested as an explanation of the use of the phrase “expecting that so-and-so will happen”, and you may even think that with this explanation you are on safe ground, as every further question is dealt with by saying that the sensation of expectation is indefinable.
There arises now the question: is this sensation to be called “the sensation of expectation”, or “the sensation of expectation that B will come?” In the first case to say that you are in a state of expectation admittedly does not fully describe the situation of expecting that so-and-so will happen. The second case is often rashly suggested as an explanation of the use of the phrase “expecting that so-and-so will happen”, and you may even think that with this explanation you are on safe ground, as every further question is dealt with by saying that the sensation of expectation is indefinable.


Now there is no objection to calling a particular sensation “the expectation that B will come”. There may even be good practical reasons for using such an expression. Only mark:– if we have explained the meaning of the phrase “expecting that B will come” in this way no phrase which is derived from this by substituting a different name for “B” is thereby explained. One might say that the phrase “expecting that B will come” is not a value of a function “expecting that x will come”. To understand this compare our case with that of the functional “I eat x”. We understand the proposition “I eat a chair” although we weren't specifically taught the meaning of the expression “eating a chair”.
Now there is no objection to calling a particular sensation “the expectation that B will come”. There may even be good practical reasons for using such an expression. Only mark:– if we have explained the meaning of the phrase “expecting that B will come” in this way no phrase which is derived from this by substituting a different name for “B” is thereby explained. One might say that the phrase “expecting that B will come” is not a value of a function “expecting that x will come”. To understand this compare our case with that of the functional “I eat x”. We understand the proposition “I eat a chair” although we weren't specifically taught the meaning of the expression “eating a chair”.


 
The role which in our present case the name “B” plays in the expression “I expect B” can be compared with that which the name “Bright” plays in the expression “Bright's disease”. Compare the grammar of this word, when it denotes a particular kind of disease, with that of the expression “Bright's disease” when it {{MS reference|Ts-309,33}} means the disease which Bright has. I will characterize the difference by saying that the word “Bright” in the first case is an index in the complex name “Bright's disease”; in the second case I shall call it an argument of the function “x's disease”. One may say that an index alludes to something, and such an allusion may be justified in all sorts of ways. Thus calling a sensation “the expectation that B will come” is giving it a complex name and “B” possibly alludes to the man whose coming had regularly been preceded by the sensation.
 
The role which in our present case the name “B” plays in the expression “I expect B” can be compared with that which the name “Bright” plays in the expression “Bright's disease”. Compare the grammar of this word, when it denotes a particular kind of disease, with that of the expression “Bright's disease” when it
 
Ts-309,33
 
means the disease which Bright has. I will characterize the difference by saying that the word “Bright” in the first case is an index in the complex name “Bright's disease”; in the second case I shall call it an argument of the function “x's disease”. One may say that an index alludes to something, and such an allusion may be justified in all sorts of ways. Thus calling a sensation “the expectation that B will come” is giving it a complex name and “B” possibly alludes to the man whose coming had regularly been preceded by the sensation.
 
 


Again we may use the phrase “expectation that B will come” not as a name but as a characteristic of certain sensations. We might, e.g., explain that a certain tension is said to be an expectation that B will come if it is relieved by B's coming. If this is how we use the phrase then it is true to say that we don't know what we expect until our expectation has been fulfilled (cf. Russell). But no one can believe that this is the only way or even the most common way of using the word “expect”. If I ask someone “whom do you expect?” and after receiving the answer ask again “are you sure that you don't expect someone else?” then, in most cases, this question would be regarded as absurd, and the answer will be something like “Surely, I must know whom I expect”.
Again we may use the phrase “expectation that B will come” not as a name but as a characteristic of certain sensations. We might, e.g., explain that a certain tension is said to be an expectation that B will come if it is relieved by B's coming. If this is how we use the phrase then it is true to say that we don't know what we expect until our expectation has been fulfilled (cf. Russell). But no one can believe that this is the only way or even the most common way of using the word “expect”. If I ask someone “whom do you expect?” and after receiving the answer ask again “are you sure that you don't expect someone else?” then, in most cases, this question would be regarded as absurd, and the answer will be something like “Surely, I must know whom I expect”.


One may characterise the meaning which Russell gives to the word “wishing” by saying that it means to him a kind of hunger. ‒ ‒ ‒ It is a hypothesis that a particular feeling of hunger will be relieved by eating a particular thing. In Russell's way of using the word “wishing” it makes no sense to say “I wished for an apple but a pear has satisfied me”. But we do sometimes say this using {{MS reference|Ts-309,34}} the word “wishing” in a way different from Russell's. In this sense we can say that the tension of wishing was relieved without the wish being fulfilled; and also that the wish was fulfilled without the tension being relieved. That is, I may, in this sense, become satisfied without my wish having been satisfied.


 
Now one might be tempted to say that the difference which we are talking about simply comes to this, that in some cases we know what we wish and in others we don't. There are certainly cases in which we say, “I feel a longing, though I don't know what I'm longing for” or, “I feel a fear, but I don't know what I'm afraid of”, or again: “I feel fear, but I'm not afraid of anything in particular”. {{MS reference|Ts-309,35}}
One may characterise the meaning which Russell gives to the word “wishing” by saying that it means to him a kind of hunger. ‒ ‒ ‒ It is a hypothesis that a particular feeling of hunger will be relieved by eating a particular thing. In Russell's way of using the word “wishing” it makes no sense to say “I wished for an apple but a pear has satisfied me”. But we do sometimes say this using
 
Ts-309,34
 
the word “wishing” in a way different from Russell's. In this sense we can say that the tension of wishing was relieved without the wish being fulfilled; and also that the wish was fulfilled without the tension being relieved. That is, I may, in this sense, become satisfied without my wish having been satisfied.
 
 
 
Now one might be tempted to say that the difference which we are talking about simply comes to this, that in some cases we know what we wish and in others we don't. There are certainly cases in which we say, “I feel a longing, though I don't know what I'm longing for” or, “I feel a fear, but I don't know what I'm afraid of”, or again: “I feel fear, but I'm not afraid of anything in particular”.
 
 
 
 
Ts-309,35
 
 


Now we may describe these cases by saying that we have certain sensations not referring to objects. The phrase “not referring to objects” introduces a grammatical distinction. If in characterising such sensations we use verbs like “fearing”, “longing”, etc., these verbs will be intransitive; “I fear” will be analogous to “I cry”. We may cry about something, but what we cry about is not a constituent of the process of crying; that is to say, we could describe all that happens when we cry without mentioning what we are crying about.
Now we may describe these cases by saying that we have certain sensations not referring to objects. The phrase “not referring to objects” introduces a grammatical distinction. If in characterising such sensations we use verbs like “fearing”, “longing”, etc., these verbs will be intransitive; “I fear” will be analogous to “I cry”. We may cry about something, but what we cry about is not a constituent of the process of crying; that is to say, we could describe all that happens when we cry without mentioning what we are crying about.


Suppose now that I suggested we should use the expression “I feel fear”, and similar ones, in a transitive way only. Whenever before we said “I have a sensation of fear” (intransitively) we will now say “I am afraid of something, but I don't know of what”. Is there an objection to this terminology?
Suppose now that I suggested we should use the expression “I feel fear”, and similar ones, in a transitive way only. Whenever before we said “I have a sensation of fear” (intransitively) we will now say “I am afraid of something, but I don't know of what”. Is there an objection to this terminology?


We may say: “There isn't, except that we are then using the word “to know” in a queer way”. Consider this case:– we have a general undirected feeling of fear. Later on, we have an experience which makes us say, “Now I know what I was afraid of. I was afraid of so-and-so happening”. Is it correct to describe my first feeling by an intransitive verb, or should I say that my fear had an object although I did not know that it had one? Both these forms of description {{MS reference|Ts-309,36}} can be used. To understand this examine the following examples:– It might be found practical to call a certain state of decay in a tooth, not accompanied by what we commonly call toothache, “unconscious toothache” and to use in such a case the expression that we have toothache, but don't know it. It is in just this sense that psychoanalysis talks of unconscious thoughts, acts of volition, etc. Now is it wrong in this sense to say that I have toothache but don't know it? There is nothing wrong about it, as it is just a new terminology and can at any time be retranslated into ordinary language. On the other hand it obviously makes use of the word “to know” in a new way. If you wish to examine how this expression is used it is helpful to ask yourself “what in this case is the process of getting to know like?” “What do we call ‘getting to know’ or, ‘finding out’?”


 
It isn't wrong, according to our new convention, to say “I have unconscious toothache”. For what more can you ask of your notation than that it should distinguish between a bad tooth which doesn't give you toothache and one which does? But the new expression misleads us by calling up pictures and analogies which make it difficult for us to go through with our convention. And it is extremely difficult to discard {{MS reference|Ts-309,37}} these pictures unless we are constantly watchful; particularly difficult when, in philosophising, we contemplate what we say about things. Thus, by the expression, “unconscious toothache” you may either be mislead into thinking that a stupendous discovery has been made, a discovery which in a sense altogether bewilders our understanding; or else you may be extremely puzzled by the expression (the puzzlement of philosophy) and perhaps ask such a question as “How is unconscious toothache possible?” You may then be tempted to deny the possibility of unconscious toothache; but the scientist will tell you that it is a proved fact that there is such a thing, and he will say it like a man who is destroying a common prejudice. He will say: “Surely it's quite simple; there are other things which you don't know of, and there can also be toothache which you don't know of. It is just a new discovery”. You won't be satisfied, but you won't know what to answer. This situation constantly arises between the scientists and the philosophers.
We may say: “There isn't, except that we are then using the word “to know” in a queer way”. Consider this case:– we have a general undirected feeling of fear. Later on, we have an experience which makes us say, “Now I know what I was afraid of. I was afraid of so-and-so happening”. Is it correct to describe my first feeling by an intransitive verb, or should I say that my fear had an object although I did not know that it had one? Both these forms of description
 
Ts-309,36
 
can be used. To understand this examine the following examples:– It might be found practical to call a certain state of decay in a tooth, not accompanied by what we commonly call toothache, “unconscious toothache” and to use in such a case the expression that we have toothache, but don't know it. It is in just this sense that psychoanalysis talks of unconscious thoughts, acts of volition, etc. Now is it wrong in this sense to say that I have toothache but don't know it? There is nothing wrong about it, as it is just a new terminology and can at any time be retranslated into ordinary language. On the other hand it obviously makes use of the word “to know” in a new way. If you wish to examine how this expression is used it is helpful to ask yourself “what in this case is the process of getting to know like?” “What do we call ‘getting to know’ or, ‘finding out’?”
 
 
 
It isn't wrong, according to our new convention, to say “I have unconscious toothache”. For what more can you ask of your notation than that it should distinguish between a bad tooth which doesn't give you toothache and one which does? But the new expression misleads us by calling up pictures and analogies which make it difficult for us to go through with our convention. And it is extremely difficult to discard
 
 
 
 
Ts-309,37
 
these pictures unless we are constantly watchful; particularly difficult when, in philosophising, we contemplate what we say about things. Thus, by the expression, “unconscious toothache” you may either be mislead into thinking that a stupendous discovery has been made, a discovery which in a sense altogether bewilders our understanding; or else you may be extremely puzzled by the expression (the puzzlement of philosophy) and perhaps ask such a question as “How is unconscious toothache possible?” You may then be tempted to deny the possibility of unconscious toothache; but the scientist will tell you that it is a proved fact that there is such a thing, and he will say it like a man who is destroying a common prejudice. He will say: “Surely it's quite simple; there are other things which you don't know of, and there can also be toothache which you don't know of. It is just a new discovery”. You won't be satisfied, but you won't know what to answer. This situation constantly arises between the scientists and the philosophers.
 
