Philosophical Grammar

, by Wittgenstein, Ludwig; Rhees, Rush; Kenny, Anthony

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ISBN: 9780520245020 | 0520245024
Cover: Paperback
Copyright: 5/30/2005

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In 1933 Ludwig Wittgenstein revised a manuscript he had compiled from his 1930-1932 notebooks, but the work as a whole was not published until 1969, asPhilosophische Grammatik.This first English translation clearly reveals the central placePhilosophical Grammaroccupies in Wittgenstein's thought and provides a link from his earlier philosophy to his later views.

Part I The Proposition and its Sense

How can one talk about ``understanding'' and ``not understanding'' a proposition?

Surely it's not a proposition until it's understood?

(1)

Understanding and signs. Frege against the formalists. Understanding like seeing a picture that makes all the rules clear; in that case the picture is itself a sign, a calculus.

``To understand a language'' -- to take in a symbolism as a whole.

Language must speak for itself.

(2)

One can say that meaning drops out of language.

In contrast: ``Did you mean that seriously or as a joke?'' When we mean (and don't just say) words it seems to us as if there were something coupled to the words.

(1)

Comparison with understanding a piece of music: for explanation I can only translate the musical picture into a picture in another medium -- and why just that picture? Comparison with understanding a picture. Perhaps we see only patches and lines -- ``we do not understand the picture''. Seeing a genre-picture in different ways.

(1)

``I understand that gesture'' -- it says something.

In a sentence a word can be felt as belonging first with one word and then with another.

A `proposition' may be what is conceived in different ways or the way of conceiving itself.

A sentence from the middle of a story I have not read.

The concept of understanding is a fluid one.

(1)

A sentence in a code: at what moment of translating does understanding begin?

The words of a sentence are arbitrary; so I replace them with letters. But now I cannot immediately think the sense of the sentence in the new expression.

The notion that we can only imperfectly exhibit our understanding: the expression of understanding has something missing that is essentially inexpressible. But in that case it makes no sense to speak of a more complete expression.

(2)

What is the criterion for an expression's being meant thus? A question about the relationship between two linguistic expressions. Sometimes a translation into another mode of representation.

(1)

Must I understand a sentence to be able to act on it? If ``to understand a sentence'' means somehow or other to act on it, then understanding cannot be a precondition for our acting on it. -- What goes on when I suddenly understand someone else? There are many possibilities here.

(1)

Isn't there a gap between an order and its execution? ``I understand it, but only because I add something to it, namely the interpretation.'' -- But if one were to say ``any sentence still stands in need of an interpretation'', that would mean: no sentence can be understood without a rider.

(1)

``Understanding a word'' -- being able to apply it. -- ``When I said `I can play chess' I really could.'' How did I know that I could? My answer will show in what way I use the word ``can''.

Being able is called a state. ``To describe a state'' can mean various things. ``After all I can't have the whole mode of application of a word in my head all at once.''

(3)

It is not a question of an instantaneous grasping. --

When a man who knows the game watches a game of chess, the experience he has when a move is made usually differs from that of someone else watching without understanding the game. But this experience is not the knowledge of the rules. -- The understanding of language seems like a background; like the ability to multiply.

When do we understand a sentence? -- When we've uttered the whole of it? Or while uttering it?

(1)

When someone interprets, or understands, a sign in one sense or another, what he is doing is taking a step in a calculus. -- ``Thought'' sometimes means a process which may accompany the utterance of a sentence and sometimes the sentence itself in the system of language.

(2)

Grammar as (e.g.) the geometry of negation. We would like to say: ``Negation has the property that when it is doubled it yields an affirmation''. But the rule doesn't give a further description of negation, it constitutes negation.

(1)

Geometry no more speaks about cubes than logic does about negation.

It looks as if one could infer from the meaning of negation that ``~ ~ p'' means p.

(1)

What does it mean to say that the ``is'' in ``The rose is red'' has a different meaning from the ``is'' in ``twice two is four''? Here we have one word but as it were different meaning-bodies with a single end surface: different possibilities of constructing sentences. The comparison of the glass cubes. The rule for the arrangement of the red sides contains the possibilities, i.e. the geometry of the cube. The cube can also serve as a notation for the rule if it belongs to a system of propositions.

(2)

``The grammatical possibilities of the negation-sign''. The T-F notation can illustrate the meaning of ``not''. The written symbol becomes a sign for negation only by the way it works -- the way it is used in the game.