 


In such a case we may clear the matter up by saying: “Let's see how the word “unconscious”, “to know”, etc. etc., is used in this case, and how it's used in others”. How far does the analogy between these uses go? We shall also try to construct new notations, in order to break the spell of those which we are accustomed to.
In such a case we may clear the matter up by saying: “Let's see how the word “unconscious”, “to know”, etc. etc., is used in this case, and how it's used in others”. How far does the analogy between these uses go? We shall also try to construct new notations, in order to break the spell of those which we are accustomed to.


 
We said that it was a way of examining the grammar (the use) of the word “to know”, to ask ourselves what, in the particular case we are examining, we should call “getting to know”. There {{MS reference|Ts-309,38}} is a temptation to think that this question is only vaguely relevant, if relevant at all, to the question: “what is the meaning of the word ‘to know’?” We seem to be on a side-track when we ask the question “What is it like in this case ‘to get to know’?” But this question really is a question concerning the grammar of the word “to know”, and this becomes clearer if we put it in the form: “What do we call ‘getting to know’?” It is part of the grammar of the word “chair” that this is what we call “to sit on a chair”, and it is a part of the grammar of the word “meaning” that this is what we call “explanation of a meaning”; in the same way to explain my criterion for another person's having toothache is to give a grammatical explanation about the word “toothache” and, in this sense, “an explanation concerning the meaning of the word ‘toothache.’”
 
We said that it was a way of examining the grammar (the use) of the word “to know”, to ask ourselves what, in the particular case we are examining, we should call “getting to know”. There
 
Ts-309,38
 
is a temptation to think that this question is only vaguely relevant, if relevant at all, to the question: “what is the meaning of the word ‘to know’?” We seem to be on a side-track when we ask the question “What is it like in this case ‘to get to know’?” But this question really is a question concerning the grammar of the word “to know”, and this becomes clearer if we put it in the form: “What do we call ‘getting to know’?” It is part of the grammar of the word “chair” that this is what we call “to sit on a chair”, and it is a part of the grammar of the word “meaning” that this is what we call “explanation of a meaning”; in the same way to explain my criterion for another person's having toothache is to give a grammatical explanation about the word “toothache” and, in this sense, “an explanation concerning the meaning of the word ‘toothache.’”
 
 


When we learnt the meaning of the phrase “so-and-so has toothache” we were pointed out certain kinds of behaviour of those who were said to have toothache. As an instance of these kinds of behaviour let us take, holding your cheek. Suppose that by observation I found that in certain cases whenever these first criteria told me a person had toothache, a red patch appeared on the person's cheek. Supposing I now said to someone “I see A has toothache, he's got a red patch on his cheek”. He may ask me “How do you know A has toothache when you see a red patch?” I should then point out that certain phenomena had always coincided with the appearance of the red patch.
When we learnt the meaning of the phrase “so-and-so has toothache” we were pointed out certain kinds of behaviour of those who were said to have toothache. As an instance of these kinds of behaviour let us take, holding your cheek. Suppose that by observation I found that in certain cases whenever these first criteria told me a person had toothache, a red patch appeared on the person's cheek. Supposing I now said to someone “I see A has toothache, he's got a red patch on his cheek”. He may ask me “How do you know A has toothache when you see a red patch?” I should then point out that certain phenomena had always coincided with the appearance of the red patch.


 
Now one may go on and ask: “How do you know that he has got {{MS reference|Ts-309,39}}
 
Now one may go on and ask: “How do you know that he has got
 
Ts-309,39


toothache when he holds his cheek?” The answer to this might be, “I say, he has toothache when he holds his cheek because I hold my cheek when I have toothache”. But what if we went on asking:– “And why do you suppose that toothache corresponds to his holding his cheek just because your toothache corresponds to your holding your cheek?” You will be at a loss to answer this question and find that here we strike rock bottom, that is we have come down to conventions. (If you suggest as an answer to the last question that, whenever we've seen people holding their cheeks and asked them “what's the matter”, they have answered, “I have toothache”, ‒ ‒ ‒ remember that this experience only co-ordinates holding your cheek with saying certain words.)
toothache when he holds his cheek?” The answer to this might be, “I say, he has toothache when he holds his cheek because I hold my cheek when I have toothache”. But what if we went on asking:– “And why do you suppose that toothache corresponds to his holding his cheek just because your toothache corresponds to your holding your cheek?” You will be at a loss to answer this question and find that here we strike rock bottom, that is we have come down to conventions. (If you suggest as an answer to the last question that, whenever we've seen people holding their cheeks and asked them “what's the matter”, they have answered, “I have toothache”, ‒ ‒ ‒ remember that this experience only co-ordinates holding your cheek with saying certain words.)


 
Let us introduce two antithetical terms in order to avoid certain elementary confusions: To the question “How do you know that so-and-so is the case”, we sometimes answer by giving “criteria” and sometimes by giving “symptoms”. If medical science calls angina an inflammation caused by a particular bacillus, and we ask in a particular case “why do you say this man has got angina?” then the answer “I have found the bacillus so-and-so in his blood” gives us the criterion, or what we may call the defining criterion of angina. If on the other hand the answer was, “His throat is inflamed”, this might give us a symptom of angina. I call “symptom” a phenomenon of which experience has taught us that it coincided, in some way or other, with the phenomenon which is our defining criterion. Then to say, “A man has angina” if this bacillus is found in him is a tautology {{MS reference|Ts-309,40}} or it is a loose way of stating the definition of “angina”. But to say, “A man has angina whenever he has an inflamed throat” is to make a hypothesis.
 
Let us introduce two antithetical terms in order to avoid certain elementary confusions: To the question “How do you know that so-and-so is the case”, we sometimes answer by giving “criteria” and sometimes by giving “symptoms”. If medical science calls angina an inflammation caused by a particular bacillus, and we ask in a particular case “why do you say this man has got angina?” then the answer “I have found the bacillus so-and-so in his blood” gives us the criterion, or what we may call the defining criterion of angina. If on the other hand the answer was, “His throat is inflamed”, this might give us a symptom of angina. I call “symptom” a phenomenon of which experience has taught us that it coincided, in some way or other, with the phenomenon which is our defining criterion. Then to say, “A man has angina” if this bacillus is found in him is a tautology
 
Ts-309,40
 
or it is a loose way of stating the definition of “angina”. But to say, “A man has angina whenever he has an inflamed throat” is to make a hypothesis.
 
 


In practice, if you were asked which phenomenon is the defining criterion and which is a symptom, you would in most cases be unable to answer this question except by making an arbitrary decision ad hoc. It may be practical to define a word by taking one phenomenon as the defining criterion, but we shall easily be persuaded to define the word by means of what, according to our first use, was a symptom. Doctors will use names of diseases without ever deciding which phenomena are to be taken as criteria and which as symptoms; and this need not be a deplorable lack of clarity. For remember that in general we don't use language according to strict rules ‒ ‒ ‒ it hasn't been taught us by means of strict rules, either. We, in our discussions on the other hand, constantly compare language with a calculus proceeding according to exact rules.
In practice, if you were asked which phenomenon is the defining criterion and which is a symptom, you would in most cases be unable to answer this question except by making an arbitrary decision ad hoc. It may be practical to define a word by taking one phenomenon as the defining criterion, but we shall easily be persuaded to define the word by means of what, according to our first use, was a symptom. Doctors will use names of diseases without ever deciding which phenomena are to be taken as criteria and which as symptoms; and this need not be a deplorable lack of clarity. For remember that in general we don't use language according to strict rules ‒ ‒ ‒ it hasn't been taught us by means of strict rules, either. We, in our discussions on the other hand, constantly compare language with a calculus proceeding according to exact rules.


 
This is a very one-sided way of looking at language. In practice we very rarely use language as such a calculus. For not only do we not think of the rules of usage ‒ ‒ ‒ of definitions, etc. ‒ ‒ ‒ while using language, but when we are asked to give such rules in most cases we aren't able to do so. We are unable clearly to circumscribe the concepts we use; not because we don't know their real definition, but because there is no real “definition” to them. To suppose that there must be would be like supposing that whenever children play with a ball they play a {{MS reference|Ts-309,41}} game according to strict rules.
 
This is a very one-sided way of looking at language. In practice we very rarely use language as such a calculus. For not only do we not think of the rules of usage ‒ ‒ ‒ of definitions, etc. ‒ ‒ ‒ while using language, but when we are asked to give such rules in most cases we aren't able to do so. We are unable clearly to circumscribe the concepts we use; not because we don't know their real definition, but because there is no real “definition” to them. To suppose that there must be would be like supposing that whenever children play with a ball they play a
 
Ts-309,41
 
game according to strict rules.
 
 


When we talk of language as a symbolism used in an exact calculus, that which is in our mind can be found in the sciences and in mathematics. Our ordinary use of language conforms to this standard of exactness only in rare cases. Why then do we in philosophizing constantly compare our use of words with one following exact rules? The answer is that the puzzles which we try to remove always spring from just this attitude towards language.
When we talk of language as a symbolism used in an exact calculus, that which is in our mind can be found in the sciences and in mathematics. Our ordinary use of language conforms to this standard of exactness only in rare cases. Why then do we in philosophizing constantly compare our use of words with one following exact rules? The answer is that the puzzles which we try to remove always spring from just this attitude towards language.


 
Consider as an example the question “What is time?” as Saint Augustine and others have asked it. At first sight what this question asks for is a definition, but then immediately the question arises: “What should we gain by a definition, as it can only lead us to other undefined terms?” And why should one be puzzled just by the lack of a definition of time, and not by the lack of a definition of “chair”? Why shouldn't we be puzzled in all cases where we haven't got a definition? Now a definition often clears up the grammar of a word. And in fact it is the grammar of the word “time” which puzzles us. We are only expressing this puzzlement by asking a slightly misleading question, the question: “What is … ?” This question is an utterance of unclarity, of mental discomfort; and it is comparable with the question “Why?” as children so often ask it. This too is an expression of a mental discomfort, and doesn't necessarily ask for either a cause or a reason. (Hertz, Principles of Mechanics). Now the puzzlement about the grammar of the word {{MS reference|Ts-309,42}} “time” arises from what one might call apparent contradictions in that grammar.
 
Consider as an example the question “What is time?” as Saint Augustine and others have asked it. At first sight what this question asks for is a definition, but then immediately the question arises: “What should we gain by a definition, as it can only lead us to other undefined terms?” And why should one be puzzled just by the lack of a definition of time, and not by the lack of a definition of “chair”? Why shouldn't we be puzzled in all cases where we haven't got a definition? Now a definition often clears up the grammar of a word. And in fact it is the grammar of the word “time” which puzzles us. We are only expressing this puzzlement by asking a slightly misleading question, the question: “What is … ?” This question is an utterance of unclarity, of mental discomfort; and it is comparable with the question “Why?” as children so often ask it. This too is an expression of a mental discomfort, and doesn't necessarily ask for either a cause or a reason. (Hertz, Principles of Mechanics). Now the puzzlement about the grammar of the word
 
Ts-309,42
 
“time” arises from what one might call apparent contradictions in that grammar.
 