(1)

If we derive geometrical propositions from a drawing or a model, then the model has the role of a sign in a game. We use the drawing of a cube again and again in different contexts. It is this sign that we take to be the cube in which the geometrical laws are already laid up.

(1)

My earlier concept of meaning originates in a primitive philosophy of language. -- Augustine on the learning of language. He describes a calculus of our language, only not everything that we call language is this calculus.

(1)

As if words didn't also have functions quite different from the naming of tables, chairs, etc. -- Here is the origin of the bad expression: a fact is a complex of objects.

(1)

In a familiar language we experience different parts of speech as different. It is only in a foreign language that we see clearly the uniformity of words.

(1)

If I decide to use a new word instead of ``red'', how would it come out that it took the place of the word ``red''?

(1)

The meaning of a word: what the explanation of its meaning explains. (If, on the other hand by ``meaning'' we mean a characteristic sensation, then the explanation of meaning would be a cause.)

(1)

Explanation can clear up misunderstandings. In that case understanding is a correlate of explanation. -- Definitions.

It seems as if the other grammatical rules for a word had to follow from its ostensive definition. But is this definition really unambiguous? One must understand a great deal of a language in order to understand the definition.

(1)

The words ``shape'', ``colour'' in the definitions determine the kind of use of the word. The ostensive definition has a different role in the grammar of each part of speech.

(1)

So how does it come about that on the strength of this definition we understand the word?

What's the sign of someone's understanding a game? Can't he learn a game simply by watching it being played? Learning and speaking without explicit rules. We are always comparing language with a game according to rules.

(2)

The names I give to bodies, shapes, colours, lengths have different grammars in each case. The meaning of a name is not the thing we point to when we give an ostensive definition of the name.

(1)

What constitutes the meaning of a word like ``perhaps''?

I know how it is used. The case is similar when someone is explaining to me a calculation ``that I don't quite understand''. ``Now I know how to go on.'' How do I know that I know how to go on?

(1)

Is the meaning really only the use of the word? Isn't it the way this use meshes with our life?

(1)

The words ``fine'', ``oh'', ``perhaps'' . . . can each be the expression of a feeling. But I don't call that feeling the meaning of the word.

I can replace the sensations by intonation and gestures.

I could also treat the word (e.g. ``oh'') itself as a gesture.

(1)

A language spoken in a uniform metre.

Relationships between tools in a toolbox.

``The meaning of a word: its role in the calculus of language.'' Imagine how we calculate with ``red''. And then: the word ``oh'' -- what corresponds now to the calculus?

(1)

Describing ball-games. Perhaps one will be unwilling to call some of them ball-games; but it is clear where the boundary is to be drawn here?

We consider language from one point of view only.

The explanation of the purpose or the effect of a word is not what we call the explanation of its meaning. It may be that if it is to achieve its effect a particular word cannot be replaced by any other, just as it may be that a gesture cannot be replaced by any other. -- We only bother about what's called the explanation of meaning and not about meaning in any other sense.

(1)

Aren't our sentences parts of a mechanism? As in a pianola? But suppose it is in bad condition? So it is not the effect but the purpose that is the sense of the signs (the holes in the pianola roll). Their purpose within the mechanism.

We need an explanation that is part of the calculus.

``A symbol is something that produces this effect.'' -- How do I know that it is the one I meant?''

We could use a colour-chart: and then our calculus would have to get along with the visible colour-sample.

(2)

``We could understand a penholder too, if we had given it a meaning.'' Does the understanding contain the whole system of its application?

When I read a sentence with understanding something happens: perhaps a picture comes into my mind. But before we call ``understanding'' is related to countless things that happen before and after the reading of this sentence.

When I don't understand a sentence -- that can be different things in different cases.

``Understanding a word'' -- that is infinitely various.

(3)

``Understanding'' is not the name of a single process but of more or less interrelated processes against a background of the actual use of a learnt language. -- We think that if I use the word ``understanding'' in all these cases there must be some one thing that happens in all of them. Well, the concept-word certainly does show a kinship but this need not be the sharing of a common property or constituent. -- The concept-word ``game''. ``By `knowledge' we mean these processes, and these, and similar ones.''

(3)

III

If for our purposes we wish to regulate the use of a word by definite rules, then alongside its fluctuating use we set a different use. But this isn't like the way physics gives a simplified description of a natural phenomenon. It is not as if we were saying something that would hold only of an ideal language.

(1)

We understand a genre-picture if we recognize what the people in it are doing. If this recognition does not come easily, there is a period of doubt followed by a familiar process of recognition. If on the other hand we take it in at first glance it is difficult to say what the understanding -- the recognition say -- consists of. There is no one thing that happens that could be called recognition.

If I want to say ``I understand it like that'' then the ``like that'' stands for a translation into a different expression. Or is it a sort of intransitive understanding?

(2)

Forgetting the meaning of a word. Different cases. The man feels, as he looks at blue objects, that the connection between the word ``blue'' and the colour has been broken off. We might restore the connection in various ways. The connection is not made by a single phenomenon, but can manifest itself in very various processes. Do I mean then that there is no such thing as understanding but only manifestations of understanding? -- a senseless question.

(1)

How does an ostensive definition work? Is it put to work again every time the word is used? Definition as a part of the calculus acts only by being applied.

(1)

In what cases shall we say that the man understands the word ``blue''? In what circumstances will he be able to say it? or to say that he understood it in the past?

If he says ``I picked the ball out by guesswork, I didn't understand the word'', ought we to believe him? ``He can't be wrong if he says that he didn't understand the word'': a remark on the grammar of the statement ``I didn't understand the word''.

(1)

We call understanding a mental state, and characterize it as a hypothetical process. Comparison between the grammar of mental processes and the grammar of brain processes.

In certain circumstances both our picking out a red object from others on demand and our being able to give the ostensive definition of the word ``red'' are regarded as signs of understanding.

We aren't interested here in the difference between thinking out loud (or in writing) and thinking in the imagination.

What we call ``understanding'' is not the behaviour that shows us the understanding, but a state of which this behaviour is a sign.

(2)

We might call the recital of the rules on its own a criterion of understanding, or alternatively tests of use on their own. Or we may regard the recital of the rules as a symptom of the man's being able to do something other than recite the rules.

To understand = to let a proposition work on one.

When one remembers the meaning of a word, the remembering is not the mental process that one imagines at first sight.

The psychological process of understanding is in the same case as the arithmetical object Three.

(1)

An explanation, a chart, is first used by being looked up, then by being looked up in the head, and finally as if it had never existed.

A rule as the cause or history behind our present behaviour is of no interest to us. But a rule can be a hypothesis, or can itself enter into the conduct of the game. If a disposition is hypothesized in the player to give the list of rules on request, it is a disposition analogous to a physiological one. In our study of symbolism there is no foreground and background.

(2)

What interests us in the sign is what is embodied in the grammar of the sign.

(1)

The ostensive definition of signs is not an application of language, but part of the grammar: something like a rule for translation from a gesture language into a word-language. -- What belongs to grammar are all the conditions necessary for comparing the proposition with reality -- all the conditions necessary for its sense.

(1)

Does our language consist of primary signs (gestures) and secondary signs (words)?

Obviously we would not be able to replace an ordinary sentence by gestures.

``Is it an accident that in order to define the signs I have to go outside the written and spoken signs?'' In that case isn't it strange that I can do anything at all with the written signs?

(1)

We say that a red label is the primary sign for the colour red, and the word a secondary sign. -- But must a Frenchman have a red image present to his mind when he understands my explanation ``red = rouge''?

(1)

Are the primary signs incapable of being misinterpreted? Can one say they don't any longer need to be understood?

(1)

A colour chart might be arranged differently or used differently, and yet the words mean the same colours as with us.

Can a green label be a sample of red?

Can it be said that when someone is painting a certain shade of green he is copying the red of a label?

A sample is not used like a name.

(1)

``Copy'' can mean various things. Various methods of comparison.

We do not understand what is meant by ``this shade of colour is a copy of this note on the violin.'' It makes no sense to speak of a projection-method for association.

(1)

We can say that we communicate by signs whether we use words or samples, but the game of acting in accordance with words is different from the game of acting in accordance with samples.

(1)

``There must be some sort of law for reading the chart. -- Otherwise how would one know how the table was to be used?'' It is part of human nature to understand pointing with the finger in the way we do.

The chart does not compel me to use it always in the same way.

(1)

Is the word ``red'' enough to enable one to look for something red? Does one need a memory image to do so?