 


It was such a “contradiction” which puzzled Saint Augustine when he argued: How is it possible that one should measure time? For the past can't be measured, as it is gone by; and the future can't be measured because it has not yet come. And the present can't be measured because it has no extension.
It was such a “contradiction” which puzzled Saint Augustine when he argued: How is it possible that one should measure time? For the past can't be measured, as it is gone by; and the future can't be measured because it has not yet come. And the present can't be measured because it has no extension.


The contradiction which here seems to arise could be called a conflict between two different usages of a word, in this case the word “measure”. Augustine, we might say, thinks of the process of measuring a length: say, the distance between two marks on a travelling band which passes us, and of which we can only see a tiny bit (the present) in front of us. Solving this puzzle will consist in comparing what we mean by “measurement” (the grammar of the word “measurement”) when applied to a distance on a travelling band with the grammar of that word when applied to time. The problem may seem simple, but its extreme difficulty is due to the fascination which the analogy between two similar structures in our language can exert on us. (It is helpful here to remember that it is sometimes almost impossible for a child to realise that one word can have two meanings).
The contradiction which here seems to arise could be called a conflict between two different usages of a word, in this case the word “measure”. Augustine, we might say, thinks of the process of measuring a length: say, the distance between two marks on a travelling band which passes us, and of which we can only see a tiny bit (the present) in front of us. Solving this puzzle will consist in comparing what we mean by “measurement” (the grammar of the word “measurement”) when applied to a distance on a travelling band with the grammar of that word when applied to time. The problem may seem simple, but its extreme difficulty is due to the fascination which the analogy between two similar structures in our language can exert on us. (It is helpful here to remember that it is sometimes almost impossible for a child to realise that one word can have two meanings).


 
Now it is clear that this problem about the concept of time asks for an answer given in the form of strict rules. The puzzle is about rules. ‒ ‒ ‒ Take another example: Socrates' question: “What is knowledge?” Here the case is even clearer, as the discussion begins with the pupil giving an example of an {{MS reference|Ts-309,43}} exact definition; and then analogous to this, a definition of the word “knowledge” is asked for. As the problem is put, it seems that there is something wrong with the ordinary use of the word “knowledge”. It appears, we don't know what it means, and that therefore, perhaps, we have no right to use it. We should reply: “There is no one exact usage of the word ‘knowledge’; but we can make up several such usages, which will more or less agree with the ways the word is actually used.
 
Now it is clear that this problem about the concept of time asks for an answer given in the form of strict rules. The puzzle is about rules. ‒ ‒ ‒ Take another example: Socrates' question: “What is knowledge?” Here the case is even clearer, as the discussion begins with the pupil giving an example of an
 
Ts-309,43
 
exact definition; and then analogous to this, a definition of the word “knowledge” is asked for. As the problem is put, it seems that there is something wrong with the ordinary use of the word “knowledge”. It appears, we don't know what it means, and that therefore, perhaps, we have no right to use it. We should reply: “There is no one exact usage of the word ‘knowledge’; but we can make up several such usages, which will more or less agree with the ways the word is actually used.
 
 


The man who is philosophically puzzled sees a law in the way a word is used, and trying to apply this law consistently, comes up against cases where it leads to paradoxical results. Very often the way the discussion of such a puzzle runs is this: First the question is asked, “What is time?” This question makes it appear that what we want is a definition. We mistakenly think that a definition is what will remove the trouble; as in certain states of indigestion we feel a kind of hunger which cannot be removed by eating. The question is then answered by a wrong definition; say: “Time is the motion of the celestial bodies”. The next step is to see that this definition is unsatisfactory. But this only means that we don't use the word “time” synonymous with motion of the celestial bodies”. However in saying that the first definition is wrong, we are now tempted to think that we must replace it by a different one, the correct one.
The man who is philosophically puzzled sees a law in the way a word is used, and trying to apply this law consistently, comes up against cases where it leads to paradoxical results. Very often the way the discussion of such a puzzle runs is this: First the question is asked, “What is time?” This question makes it appear that what we want is a definition. We mistakenly think that a definition is what will remove the trouble; as in certain states of indigestion we feel a kind of hunger which cannot be removed by eating. The question is then answered by a wrong definition; say: “Time is the motion of the celestial bodies”. The next step is to see that this definition is unsatisfactory. But this only means that we don't use the word “time” synonymous with motion of the celestial bodies”. However in saying that the first definition is wrong, we are now tempted to think that we must replace it by a different one, the correct one.


 
Compare with this the case of the definition of number. Here the explanation that a number is the same thing as a numeral satisfies that craving for a definition. And it is very {{MS reference|Ts-309,44}} difficult not to ask: “Well, if it isn't the numeral, what is it?”
 
Compare with this the case of the definition of number. Here the explanation that a number is the same thing as a numeral satisfies that craving for a definition. And it is very
 
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difficult not to ask: “Well, if it isn't the numeral, what is it?”
 
 


Philosophy, as we use the word, is a fight against the fascination which forms of expression exert upon us.
Philosophy, as we use the word, is a fight against the fascination which forms of expression exert upon us.


I want you to remember that words have those meanings which we have given them; and we give them meanings by explanations. I may have given a definition of a word and used the word accordingly, or those who taught me the use of the word may have given me the explanation. Or else we might, by explanation of a word, mean the explanation which, on being asked, we are ready to give. That is, if we are ready to give an explanation; in most cases we aren't. Many words in this sense then don't have a strict meaning. But this is not a defect. To think it is would be like saying that the light of my reading lamp is no real light at all because it has no sharp boundary.
I want you to remember that words have those meanings which we have given them; and we give them meanings by explanations. I may have given a definition of a word and used the word accordingly, or those who taught me the use of the word may have given me the explanation. Or else we might, by explanation of a word, mean the explanation which, on being asked, we are ready to give. That is, if we are ready to give an explanation; in most cases we aren't. Many words in this sense then don't have a strict meaning. But this is not a defect. To think it is would be like saying that the light of my reading lamp is no real light at all because it has no sharp boundary.


Philosophers very often talk about investigating, analysing, the meaning of words. But let's not forget that a word hasn't got a meaning given to it, as it were, by a power independent of us, so that there can be a kind of scientific investigation into what the word really means. A word has the meaning someone has given to it.
Philosophers very often talk about investigating, analysing, the meaning of words. But let's not forget that a word hasn't got a meaning given to it, as it were, by a power independent of us, so that there can be a kind of scientific investigation into what the word really means. A word has the meaning someone has given to it.


 
There are words with several clearly defined meanings. It is easy to tabulate these meanings. And there are words of which one might say: they are used in a thousand different ways which gradually merge into one another. No wonder that we can't tabulate strict rules for their use. {{MS reference|Ts-309,45}}
 
There are words with several clearly defined meanings. It is easy to tabulate these meanings. And there are words of which one might say: they are used in a thousand different ways which gradually merge into one another. No wonder that we can't tabulate strict rules for their use.
 
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It is wrong to say that in philosophy we consider an ideal language as opposed to our ordinary one. For this makes it appear as though we thought we could improve on ordinary language. But ordinary language is all right. Whenever we make up “ideal languages” it is not in order to replace our ordinary language by them; but just to remove some trouble, caused in someone's mind by thinking that he has got hold of the exact use of a common word. That is also why our method is not merely to enumerate actual usages of words, but rather deliberately to invent new ones, some of them because of their absurd appearance.
It is wrong to say that in philosophy we consider an ideal language as opposed to our ordinary one. For this makes it appear as though we thought we could improve on ordinary language. But ordinary language is all right. Whenever we make up “ideal languages” it is not in order to replace our ordinary language by them; but just to remove some trouble, caused in someone's mind by thinking that he has got hold of the exact use of a common word. That is also why our method is not merely to enumerate actual usages of words, but rather deliberately to invent new ones, some of them because of their absurd appearance.


When we say that by our method we try to counteract the misleading effect of certain analogies, it is important that you should understand that the idea of an analogy being misleading is nothing sharply defined. No sharp boundary can be drawn round the cases in which we should say that a man was misled by an analogy. The use of expressions constructed on analogical patterns stresses analogies between cases often far apart. And by doing this these expressions may be extremely useful. It is, in most cases, impossible to show an exact point where an analogy begins to mislead us. Every particular notation stresses some particular point of view. If, e.g., we call our investigations “philosophy”, this title, on the one hand, seems appropriate, on the other hand it certainly has misled people. (One might say that the subject we are dealing with is one of the heirs of the subject which we used to call “philosophy”.) The cases in which particularly, we wish to say that someone {{MS reference|Ts-309,46}} is misled by a form of expression are those in which we would say: “he wouldn't talk as he does if he were aware of this difference in the grammar of such-and-such words, or if he were aware of this other possibility of expression” and so on. Thus we may say of some philosophizing mathematicians that they are obviously not aware of the difference between the many different usages of the word “proof”; and that they are not clear about the difference between the uses of the word “kind”, when they talk of kinds of numbers, kinds of proofs, as thought the word “kind” here meant the same thing as in the context, “kinds of apples”. Or, we may say, they are not aware of the different meanings of the word “discovery”, when in one case we talk of the discovery of the construction of the pentagon and in the other case of the discovery of the South Pole.


 
Now when we distinguished a transitive and an intransitive use of such words as “longing”, “fearing”, “expecting”, etc., we said that someone might try to smooth over our difficulties by saying: “The difference between the two cases is simply that in one case we know what we are longing for and in the other we don't”. Now who says this, I think, obviously doesn't see the difference which he tried to explain away reappears when we carefully consider the use of the word “to know” in the two cases. The expression “the difference is simply … ” makes it appear as though we had analysed the case and found a simple analysis; as when we point out that two substances with very different names hardly differ in composition. {{MS reference|Ts-309,47}}
When we say that by our method we try to counteract the misleading effect of certain analogies, it is important that you should understand that the idea of an analogy being misleading is nothing sharply defined. No sharp boundary can be drawn round the cases in which we should say that a man was misled by an analogy. The use of expressions constructed on analogical patterns stresses analogies between cases often far apart. And by doing this these expressions may be extremely useful. It is, in most cases, impossible to show an exact point where an analogy begins to mislead us. Every particular notation stresses some particular point of view. If, e.g., we call our investigations “philosophy”, this title, on the one hand, seems appropriate, on the other hand it certainly has misled people. (One might say that the subject we are dealing with is one of the heirs of the subject which we used to call “philosophy”.) The cases in which particularly, we wish to say that someone
 
Ts-309,46
 
is misled by a form of expression are those in which we would say: “he wouldn't talk as he does if he were aware of this difference in the grammar of such-and-such words, or if he were aware of this other possibility of expression” and so on. Thus we may say of some philosophizing mathematicians that they are obviously not aware of the difference between the many different usages of the word “proof”; and that they are not clear about the difference between the uses of the word “kind”, when they talk of kinds of numbers, kinds of proofs, as thought the word “kind” here meant the same thing as in the context, “kinds of apples”. Or, we may say, they are not aware of the different meanings of the word “discovery”, when in one case we talk of the discovery of the construction of the pentagon and in the other case of the discovery of the South Pole.
 