An order. Is the real order ``Do now what you remember doing then?''

If the colour sample appears darker than I remember it being yesterday, I need not agree with my memory.

(1)

``Paint from memory the colour of the door of your room'' is no more unambiguous than ``paint the green you see on this chart.''

I see the colour of the flower and recognize it.

Even if I say ``no, this colour is brighter than the one I saw there,'' there is no process of comparing two simultaneously given shades of colour.

Think of reading aloud from a written test (or writing to dictation).

(1)

``Why do you choose this colour when given this order?'' -- ``Because this colour is opposite to the word `red' in my chart.'' In that case there is no sense in this question: ``Why do you call `red' the colour in the chart opposite the word `red'?''

The connection between ``language and reality'' is made by definitions of words -- which belong to grammar.

(1)

A gesture language used to communicate with people who have no word-language in common with us. Do we feel there too the need to go outside language to explain its signs?

The correlation between objects and names is a part of the symbolism. It gives the wrong idea if you say that the connection is a psychological one.

(1)

Someone copies a figure on the scale of 1 to 10. Is the understanding of the general rule of such mapping contained in the process of copying?

Or was the process merely in agreement with that rule, but also in agreement with other rules?

(1)

Even if my pencil doesn't always do justice to the model, my intention always does.

(1)

For our studies it can never be essential that a symbolic phenomenon occurs in the mind and not on paper.

An explanation of a sign can replace the sign itself -- this contrasts with causal explanation.

(1)

Reading. -- Deriving a translation from the original may also be a visible process.

Always what represents is the system in which a sign is used.

If `mental' processes can be true and false, their descriptions must be able to as well.

(2)

Every case of deriving an action from a command is the same kind of thing as the written derivation of a result.

``I write the number `16' here because it says `x2' there.''

It might appear that some causality was operating here, but that would be a confusion between `reason' and `cause'.

101

(1)

``That's him'' -- that contains the whole problem of representation.

I make a plan: I see myself acting thus and so. ``How do I know that it's myself?'' Or ``How do I know that the word `I' stands for me?''

The delusion that in thought the objects do what the proposition states about them.

``I meant the victor of Austerlitz'' -- the past tense, which looks as if it was giving a description, is deceptive.

102

(1)

``How does one think a proposition? How does thought use its expression?''

Let's compare belief with the utterance of a sentence: the processes in the larynx etc. accompany the spoken sentence which alone interests us -- not as part of a mechanism, but as part of a calculus.

We think we can't describe thought after the event because the delicate processes have been lost sight of.

What is the function of thought? Its effect does not interest us.

103

(2)

But if thinking consists only in writing or speaking, why shouldn't a machine do it?

Could a machine be in pain?

It is a travesty of the truth to say: thinking is an activity of our mind, as writing is an activity of the hand.

105

(1)

`Thinking' `Language' are fluid concepts.

The expression ``mental process'' is meant to distinguish `experience' from `physical processes'; or else we talk of `unconscious thoughts' -- of processes in a mind-model; or else the word ``thought'' is taken as synonymous with ``sense of a sentence''.

106

(1)

The idea that one language in contrast to others can have an order of words which corresponds to the order of thinking.

Is it, as it were, a contamination of the sense that we express it in a particular language? Does it impair the rigour and purity of the proposition 25 x 25 = 625 that it is written down in a particular number system?

Thought can only be something common-or-garden. But we are affected by this concept as we are by that of the number one.

107

(2)

What does man think for? There is no such thing as a ``thought-experiment''. I believe that more boilers would explode if people did not calculate when making boilers. Does it follow that there will in fact be fewer? The belief that fire will burn me is of the same nature as the fear that it will burn me.

109

(1)

My assumption that this house won't collapse may be the utterance of a sentence which is part of a calculation. I do have reasons for it. What counts as a reason for an assumption determines a calculus. -- So is the calculus something we adopt arbitrarily? No more so than the fear of fire.

As long as we remain in the province of true-false games a change of grammar can only lead us from one game to another, and never from something true to something false.

110

(2)

What is a proposition? -- Do we have a single general concept of proposition?

112

(1)

``What happens when a new proposition is taken into the language: what is the criterion for its being a proposition?''

In this respect the concept of number is like the concept of proposition. On the other hand the concept of cardinal number can be called a rigorously circumscribed concept, that's to say it's a concept in a different sense of the word.

113

(1)

I possess the concept `language' from the languages I have learnt. ``But language can expand'': if ``expand'' makes sense here, I must now be able to specify how I imagine such an expansion.

No sign leads us beyond itself.

Does every newly constructed language broaden the concept of language? -- Comparison with the concept of number.

114

(1)

The indeterminacy of generality is not a logical indeterminacy.

The task of philosophy is not to create an ideal language, but to clarify the use of existing language.

I'm allowed to use the word ``rule'' without first tabulating the rules for the word. -- If philosophy was concerned with the concept of the calculus of all calculi, there would be such a thing as metaphilosophy. But there is not.

115

(1)

It isn't on the strength of a particular property, the property of being a rule, that we speak of the rules of a game. -- We use the word ``rule'' in contrast to ``word'', ``projection'' and some other words.

116

(1)

We learnt the meaning of the word ``plant'' by examples. And if we disregard hypothetical dispositions, these examples stand only for themselves. --

The grammatical pace of the word ``game'' ``rule'' etc is given by examples in rather the way in which the place of a meeting is specified by saying that it will take place beside such and such a tree.

117

(1)

Meaning as something which comes before our minds when we hear a word.

``Show the children a game''.

The sentence ``The Assyrians knew various games'' would strike us as curious since we wouldn't be certain that we could give an example.

118

(1)

Examples of the use of the word ``wish''. Our aim is not to give a theory of wishing, which would have to explain every case of wishing.

The use of the words ``proposition'', ``language'', etc. has the haziness of the normal use of concept-words in our language.

119

(2)

The philosophy of logic speaks of sentences and words in the sense in which we speak of them in ordinary life.

(We are not justified in having any more scruples about our language than the chess player has about chess, namely none.)

121

(1)

Sounding like a sentence. We don't call everything `that sounds like a sentence' a sentence. -- If we disregard sounding like a sentence do we still have a general concept of proposition?

The example of a language in which the order of the words in a sentence is the reverse of the present one.

122

(1)

The definition ``A proposition is whatever can be true or false''. -- The words ``true'' and ``false'' are items in a particular notation for the truth-functions.

Does `` `p' is true'' state anything about the sign `p'?

123

(1)

In the schema ``This is how things stand'' the ``how things stand'' is a handle for the truth-functions.

A general propositional form determines a proposition as part of a calculus.

124

(1)

The rules that say that such and such a combination of words yields no sense.

``How do I know that red can't be cut into bits?'' is not a question. I must begin with the distinction between sense and nonsense. I can't give it a foundation.

125

(2)

``How must we make the grammatical rules for words if they are to give a sentence sense?'' --

A proposition shows the possibility of the state of affairs it describes. ``Possible'' here means the same as ``conceivable''; representable in a particular system of propositions.

The proposition ``I can imagine such and such a colour transition connects the linguistic representation with another form of representation; it is a proposition of grammar.

127

(1)

It looks as if we could say: Word-language allows of senseless combinations of words, but the language of imagining does not allow us to imagine anything senseless.

``Can you imagine it's being otherwise?'' -- How strange that one should be able to say that such and such a state of affairs is inconceivable!

128

(2)

The role of a proposition in the calculus is its sense.

It is only in language that something is a proposition. To understand a proposition is to understand a language.

130

(2)

VII

Symbols appear to be of their nature unsatisfied.

A proposition seems to demand that reality be compared with it.

``A proposition like a ruler laid against reality.''

132

(1)

If you see the expression of an expectation you see what is being expected.

It looks as if the ultimate thing sought by an order had to remain unexpressed. -- As if the sign was trying to communicate with us.

A sign does its job only in a grammatical system.

132

(1)

It seems as if the expectation and the fact satisfying the expectation fitted together somehow. Solids and hollows. -- Expectation is not related to its satisfaction in the same way as hunger is related to its satisfaction.

133

(1)

The strange thing that the event I expected isn't distinct from the one I expected. -- ``The report was not so loud as I had expected.''

``How can you say that the red which you see in front of you is the same as the red you imagined?'' -- One takes the meaning of the word ``red'' as being the sense of a proposition saying that something is red.

134

(1)

A red patch looks different from one that is not red. But it would be odd to say ``a red patch looks different when it is there from when it isn't there''. Or: ``How do you know that you are expecting a red patch?''