 
 
Now when we distinguished a transitive and an intransitive use of such words as “longing”, “fearing”, “expecting”, etc., we said that someone might try to smooth over our difficulties by saying: “The difference between the two cases is simply that in one case we know what we are longing for and in the other we don't”. Now who says this, I think, obviously doesn't see the difference which he tried to explain away reappears when we carefully consider the use of the word “to know” in the two cases. The expression “the difference is simply … ” makes it appear as though we had analysed the case and found a simple analysis; as when we point out that two substances with very different names hardly differ in composition.
 
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We said in this case that we might use both expressions: “we feel a longing” (where “longing” is used intransitively) and “we feel a longing and don't know what we are longing for”. It may seem queer to say that we may correctly use either of two forms of expression which seem to contradict each other; but such cases are very frequent.
We said in this case that we might use both expressions: “we feel a longing” (where “longing” is used intransitively) and “we feel a longing and don't know what we are longing for”. It may seem queer to say that we may correctly use either of two forms of expression which seem to contradict each other; but such cases are very frequent.
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Let us use the following example to clear this up. We say that the equation x² = ‒ 1 has the solution ± √‒1. There was a time when one said that this equation had no solution. Now this statement, whether agreeing or disagreeing with the one which told us the solutions, certainly hasn't its multiplicity. But we can easily give it that multiplicity by saying that an equation x² + ax + b = 0 hasn't got a solution but comes α near to the nearest solution which is β. Analogously we can say either “A straight line always intersects a circle; sometimes in real, sometimes in complex points”, or, “A straight line either intersects a circle, or it doesn't and is α far from doing so. These two statements mean exactly the same. They will be more or less satisfactory according to the way a man wishes to look at it. He may wish to make the difference between intersecting and not intersecting as inconspicuous as possible. Or on the other hand he may wish to stress it; and either tendency may be justified, say, by his particular practical purposes. But this may not be the reason at all why he prefers one form of expression to the other. Which form he prefers, and whether he has a preference at all, often depends on general, deeply rooted
Let us use the following example to clear this up. We say that the equation x² = ‒ 1 has the solution ± √‒1. There was a time when one said that this equation had no solution. Now this statement, whether agreeing or disagreeing with the one which told us the solutions, certainly hasn't its multiplicity. But we can easily give it that multiplicity by saying that an equation x² + ax + b = 0 hasn't got a solution but comes α near to the nearest solution which is β. Analogously we can say either “A straight line always intersects a circle; sometimes in real, sometimes in complex points”, or, “A straight line either intersects a circle, or it doesn't and is α far from doing so. These two statements mean exactly the same. They will be more or less satisfactory according to the way a man wishes to look at it. He may wish to make the difference between intersecting and not intersecting as inconspicuous as possible. Or on the other hand he may wish to stress it; and either tendency may be justified, say, by his particular practical purposes. But this may not be the reason at all why he prefers one form of expression to the other. Which form he prefers, and whether he has a preference at all, often depends on general, deeply rooted {{MS reference|Ts-309,48}} tendencies of his thinking.
 
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tendencies of his thinking.
 
 


Should we say that there are cases when a man despises another man and doesn't know it; or should we describe such cases by saying that he doesn't despise him but unintentionally behaves towards him in a way ‒ ‒ ‒ speaks to him in a tone of voice, etc., ‒ ‒ ‒ which in general would go together with despising him. Either form of expression is correct; but they may betray different tendencies of mind.
Should we say that there are cases when a man despises another man and doesn't know it; or should we describe such cases by saying that he doesn't despise him but unintentionally behaves towards him in a way ‒ ‒ ‒ speaks to him in a tone of voice, etc., ‒ ‒ ‒ which in general would go together with despising him. Either form of expression is correct; but they may betray different tendencies of mind.


 
Let us revert to examining the grammar of the expressions “to wish”, “to expect”, “to long for”, etc., and consider that most important case in which the expression, “I wish so-and-so to happen” is the direct description of a conscious process. That is to say, the case in which we should be inclined to answer the question “Are you sure that it is this you wish?” by saying: “Surely I must know what I wish”. Now compare this answer to the one which most of us would give to the question: “Do you know the ABC?” Has the emphatic assertion that you know it a sense analogous to that of the former assertion? Both assertions in a way brush aside the question. But the former doesn't wish to say “Surely I know such a simple thing as this” but rather: “The question which you asked me makes no sense”. We might say: We adopt in this case a wrong method of brushing aside the question. “Of course I know” could here be replaced by “of course, there is no doubt” and this interpreted to mean “It makes, in this case, no sense to talk of a doubt”. In this way the answer “Of course I know what I wish” can be {{MS reference|Ts-309,49}} interpreted to be a grammatical statement.
 
Let us revert to examining the grammar of the expressions “to wish”, “to expect”, “to long for”, etc., and consider that most important case in which the expression, “I wish so-and-so to happen” is the direct description of a conscious process. That is to say, the case in which we should be inclined to answer the question “Are you sure that it is this you wish?” by saying: “Surely I must know what I wish”. Now compare this answer to the one which most of us would give to the question: “Do you know the ABC?” Has the emphatic assertion that you know it a sense analogous to that of the former assertion? Both assertions in a way brush aside the question. But the former doesn't wish to say “Surely I know such a simple thing as this” but rather: “The question which you asked me makes no sense”. We might say: We adopt in this case a wrong method of brushing aside the question. “Of course I know” could here be replaced by “of course, there is no doubt” and this interpreted to mean “It makes, in this case, no sense to talk of a doubt”. In this way the answer “Of course I know what I wish” can be
 
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interpreted to be a grammatical statement.
 
 


It is similar when we ask “Has this room a length?”, and some one answers: “Of course it has”. He might have answered “Don't ask nonsense”. On the other hand “The room has length” can be used as a grammatical statement. It then says that a sentence of the form “The room is ‒ ‒ ‒ feet long” makes sense.
It is similar when we ask “Has this room a length?”, and some one answers: “Of course it has”. He might have answered “Don't ask nonsense”. On the other hand “The room has length” can be used as a grammatical statement. It then says that a sentence of the form “The room is ‒ ‒ ‒ feet long” makes sense.


A great many philosophical difficulties are connected with that sense of the expressions “to wish”, “to think”, etc., which we are now considering. These can all be summed up in the question: “How can one think what is not the case?”
A great many philosophical difficulties are connected with that sense of the expressions “to wish”, “to think”, etc., which we are now considering. These can all be summed up in the question: “How can one think what is not the case?”


This is a beautiful example of a philosophical question. It asks “How can one … ?” and while this puzzles us we must admit that nothing is easier than to think what is not the case. I mean, this shows us again that the difficulty which we are in does not arise through our inability to imagine how thinking something is done; just as the philosophical difficulty about the measurement of time did not arise through our inability to imagine how time was actually measured. I say this because sometimes it almost seems as though our difficulty were one of remembering exactly what happened when we thought something, a difficulty of introspection, or something of the sort; whereas in fact it arises when we look at the facts through the medium of a misleading form of expression.
This is a beautiful example of a philosophical question. It asks “How can one … ?” and while this puzzles us we must admit that nothing is easier than to think what is not the case. I mean, this shows us again that the difficulty which we are in does not arise through our inability to imagine how thinking something is done; just as the philosophical difficulty about the measurement of time did not arise through our inability to imagine how time was actually measured. I say this because sometimes it almost seems as though our difficulty were one of remembering exactly what happened when we thought something, a difficulty of introspection, or something of the sort; whereas in fact it arises when we look at the facts through the medium of a misleading form of expression.


 
“How can one think what is not the case? If I think that King's College is on fire when it is not on fire, the fact of its being on fire does not exist. Then how can I think it? {{MS reference|Ts-309,50}}
 
“How can one think what is not the case? If I think that King's College is on fire when it is not on fire, the fact of its being on fire does not exist. Then how can I think it?
 
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How can we hang a thief who doesn't exist?” Our answer could be put in this form: “I can't hang him when he doesn't exist; but I can look for him when he doesn't exist”.
How can we hang a thief who doesn't exist?” Our answer could be put in this form: “I can't hang him when he doesn't exist; but I can look for him when he doesn't exist”.


We are here misled by the substantives “object of thought” and “fact”, and by the different meanings of the word “exist”.
We are here misled by the substantives “object of thought” and “fact”, and by the different meanings of the word “exist”.


Talking of the fact as a “complex of objects” springs from this confusion (cf. Tractatus Logico-philosophicus). Supposing we asked: “How can one imagine what does not exist?” The answer seems to be: “If we do, we imagine non-existent combinations of existing elements”. A centaur doesn't exist, but a man's head and torso and arms and a horse's legs do exist. “But can't we imagine an object utterly different from any one which exists?” ‒ ‒ ‒ We should be inclined to answer: “No; the elements, individuals, must exist. If redness, roundness and sweetness did not exist, we could not imagine them”.
Talking of the fact as a “complex of objects” springs from this confusion (cf. Tractatus Logico-philosophicus). Supposing we asked: “How can one imagine what does not exist?” The answer seems to be: “If we do, we imagine non-existent combinations of existing elements”. A centaur doesn't exist, but a man's head and torso and arms and a horse's legs do exist. “But can't we imagine an object utterly different from any one which exists?” ‒ ‒ ‒ We should be inclined to answer: “No; the elements, individuals, must exist. If redness, roundness and sweetness did not exist, we could not imagine them”.


 
But what do you mean by “redness exists”? My watch exists, if it hasn't been pulled to pieces, if it hasn't been destroyed. What would we call “destroying redness”? We might of course mean destroying all red objects; but would this make it impossible to imagine a red object? Supposing to this one answered: “But surely, red objects must have existed and you must have seen them?” ‒ ‒ ‒ But how do you know that this is so? Suppose I said “Exerting a pressure on your eyeball produces a red image”. Couldn't the way by which you first became acquainted with red have been this? And why shouldn't it have been just imagining a red patch? (The difficulty which you will feel {{MS reference|Ts-309,51}} here will have to be discussed at a later occasion).
 
But what do you mean by “redness exists”? My watch exists, if it hasn't been pulled to pieces, if it hasn't been destroyed. What would we call “destroying redness”? We might of course mean destroying all red objects; but would this make it impossible to imagine a red object? Supposing to this one answered: “But surely, red objects must have existed and you must have seen them?” ‒ ‒ ‒ But how do you know that this is so? Suppose I said “Exerting a pressure on your eyeball produces a red image”. Couldn't the way by which you first became acquainted with red have been this? And why shouldn't it have been just imagining a red patch? (The difficulty which you will feel
 
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here will have to be discussed at a later occasion).
 
 


We may now be inclined to say: “As the fact which would make our thought true if it existed does not always exist, it is not the fact which we think”. But this just depends upon how I wish to use the word “fact”. Why shouldn't I say: “I believe the fact that the college is on fire”? It is just a clumsy expression for saying: “I believe that the college is on fire”. To say “It is not the fact which we believe”, is itself the result of a confusion. We think we are saying something like: “It isn't the sugar-cane which we eat but the sugar”, “It isn't Mr. Smith who hangs in the gallery, but his picture”.
We may now be inclined to say: “As the fact which would make our thought true if it existed does not always exist, it is not the fact which we think”. But this just depends upon how I wish to use the word “fact”. Why shouldn't I say: “I believe the fact that the college is on fire”? It is just a clumsy expression for saying: “I believe that the college is on fire”. To say “It is not the fact which we believe”, is itself the result of a confusion. We think we are saying something like: “It isn't the sugar-cane which we eat but the sugar”, “It isn't Mr. Smith who hangs in the gallery, but his picture”.


The next step we are inclined to take is to think that as the object of our thought isn't the fact it is a shadow of the fact. There are different names for this shadow, e.g. “proposition”, “sense of the sentence”.
The next step we are inclined to take is to think that as the object of our thought isn't the fact it is a shadow of the fact. There are different names for this shadow, e.g. “proposition”, “sense of the sentence”.


But this doesn't remove our difficulty. For the question now is: “How can something be the shadow of a fact which doesn't exist?”
But this doesn't remove our difficulty. For the question now is: “How can something be the shadow of a fact which doesn't exist?”


I can express our trouble in a different form by saying: “How can we know what the shadow is a shadow of?” ‒ ‒ ‒ The shadow would be some sort of portrait; and therefore I can restate our problem by asking: “What makes a portrait a portrait of Mr. N?” The answer which might first suggest itself is: “The similarity between the portrait and Mr. N”. This answer in fact shows what we had in mind when we talked {{MS reference|Ts-309,52}} of the shadow of a fact. It is quite clear, however, that similarity does not constitute our idea of a portrait; for it is in the essence of this idea that it should make sense to talk of a good or a bad portrait. In other words, it is essential that the shadow should be capable of representing things as in fact they are not.


An obvious, and correct, answer to the question “What makes the portrait the portrait of so-and-so?” is that it is the intention. But if we wish to know what it means “intending this to be a portrait of so-and-so” let's see what actually happens when we intend this. Remember the occasion when we talked of what happened when we expect someone from four to four-thirty. To intend a picture to be the portrait of so-and-so (on the part of the painter, e.g.) is neither a particular state of mind nor a particular mental process. But there are a great many combinations of actions and states of mind which we should call “intending … ” It might have been that he was told to paint a portrait of N, and sat down before N, going through certain actions which we call “copying N's face”. One might object to this by saying that the essence of copying is the intention to copy. I should answer that there are a great many different processes which we call “copying something”. Take an instance. I draw an ellipse on a sheet of paper and ask you to copy it. What characterises the process of copying? For it is clear that it isn't the {{MS reference|Ts-309,53}} fact that you draw a similar ellipse. You might have tried to copy it and not succeeded; or you might have drawn an ellipse with a totally different intention, and it happened to be like the one you should have copied. So what do you do when you try to copy the ellipse? Well, you look at it, draw something on a piece of paper, perhaps measure what you have drawn, perhaps you curse if you find that it doesn't agree with the model or perhaps you say “I am going to copy this ellipse” and just draw an ellipse like it. There are an endless variety of actions and words, having a family likeness to each other, which we call “trying to copy”.


I can express our trouble in a different form by saying: “How can we know what the shadow is a shadow of?” ‒ ‒ ‒ The shadow would be some sort of portrait; and therefore I can restate our problem by asking: “What makes a portrait a portrait of Mr. N?” The answer which might first suggest itself is: “The similarity between the portrait and Mr. N”. This answer in fact shows what we had in mind when we talked
Suppose we said “that a picture is a portrait of a particular object consists in its being derived from that object in a particular way”. Now it is easy to describe what we should call “processes of deriving a picture from an object” (roughly speaking, processes of projection). But there is a peculiar difficulty about admitting that any such process is what we call “intentional representation”. For describe whatever process (activity) of projection we may, there is a way of reinterpreting this projection. Therefore ‒ ‒ ‒ one is tempted to say ‒ ‒ ‒ such a process can never be the intention itself. For we could always have intended the opposite by re-interpreting the process of projection. Imagine this case: We give someone an order to walk in a certain direction by pointing, or drawing an arrow which points in the direction. Suppose drawing arrows is the language in which generally we {{MS reference|Ts-309,54}} give such an order. Couldn't such an order be interpreted to mean that the man who gets it is to walk in the direction opposite to that of the arrow? This could obviously be done by adding to our arrow some symbols which we might call “an interpretation”. It is easy to imagine a case in which, say, to deceive someone, we might make an arrangement that an order should be carried out in the sense opposite to its normal one. The symbol which adds the interpretation to our original arrow could, for instance, be another arrow. Whenever we interpret a symbol in one way or another, the interpretation is a new symbol added to the old one.
 
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of the shadow of a fact. It is quite clear, however, that similarity does not constitute our idea of a portrait; for it is in the essence of this idea that it should make sense to talk of a good or a bad portrait. In other words, it is essential that the shadow should be capable of representing things as in fact they are not.
 
 
 
An obvious, and correct, answer to the question “What makes the portrait the portrait of so-and-so?” is that it is the intention. But if we wish to know what it means “intending this to be a portrait of so-and-so” let's see what actually happens when we intend this. Remember the occasion when we talked of what happened when we expect someone from four to four-thirty. To intend a picture to be the portrait of so-and-so (on the part of the painter, e.g.) is neither a particular state of mind nor a particular mental process. But there are a great many combinations of actions and states of mind which we should call “intending … ” It might have been that he was told to paint a portrait of N, and sat down before N, going through certain actions which we call “copying N's face”. One might object to this by saying that the essence of copying is the intention to copy. I should answer that there are a great many different processes which we call “copying something”. Take an instance. I draw an ellipse on a sheet of paper and ask you to copy it. What characterises the process of copying? For it is clear that it isn't the
 
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fact that you draw a similar ellipse. You might have tried to copy it and not succeeded; or you might have drawn an ellipse with a totally different intention, and it happened to be like the one you should have copied. So what do you do when you try to copy the ellipse? Well, you look at it, draw something on a piece of paper, perhaps measure what you have drawn, perhaps you curse if you find that it doesn't agree with the model or perhaps you say “I am going to copy this ellipse” and just draw an ellipse like it. There are an endless variety of actions and words, having a family likeness to each other, which we call “trying to copy”.
 
 
 
Suppose we said “that a picture is a portrait of a particular object consists in its being derived from that object in a particular way”. Now it is easy to describe what we should call “processes of deriving a picture from an object” (roughly speaking, processes of projection). But there is a peculiar difficulty about admitting that any such process is what we call “intentional representation”. For describe whatever process (activity) of projection we may, there is a way of reinterpreting this projection. Therefore ‒ ‒ ‒ one is tempted to say ‒ ‒ ‒ such a process can never be the intention itself. For we could always have intended the opposite by re-interpreting the process of projection. Imagine this case: We give someone an order to walk in a certain direction by pointing, or drawing an arrow which points in the direction. Suppose drawing arrows is the language in which generally we
 
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give such an order. Couldn't such an order be interpreted to mean that the man who gets it is to walk in the direction opposite to that of the arrow? This could obviously be done by adding to our arrow some symbols which we might call “an interpretation”. It is easy to imagine a case in which, say, to deceive someone, we might make an arrangement that an order should be carried out in the sense opposite to its normal one. The symbol which adds the interpretation to our original arrow could, for instance, be another arrow. Whenever we interpret a symbol in one way or another, the interpretation is a new symbol added to the old one.
 
 


Now we might say that whenever we give someone an order by showing him an arrow, and don't do it “automatically”, we mean the arrow in one way or another. And this process of meaning, of whatever kind it may be, can be represented by another arrow (pointing in the same or the opposite sense to the first). In this picture which we make of “meaning and saying” it is essential that we should imagine the processes of saying and meaning to take place in two different spheres.
Now we might say that whenever we give someone an order by showing him an arrow, and don't do it “automatically”, we mean the arrow in one way or another. And this process of meaning, of whatever kind it may be, can be represented by another arrow (pointing in the same or the opposite sense to the first). In this picture which we make of “meaning and saying” it is essential that we should imagine the processes of saying and meaning to take place in two different spheres.


 
Is it then correct to say that no arrow could be the meaning, as every arrow could be meant the opposite way? ‒ ‒ ‒ Suppose we write down the scheme of saying and meaning by a column of arrows one below the other. {{MS reference|Ts-309,55}}
 
Is it then correct to say that no arrow could be the meaning, as every arrow could be meant the opposite way? ‒ ‒ ‒ Suppose we write down the scheme of saying and meaning by a column of arrows one below the other.
 
 
 
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Then if this scheme is to serve our purpose at all, it must show us which of the three levels is the level of meaning. I can, e.g., make a scheme with three levels, the bottom level always being the level of meaning. But adopt whatever model or scheme you may, it will have a bottom level, and there will be no such thing as an interpretation of that. To say in this case that every arrow can still be interpreted would only mean that I could always make a different model of saying and meaning which had one more level than the one I am using.
Then if this scheme is to serve our purpose at all, it must show us which of the three levels is the level of meaning. I can, e.g., make a scheme with three levels, the bottom level always being the level of meaning. But adopt whatever model or scheme you may, it will have a bottom level, and there will be no such thing as an interpretation of that. To say in this case that every arrow can still be interpreted would only mean that I could always make a different model of saying and meaning which had one more level than the one I am using.


Let us put it in this way:– What one wishes to say is: “Every sign is capable of interpretation; but the meaning mustn't be capable of interpretation. It is the last interpretation.” Now I assume that you take the meaning to be a process accompanying the saying, and that it is translatable into, and so far equivalent to, a further sign. You have therefore further to tell me what you take to be the distinguishing mark between a sign and the meaning. If you do so, e.g., by saying that the meaning is the arrow which you imagine as opposed to any which you may draw or produce in any other way you thereby say, that you will call no further arrow an interpretation of the one which you have imagined.
Let us put it in this way:– What one wishes to say is: “Every sign is capable of interpretation; but the meaning mustn't be capable of interpretation. It is the last interpretation.” Now I assume that you take the meaning to be a process accompanying the saying, and that it is translatable into, and so far equivalent to, a further sign. You have therefore further to tell me what you take to be the distinguishing mark between a sign and the meaning. If you do so, e.g., by saying that the meaning is the arrow which you imagine as opposed to any which you may draw or produce in any other way you thereby say, that you will call no further arrow an interpretation of the one which you have imagined.


 
All this will become clearer if we consider what it is that really happens when we say a thing and mean what we say. ‒ ‒ ‒ Let us ask ourselves: If we say to someone “I should be delighted to see you” and mean it, does a conscious process run alongside these words, a process which could itself be {{MS reference|Ts-309,56}} translated into spoken words? This will hardly ever be the case.
 
All this will become clearer if we consider what it is that really happens when we say a thing and mean what we say. ‒ ‒ ‒ Let us ask ourselves: If we say to someone “I should be delighted to see you” and mean it, does a conscious process run alongside these words, a process which could itself be
 
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translated into spoken words? This will hardly ever be the case.
 
 


But let us imagine an instance in which it does happen. Supposing I had a habit of accompanying every English sentence which I said aloud by a German sentence spoken to myself inwardly. If then, for some reason or other, you call the silent sentence the meaning of the one spoken aloud, the process of meaning accompanying the process of saying would be one which could itself be translated into outward signs. Or, before any sentence which we say aloud we say its meaning (whatever it may be) to ourselves in a kind of aside. An example at least similar to the case we want would be saying one thing and at the same time seeing a picture before our mind's eye which is the meaning and agrees or disagrees with what we say. Such cases and similar ones exist, but they are not at all what happens as a rule when we say something and mean it, or mean something else. There are of course real cases in which what we call meaning is a definite conscious process accompanying, preceding, or following the verbal expression and itself a verbal expression of some sort or translatable into one. A typical example of this is the “aside” on the stage.
But let us imagine an instance in which it does happen. Supposing I had a habit of accompanying every English sentence which I said aloud by a German sentence spoken to myself inwardly. If then, for some reason or other, you call the silent sentence the meaning of the one spoken aloud, the process of meaning accompanying the process of saying would be one which could itself be translated into outward signs. Or, before any sentence which we say aloud we say its meaning (whatever it may be) to ourselves in a kind of aside. An example at least similar to the case we want would be saying one thing and at the same time seeing a picture before our mind's eye which is the meaning and agrees or disagrees with what we say. Such cases and similar ones exist, but they are not at all what happens as a rule when we say something and mean it, or mean something else. There are of course real cases in which what we call meaning is a definite conscious process accompanying, preceding, or following the verbal expression and itself a verbal expression of some sort or translatable into one. A typical example of this is the “aside” on the stage.


But what tempts us to think of the meaning of what we say as a process essentially of the kind which we have described is the analogy between the forms of expression:
But what tempts us to think of the meaning of what we say as a process essentially of the kind which we have described is the analogy between the forms of expression:


“to say something”
:“to say something”
 
:“to mean something”, {{MS reference|Ts-309,57}}
“to mean something”,
 
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which seem to refer to two parallel processes.
which seem to refer to two parallel processes.


A process accompanying our words which one might call the “process of meaning them”, is the modulation of the voice in which we speak the words; or one of the processes, similar to this like the play of facial expression. These accompany the spoken words not in the way a German sentence might accompany an English sentence, or writing a sentence accompany speaking a sentence; but in the sense in which the tune of a song accompanies its words. This tune corresponds to the “feeling” with which we say the sentence. And I wish to point out that this feeling is the expression with which the sentence is said, or something similar to this expression.
A process accompanying our words which one might call the “process of meaning them”, is the modulation of the voice in which we speak the words; or one of the processes, similar to this like the play of facial expression. These accompany the spoken words not in the way a German sentence might accompany an English sentence, or writing a sentence accompany speaking a sentence; but in the sense in which the tune of a song accompanies its words. This tune corresponds to the “feeling” with which we say the sentence. And I wish to point out that this feeling is the expression with which the sentence is said, or something similar to this expression.


Let us revert to our question: “What is the object of a thought?” (e.g. when we say, “I think that King's College is on fire”).
Let us revert to our question: “What is the object of a thought?” (e.g. when we say, “I think that King's College is on fire”).


The question as we put it is already the expression of several confusions. This is shown by the mere fact that it almost sounds like a question of physics; like asking: “What are the ultimate constituents of matter?” (It is a typically metaphysical question; the characteristic of a metaphysical question being that we express an unclarity about the grammar of words in the form of a scientific question.)
The question as we put it is already the expression of several confusions. This is shown by the mere fact that it almost sounds like a question of physics; like asking: “What are the ultimate constituents of matter?” (It is a typically metaphysical question; the characteristic of a metaphysical question being that we express an unclarity about the grammar of words in the form of a scientific question.)


 
One of the origins of our question is the two-fold use of the propositional function “I think X”. We say “I think that so-and-so will happen” or “that so-and-so is the case”, and also “I think just the same thing as he”; and we say “I expect {{MS reference|Ts-309,58}} him”, and also “I expect that he will come”. Compare “I expect him” and “I shoot him”. We can't shoot him if he isn't there. This is how the question arises: “How can we expect something that is not the case?”, “How can we expect a fact which does not exist?”
 
One of the origins of our question is the two-fold use of the propositional function “I think X”. We say “I think that so-and-so will happen” or “that so-and-so is the case”, and also “I think just the same thing as he”; and we say “I expect
 
Ts-309,58
 
him”, and also “I expect that he will come”. Compare “I expect him” and “I shoot him”. We can't shoot him if he isn't there. This is how the question arises: “How can we expect something that is not the case?”, “How can we expect a fact which does not exist?”
 
 


The way out of this difficulty seems to be: what we expect is not the fact, but a shadow of the fact; as it were, the next thing to the fact. We have said that this is only pushing the question one step further back. There are several origins to this idea of a shadow. One of them is this: we say “Surely two sentences of different languages can have the same sense”; and we argue, “therefore the sense is not the same as the sentence”, and ask the question “What is the sense?” And we make of “it” a shadowy being, one of the many which we create when we wish to give meaning to substantives to which no material objects correspond.
The way out of this difficulty seems to be: what we expect is not the fact, but a shadow of the fact; as it were, the next thing to the fact. We have said that this is only pushing the question one step further back. There are several origins to this idea of a shadow. One of them is this: we say “Surely two sentences of different languages can have the same sense”; and we argue, “therefore the sense is not the same as the sentence”, and ask the question “What is the sense?” And we make of “it” a shadowy being, one of the many which we create when we wish to give meaning to substantives to which no material objects correspond.


 
Another source of the idea of a shadow being the object of our thought is this: We imagine the shadow to be a picture the intention of which can not be questioned, that is, a picture which we don't interpret in order to understand it, but which we understand without interpreting it. Now there are pictures of which we should say that we interpret them, that is, translate them into a different kind of picture, in order to understand them; and pictures of which we should say that we understand them immediately, without any further interpretation. If you see a telegram written in cipher, and you know the key to this {{MS reference|Ts-309,59}} cipher, you will, in general, not say that you understand the telegram before you have translated it into ordinary language. Of course you have only replaced one kind of symbols for another; and yet if now you read the telegram in your language no further process of interpretation will take place. ‒ ‒ ‒ Or rather, you may now, in certain cases, again translate this telegram, say into a picture; but then too you have only replaced one set of symbols by another.
 
Another source of the idea of a shadow being the object of our thought is this: We imagine the shadow to be a picture the intention of which can not be questioned, that is, a picture which we don't interpret in order to understand it, but which we understand without interpreting it. Now there are pictures of which we should say that we interpret them, that is, translate them into a different kind of picture, in order to understand them; and pictures of which we should say that we understand them immediately, without any further interpretation. If you see a telegram written in cipher, and you know the key to this
 
Ts-309,59
 
cipher, you will, in general, not say that you understand the telegram before you have translated it into ordinary language. Of course you have only replaced one kind of symbols for another; and yet if now you read the telegram in your language no further process of interpretation will take place. ‒ ‒ ‒ Or rather, you may now, in certain cases, again translate this telegram, say into a picture; but then too you have only replaced one set of symbols by another.
 
 


The shadow, as we think of it, is some sort of a picture; in fact, what we mean by it is something very much like an image which comes before our mind's eye; and this again is something not unlike a painted representation in the ordinary sense. A source of the idea of the shadow certainly is the fact that in some cases saying, hearing or reading a sentence brings images before our mind's eye, images which more or less strictly correspond to the sentence, and which are therefore, in a sense, translations of this sentence into a pictorial language. ‒ ‒ ‒ But it is absolutely essential for the picture which we imagine the shadow to be that it is what I shall call a “picture by similarity”. I don't mean by this that it is a picture similar to what it is intended to represent, but that it is a picture which is correct only when it is similar to what it represents. One might use for this kind of picture the word “copy”. Roughly speaking, copies are good pictures when they can easily be mistaken for what they represent.
The shadow, as we think of it, is some sort of a picture; in fact, what we mean by it is something very much like an image which comes before our mind's eye; and this again is something not unlike a painted representation in the ordinary sense. A source of the idea of the shadow certainly is the fact that in some cases saying, hearing or reading a sentence brings images before our mind's eye, images which more or less strictly correspond to the sentence, and which are therefore, in a sense, translations of this sentence into a pictorial language. ‒ ‒ ‒ But it is absolutely essential for the picture which we imagine the shadow to be that it is what I shall call a “picture by similarity”. I don't mean by this that it is a picture similar to what it is intended to represent, but that it is a picture which is correct only when it is similar to what it represents. One might use for this kind of picture the word “copy”. Roughly speaking, copies are good pictures when they can easily be mistaken for what they represent.


 
A plane projection of one hemisphere of our terrestrial {{MS reference|Ts-309,60}} globe is not a picture by similarity or a copy in this sense. It would be conceivable that I portrayed some one's face by projecting it in some queer way, though correctly according to the adopted rule of projection, on a piece of paper, in such a way that no one would normally call the projection “a good portrait of so-and-so” because it would not look a bit like him.
 
A plane projection of one hemisphere of our terrestrial
 
Ts-309,60
 
globe is not a picture by similarity or a copy in this sense. It would be conceivable that I portrayed some one's face by projecting it in some queer way, though correctly according to the adopted rule of projection, on a piece of paper, in such a way that no one would normally call the projection “a good portrait of so-and-so” because it would not look a bit like him.
 
 


If we keep in mind the possibility of a picture which, though correct, has no similarity with its object, the interpolation of a shadow between the sentence and reality loses all point. For now the sentence itself can serve as such a shadow. The sentence is just such a picture, which hasn't the slightest similarity with what it represents. If we were doubtful about how the sentence “King's College is on fire” can be a picture of King's College on fire, we need only ask ourselves: “How should we explain what the sentence means?” Such an explanation might consist of ostensive definitions. We should say, e.g., “this is King's College” (pointing to the building), “this is a fire” (pointing to a fire). This is the way we connect words with things.
If we keep in mind the possibility of a picture which, though correct, has no similarity with its object, the interpolation of a shadow between the sentence and reality loses all point. For now the sentence itself can serve as such a shadow. The sentence is just such a picture, which hasn't the slightest similarity with what it represents. If we were doubtful about how the sentence “King's College is on fire” can be a picture of King's College on fire, we need only ask ourselves: “How should we explain what the sentence means?” Such an explanation might consist of ostensive definitions. We should say, e.g., “this is King's College” (pointing to the building), “this is a fire” (pointing to a fire). This is the way we connect words with things.


 
The idea that that which we wish to happen must be present as a shadow in our wish is deeply rooted in our forms of expression. But, in fact, we might say that it is only the next best absurdity to the one which we should really like to say. If it weren't too absurd we should say that the fact which we wish for must be present in our wish. For how can we wish just this to happen if just this isn't present in our wish? {{MS reference|Ts-309,61}}
 
The idea that that which we wish to happen must be present as a shadow in our wish is deeply rooted in our forms of expression. But, in fact, we might say that it is only the next best absurdity to the one which we should really like to say. If it weren't too absurd we should say that the fact which we wish for must be present in our wish. For how can we wish just this to happen if just this isn't present in our wish?
 
Ts-309,61


It is quite true to say: The mere shadow won't do; for it stops short before the object; and we want the wish to contain the object itself. ‒ ‒ ‒ We want that the wish that Mr. Smith should come into this room should wish that just Mr. Smith, and no substitute, should do the coming, and no substitute for that, into my room, and no substitute for that. But this is exactly what we said.
It is quite true to say: The mere shadow won't do; for it stops short before the object; and we want the wish to contain the object itself. ‒ ‒ ‒ We want that the wish that Mr. Smith should come into this room should wish that just Mr. Smith, and no substitute, should do the coming, and no substitute for that, into my room, and no substitute for that. But this is exactly what we said.


 
Our confusion could be described in this way: Quite in accordance with our usual form of expression we think of the fact which we wish for as of a thing which is not yet here, and to which, therefore, I cannot point. Now in order to understand the grammar of our expression “object of our wish” let's just consider the answer which we give to the question: “What is the object of your wish?” The answer to this question of course is “I wish that so-and-so should happen”. Now what would the answer be if we went on asking: “And what is the object of this wish?” It could only consist in a repetition of our previous expression of the wish, or else in a translation into some other form of expression. We might, e.g., state what we wished in other words or illustrate it by a picture, etc., etc. Now when we are under the impression that what we call the object of our wish is, as it were, a man who has not yet entered our room, and therefore can't yet be seen, we imagine that any explanation of what it is we wish is only the next best thing to that explanation which would show the actual fact, ‒ ‒ ‒ which, we are afraid, can't yet be {{MS reference|Ts-309,62}} shown as it has not yet entered. ‒ ‒ ‒ It is as though I said to some one “I am expecting Mr. Smith”, and he asked me “Who is Mr. Smith?”, and I answered, “I can't show him to you now, as he isn't there. All I can show you is a picture of him”. It then seems as though I could never entirely explain what I wished until it had actually happened. But of course this is not the case. The truth is that I needn't be able to give a better explanation of what I wished after the wish was fulfilled than before; for I might perfectly well have shown Mr. Smith to my friend, and have shown him what “coming in” means, and have shown him what my room is, before Mr. Smith came into my room.
 
Our confusion could be described in this way: Quite in accordance with our usual form of expression we think of the fact which we wish for as of a thing which is not yet here, and to which, therefore, I cannot point. Now in order to understand the grammar of our expression “object of our wish” let's just consider the answer which we give to the question: “What is the object of your wish?” The answer to this question of course is “I wish that so-and-so should happen”. Now what would the answer be if we went on asking: “And what is the object of this wish?” It could only consist in a repetition of our previous expression of the wish, or else in a translation into some other form of expression. We might, e.g., state what we wished in other words or illustrate it by a picture, etc., etc. Now when we are under the impression that what we call the object of our wish is, as it were, a man who has not yet entered our room, and therefore can't yet be seen, we imagine that any explanation of what it is we wish is only the next best thing to that explanation which would show the actual fact, ‒ ‒ ‒ which, we are afraid, can't yet be
 
Ts-309,62
 
shown as it has not yet entered. ‒ ‒ ‒ It is as though I said to some one “I am expecting Mr. Smith”, and he asked me “Who is Mr. Smith?”, and I answered, “I can't show him to you now, as he isn't there. All I can show you is a picture of him”. It then seems as though I could never entirely explain what I wished until it had actually happened. But of course this is not the case. The truth is that I needn't be able to give a better explanation of what I wished after the wish was fulfilled than before; for I might perfectly well have shown Mr. Smith to my friend, and have shown him what “coming in” means, and have shown him what my room is, before Mr. Smith came into my room.
 
 


Our difficulty could be put this way: We think about things, ‒ ‒ ‒ but how do these things enter into our thoughts? We think about Mr. Smith; but Mr. Smith need not be present. A picture of him won't do; for how are we to know whom it represents. In fact no substitutes for him will do. Then how can he himself be an object of our thoughts? (I am here using the expression “object of our thought” in a way different from that in which I have used it before. I mean a thing I am thinking about, not “that which I am thinking”.)
Our difficulty could be put this way: We think about things, ‒ ‒ ‒ but how do these things enter into our thoughts? We think about Mr. Smith; but Mr. Smith need not be present. A picture of him won't do; for how are we to know whom it represents. In fact no substitutes for him will do. Then how can he himself be an object of our thoughts? (I am here using the expression “object of our thought” in a way different from that in which I have used it before. I mean a thing I am thinking about, not “that which I am thinking”.)


 
We said the connection between our thinking, or speaking, about a man and the man himself was made when, in order to explain the meaning of the word “Mr. Smith” we pointed to him, saying “this is Mr. Smith”. And there is nothing mysterious about this connection. I mean, there is no queer mental act which somehow conjured up Mr. Smith in our minds when he really {{MS reference|Ts-309,63}} isn't there. What makes it difficult to see that this is the connection is a peculiar form of expression of ordinary language, which makes it appear that the connection between our thought (or the expression of our thought) and the thing we think about must have subsisted during the act of thinking.
 
We said the connection between our thinking, or speaking, about a man and the man himself was made when, in order to explain the meaning of the word “Mr. Smith” we pointed to him, saying “this is Mr. Smith”. And there is nothing mysterious about this connection. I mean, there is no queer mental act which somehow conjured up Mr. Smith in our minds when he really
 
Ts-309,63
 
isn't there. What makes it difficult to see that this is the connection is a peculiar form of expression of ordinary language, which makes it appear that the connection between our thought (or the expression of our thought) and the thing we think about must have subsisted during the act of thinking.
 
 


“Isn't it queer that in Europe we should be able to mean somebody who is in America?” ‒ ‒ ‒ If someone had said “Napoleon was crowned in 1804”, and we asked him “Did you mean the man who won the battle of Austerlitz?” he might say “Yes, I meant him”. And the use of the past tense “meant” might make it appear as though the idea of Napoleon having won the battle of Austerlitz must have been present in the man's mind when he said that Napoleon was crowned in 1804.
“Isn't it queer that in Europe we should be able to mean somebody who is in America?” ‒ ‒ ‒ If someone had said “Napoleon was crowned in 1804”, and we asked him “Did you mean the man who won the battle of Austerlitz?” he might say “Yes, I meant him”. And the use of the past tense “meant” might make it appear as though the idea of Napoleon having won the battle of Austerlitz must have been present in the man's mind when he said that Napoleon was crowned in 1804.


Someone says, “Mr. N will come to see me this afternoon”; I ask “Do you mean him?” pointing to someone present, and he answers “Yes”. In this conversation a connection was established between the word, “Mr. N” and Mr. N. But we are tempted to think that while my friend said, “Mr. N will come to see me”, and meant what he said, his mind must have made the connection.
Someone says, “Mr. N will come to see me this afternoon”; I ask “Do you mean him?” pointing to someone present, and he answers “Yes”. In this conversation a connection was established between the word, “Mr. N” and Mr. N. But we are tempted to think that while my friend said, “Mr. N will come to see me”, and meant what he said, his mind must have made the connection.


This is partly what makes us think of meaning or thinking as a peculiar mental activity; the word “mental” indicating that we mustn't expect to understand how these things work.
This is partly what makes us think of meaning or thinking as a peculiar mental activity; the word “mental” indicating that we mustn't expect to understand how these things work.


 
What we said of thinking can also be applied to imagining. Someone says, he imagines King's College on fire. We ask him: “How do you know that it's King's College you imagine on fire? Couldn't it be a different building, very much like it? In {{MS reference|Ts-309,64}} fact, is your imagination so absolutely exact that there might not be a dozen buildings whose representation your image could be?” ‒ ‒ ‒ And still you say: “There's no doubt I imagine King's College and no other building”. But can't saying this be making the very connection we want? For saying it is like writing the words “Portrait of Mr. So-and-so” under a picture. It might have been that while you imagined King's College on fire you said the words “King's College is on fire”. But in very many cases you certainly don't speak explanatory words in your mind while you have the image. And consider, even if you do, you are not going the whole way from your image to King's College, but only to the words “King's College”. The connection between these words and King's College was, perhaps, made at another time.
 
What we said of thinking can also be applied to imagining. Someone says, he imagines King's College on fire. We ask him: “How do you know that it's King's College you imagine on fire? Couldn't it be a different building, very much like it? In
 
Ts-309,64
 
fact, is your imagination so absolutely exact that there might not be a dozen buildings whose representation your image could be?” ‒ ‒ ‒ And still you say: “There's no doubt I imagine King's College and no other building”. But can't saying this be making the very connection we want? For saying it is like writing the words “Portrait of Mr. So-and-so” under a picture. It might have been that while you imagined King's College on fire you said the words “King's College is on fire”. But in very many cases you certainly don't speak explanatory words in your mind while you have the image. And consider, even if you do, you are not going the whole way from your image to King's College, but only to the words “King's College”. The connection between these words and King's College was, perhaps, made at another time.
 
 


The fault which in all our reasoning about these matters we are inclined to make is thinking that images and experiences of all sorts, which are in some sense closely connected with each other, must be present in our mind at the same time. If we sing a tune we know by heart, or say the alphabet, the notes and letters seem to hang together; and each seems to draw out the next as though they were pearls strung on a thread, and by pulling out one I pulled out the one following it.
The fault which in all our reasoning about these matters we are inclined to make is thinking that images and experiences of all sorts, which are in some sense closely connected with each other, must be present in our mind at the same time. If we sing a tune we know by heart, or say the alphabet, the notes and letters seem to hang together; and each seems to draw out the next as though they were pearls strung on a thread, and by pulling out one I pulled out the one following it.


 
Now there is no doubt that seeing the picture of a string of beads being pulled out of a box through a hole in the lid, I should say: “These beads must all have been together in the box before”. But it is easy to see that this is making a {{MS reference|Ts-309,65}}
 
Now there is no doubt that seeing the picture of a string of beads being pulled out of a box through a hole in the lid, I should say: “These beads must all have been together in the box before”. But it is easy to see that this is making a
 
Ts-309,65


hypothesis. I should have seen the same picture if the beads had gradually come into existence in the hole of the lid. We easily overlook the distinction between stating a conscious mental event, and making a hypothesis about what one might call the mechanism of the mind. All the more as such hypotheses or pictures of the working of our mind are embodied in many of the forms of expression of our everyday language. The past tense “meant” in the sentence “I meant the man who won the battle of Austerlitz” is only part of such a picture, the mind being conceived as a place in which what we remember is kept, stored, before we expresses it. If I whistle a tune I know well and am interrupted in the middle, if then someone asked me “did you know how to go on?” I should answer “yes I did”. What sort of process is this knowing how to go on? It might appear as though the whole continuation of the tune had to be present while I knew how to go on.
hypothesis. I should have seen the same picture if the beads had gradually come into existence in the hole of the lid. We easily overlook the distinction between stating a conscious mental event, and making a hypothesis about what one might call the mechanism of the mind. All the more as such hypotheses or pictures of the working of our mind are embodied in many of the forms of expression of our everyday language. The past tense “meant” in the sentence “I meant the man who won the battle of Austerlitz” is only part of such a picture, the mind being conceived as a place in which what we remember is kept, stored, before we expresses it. If I whistle a tune I know well and am interrupted in the middle, if then someone asked me “did you know how to go on?” I should answer “yes I did”. What sort of process is this knowing how to go on? It might appear as though the whole continuation of the tune had to be present while I knew how to go on.


Ask yourself such a question as: “How long does it take to know how to go on?” Or is it an instantaneous process? Aren't we making a mistake like mixing up the existence of a gramophone record of a tune with the existence of the tune? And aren't we assuming that whenever a tune passes through existence there must be some sort of a gramophone record of it from which it is played?
Ask yourself such a question as: “How long does it take to know how to go on?” Or is it an instantaneous process? Aren't we making a mistake like mixing up the existence of a gramophone record of a tune with the existence of the tune? And aren't we assuming that whenever a tune passes through existence there must be some sort of a gramophone record of it from which it is played?


 
Consider the following example: A gun is fired in my presence and I say: “This crash wasn't as loud as I had {{MS reference|Ts-309,66}}
 
Consider the following example: A gun is fired in my presence and I say: “This crash wasn't as loud as I had
 
Ts-309,66


expected”. Someone asks me: “How is this possible? Was there a crash, louder than that of a gun, in your imagination?” I must confess that there was nothing of the sort. Now he says: “Then you didn't really expect a louder crash, ‒ ‒ ‒ but perhaps the shadow of one. ‒ ‒ ‒ And how did you know that it was the shadow of a louder crash?” ‒ ‒ ‒ Let's see what, in such a case, might really have happened. Perhaps in waiting for the report I opened my mouth, held on to something to steady myself, and perhaps I said: “This is going to be terrible”. Then, when the explosion was over: “It wasn't so loud after all”. ‒ ‒ ‒ Certain tensions in my body relax. But what is the connection between these tensions, opening my mouth, etc., and a real louder crash? Perhaps this connection was made by having heard such a crash and having had the experiences mentioned.
expected”. Someone asks me: “How is this possible? Was there a crash, louder than that of a gun, in your imagination?” I must confess that there was nothing of the sort. Now he says: “Then you didn't really expect a louder crash, ‒ ‒ ‒ but perhaps the shadow of one. ‒ ‒ ‒ And how did you know that it was the shadow of a louder crash?” ‒ ‒ ‒ Let's see what, in such a case, might really have happened. Perhaps in waiting for the report I opened my mouth, held on to something to steady myself, and perhaps I said: “This is going to be terrible”. Then, when the explosion was over: “It wasn't so loud after all”. ‒ ‒ ‒ Certain tensions in my body relax. But what is the connection between these tensions, opening my mouth, etc., and a real louder crash? Perhaps this connection was made by having heard such a crash and having had the experiences mentioned.


 
Examine expressions like: “having an idea in one's mind”, “analysing the idea before one's mind”. In order not to be misled by them see what really happens when, say, in writing a letter you are looking for the words which correctly express the idea which is “before your mind”. To say that we are trying to express the idea which is before our mind is to use a metaphor, one which very naturally suggests itself; and which is all right so long as it doesn't mislead us when we are philosophizing. For when we recall what really happens in such cases we find a great variety of processes more or less akin to each other. ‒ ‒ ‒ We might be inclined to say that in all such cases, at any rate, we are guided by something before our mind. {{MS reference|Ts-309,67}}
 
Examine expressions like: “having an idea in one's mind”, “analysing the idea before one's mind”. In order not to be misled by them see what really happens when, say, in writing a letter you are looking for the words which correctly express the idea which is “before your mind”. To say that we are trying to express the idea which is before our mind is to use a metaphor, one which very naturally suggests itself; and which is all right so long as it doesn't mislead us when we are philosophizing. For when we recall what really happens in such cases we find a great variety of processes more or less akin to each other. ‒ ‒ ‒ We might be inclined to say that in all such cases, at any rate, we are guided by something before our mind.
 
Ts-309,67


But then the words “guided” and “thing before our mind” are used in as many senses as the words “idea” and “expression of an idea”.
But then the words “guided” and “thing before our mind” are used in as many senses as the words “idea” and “expression of an idea”.


The phrase “to express an idea which is before our mind” suggests that what we are trying to express in words is already expressed, only in a different language; that this expression is before our mind's eye; and that what we do is to translate from the mental into the verbal language. In most cases which we call “expressing an idea, etc.” something very different happens. Imagine what it is that happens in cases such as this: I am looking for a word. Several words are suggested and I reject them. Finally one is proposed and I say: “That is what I meant!”
The phrase “to express an idea which is before our mind” suggests that what we are trying to express in words is already expressed, only in a different language; that this expression is before our mind's eye; and that what we do is to translate from the mental into the verbal language. In most cases which we call “expressing an idea, etc.” something very different happens. Imagine what it is that happens in cases such as this: I am looking for a word. Several words are suggested and I reject them. Finally one is proposed and I say: “That is what I meant!”


(We should be inclined to say that the proof of the impossibility of trisecting the angle with ruler and compasses analyses our idea of the trisection of an angle. But the proof gives us a new idea of trisection, one which we didn't have before the proof constructed it. The proof led us a road which we were inclined to go; but it led us away from where we were, and didn't just show us clearly the place where we had been all the time.)
(We should be inclined to say that the proof of the impossibility of trisecting the angle with ruler and compasses analyses our idea of the trisection of an angle. But the proof gives us a new idea of trisection, one which we didn't have before the proof constructed it. The proof led us a road which we were inclined to go; but it led us away from where we were, and didn't just show us clearly the place where we had been all the time.)


Let us now revert to the point where we said that we gained nothing by assuming that a shadow must intervene between the expression of our thought and the reality with which our thought is concerned. We said that if we wanted a picture of reality the sentence itself is such a picture (though not a {{MS reference|Ts-309,68}} “picture by similarity”).


 
I have been trying in all this to remove the temptation to think that there “must be” what is called a mental process of thinking, hoping, wishing, believing, etc., independent of the process of expressing a thought, a hope, a wish, etc. And I want to give you the following rule of thumb: If you are puzzled about the nature of thought, belief, knowledge, and the like, substitute for the thought the expression of the thought etc. The difficulty which lies in this substitution, and at the same time the whole point of it, is this: the expression of belief, thought, etc., is just a sentence; ‒ ‒ ‒ and the sentence has sense only as a member of a system of language; as one expression within a calculus. Now we are tempted to imagine this calculus, as it were, as a permanent background to every sentence which we say, and to think that, although the sentence as written on a piece of paper or spoken stands isolated, in the mental act of thinking the calculus is there ‒ ‒ ‒ all in a lump. The mental act seems to perform in a miraculous way what could not be performed by any act of manipulating symbols. Now when the temptation to think that in some sense the whole calculus must be present at the same time vanishes, there is no more point in postulating the existence of a peculiar kind of mental act alongside of our expression. This, of course, doesn't mean that we have shown that peculiar acts of consciousness do not accompany the expressions of our thoughts! Only we no longer say that they must accompany them. {{MS reference|Ts-309,69}}
Let us now revert to the point where we said that we gained nothing by assuming that a shadow must intervene between the expression of our thought and the reality with which our thought is concerned. We said that if we wanted a picture of reality the sentence itself is such a picture (though not a
 
Ts-309,68
 
“picture by similarity”).
 
 
 
I have been trying in all this to remove the temptation to think that there “must be” what is called a mental process of thinking, hoping, wishing, believing, etc., independent of the process of expressing a thought, a hope, a wish, etc. And I want to give you the following rule of thumb: If you are puzzled about the nature of thought, belief, knowledge, and the like, substitute for the thought the expression of the thought etc. The difficulty which lies in this substitution, and at the same time the whole point of it, is this: the expression of belief, thought, etc., is just a sentence; ‒ ‒ ‒ and the sentence has sense only as a member of a system of language; as one expression within a calculus. Now we are tempted to imagine this calculus, as it were, as a permanent background to every sentence which we say, and to think that, although the sentence as written on a piece of paper or spoken stands isolated, in the mental act of thinking the calculus is there ‒ ‒ ‒ all in a lump. The mental act seems to perform in a miraculous way what could not be performed by any act of manipulating symbols. Now when the temptation to think that in some sense the whole calculus must be present at the same time vanishes, there is no more point in postulating the existence of a peculiar kind of mental act alongside of our expression. This, of course, doesn't mean that we have shown that peculiar acts of consciousness do not accompany the expressions of our thoughts! Only we no longer say that they must accompany them.
 
Ts-309,69
 
 


“But the expression of our thoughts can always lie, for we may say one thing and mean another”. Imagine the many different things which happen when we say one thing and mean another! ‒ ‒ ‒ Make the following experiment: say the sentence “It is hot in this room”, and mean: “it is cold”. Observe closely what you are doing.
“But the expression of our thoughts can always lie, for we may say one thing and mean another”. Imagine the many different things which happen when we say one thing and mean another! ‒ ‒ ‒ Make the following experiment: say the sentence “It is hot in this room”, and mean: “it is cold”. Observe closely what you are doing.


We could easily imagine beings who do their private thinking by means of “asides” and who manage their lies by saying one thing aloud, following it up by an aside saying the opposite.
We could easily imagine beings who do their private thinking by means of “asides” and who manage their lies by saying one thing aloud, following it up by an aside saying the opposite.


“But meaning, thinking, etc., are private experiences. They are not activities like writing, speaking, etc.” ‒ ‒ ‒ But why shouldn't they be the specific private experiences of writing, ‒ ‒ ‒ the muscular, visual, tactile sensations of writing or speaking?
“But meaning, thinking, etc., are private experiences. They are not activities like writing, speaking, etc.” ‒ ‒ ‒ But why shouldn't they be the specific private experiences of writing, ‒ ‒ ‒ the muscular, visual, tactile sensations of writing or speaking?


Make the following experiment: say and mean a sentence, e.g.– “It will probably rain tomorrow”. Now think the same thought again, mean what you just meant, but without saying anything (neither aloud or to yourself). If thinking that it will rain tomorrow accompanied saying that it will rain tomorrow, then just do the first activity and leave out the second. ‒ ‒ ‒ If thinking and speaking stood in the relation of the words and the melody of a song, we could leave out the speaking and do the thinking just as we can sing the tune without the words.
Make the following experiment: say and mean a sentence, e.g.– “It will probably rain tomorrow”. Now think the same thought again, mean what you just meant, but without saying anything (neither aloud or to yourself). If thinking that it will rain tomorrow accompanied saying that it will rain tomorrow, then just do the first activity and leave out the second. ‒ ‒ ‒ If thinking and speaking stood in the relation of the words and the melody of a song, we could leave out the speaking and do the thinking just as we can sing the tune without the words.


 
But can't one at any rate speak and leave out the thinking? {{MS reference|Ts-309,70}}
 
But can't one at any rate speak and leave out the thinking?
 
Ts-309,70


Certainly, ‒ ‒ ‒ but observe what sort of thing you are doing if you speak without thinking. Observe first of all that the process which we might call “speaking and meaning what you speak” is not necessarily distinguished from that of thoughtlessly speaking by what happens at the time when you speak. What distinguishes the two might very well be what happens before or after you speak.
Certainly, ‒ ‒ ‒ but observe what sort of thing you are doing if you speak without thinking. Observe first of all that the process which we might call “speaking and meaning what you speak” is not necessarily distinguished from that of thoughtlessly speaking by what happens at the time when you speak. What distinguishes the two might very well be what happens before or after you speak.
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