135

(1)

How can I expect the event, when it isn't yet there at all? -- I can imagine a stag that is not there, in this meadow, but not kill one that is not there. -- It is not the expected thing that is the fulfilment, but rather its coming about. It is difficult for us to shake off this comparison: a man makes his appearance -- an event makes its appearance.

136

(2)

A search for a particular thing (e.g. my stick) is a particular kind of search, and differs from a search for something else because of what one does (says, thinks) while searching, not because of what one finds. -- Contrast looking for the trisection of the angle.

138

(1)

The symptoms of expectation are not the expression of expectation.

In the sentence ``I expect that he is coming'' is one using the words ``he is coming'' in a different sense from the one they have in the assertion ``he is coming''?

What makes it the expectation precisely of him?

Various definitions of ``expecting a person X''.

It isn't a later experience that decides what we are expecting. ``Let us put the expression of expectation in place of the expectation.''

138

(2)

Expectation as preparatory behaviour.

``Expectation is a thought''

If hunger is called a wish it is a hypothesis that just that will satisfy the wish.

In ``I have been expecting him all day'' ``expect'' does not mean a persistent condition.

140

(1)

When I expect someone, -- what happens?

What does the process of wanting to eat an apple consist in?

141

(1)

Intention and intentionality. --

``The thought that p is the case doesn't presuppose that it is the case; yet I can't think that something is red if the colour red does not exist.'' Here we mean the existence of a red sample as part of our language.

142

(1)

It's beginning to look somehow as if intention could never be recognized as intention from the outside. But the point is that one has to read off from a thought that it is the thought that such and such is the case.

143

(1)

This is connected with the question whether a machine could think. This is like when we say: ``The will can't be a phenomenon, for whatever phenomenon you take is something that simply happens, not something we do.'' But there's no doubt that you also have experiences when you move your arm voluntarily, although the phenomena of doing are indeed different from the phenomena of observing. But there are very different cases here.

144

(1)

The intention seems to interpret, to give the final interpretation.

Imagine an `abstract' sign-language translated into an unambiguous picture-language. Here there seem to be no further possibilities of interpretation. -- We might say we didn't enter into the sign-language but did enter into the painted picture. Examples: picture, cinema, dream.

145

(2)

What happens is not that this symbol cannot be further interpreted, but: I do no interpreting.

I imagine N. No interpretation accompanies this image; what gives the image its interpretation is the path on which it lies.

147

(1)

We want to say: ``Meaning is essentially a mental process, not a process in dead matter.'' -- What we are dissatisfied with here is the grammar of process, not the specific kind of process.

148

(1)

Doesn't the system of language provide me with a medium in which the proposition is no longer dead? -- ``Even if the expression of the wish is the wish, still the whole language isn't present during this expression.'' But that is not necessary.

149

(1)

In the gesture we don't see the real shadow of the fulfilment, the unambiguous shadow that admits of no further interpretation.

149

(1)

It's only considering the linguistic manifestation of a wish that makes it appear that my wish prefigures the fulfilment. -- Because it's the wish that just that were the case. -- It is in language that wish and fulfilment meet.

150

(2)

``A proposition isn't a mere series of sounds, it is something more.'' Don't I see a sentence as part of a system of consequences?

152

(2)

``This queer thing, thought.'' -- It strikes us as queer when we say that it connects objects in the mind. -- We're all ready to pass from it to the reality. -- ``How was it possible for thought to deal with the very person himself?'' Here I am being astonished by my own linguistic expression and momentarily misunderstanding it.

154

(1)

``When I think of what will happen tomorrow I am mentally already in the future.'' -- Similarly people think that the endless series of cardinal numbers is somehow before our mind's eye, whenever we can use that expression significantly.

A thought experiment is like a drawing of an experiment that is not carried out.

155

(1)

We said ``one cannot recognize intention as intention from the outside'' -- i.e. that it is not something that happens, or happens to us, but something we do. It is almost as if we said: we cannot see ourselves going to a place, because it is we who are doing the going. One does have a particular experience if one is doing the going oneself.

156

(1)

Fulfilment of expectation doesn't consist in some third thing's happening, such as a feeling of satisfaction.

157

(2)

VIII

A description of language must achieve the same result as language itself.

Suppose someone says that one can infer from a propsotion the fact that verifies it. What can one infer from a proposition apart from itself?

The shadowy anticipation of a fact consists in our being able already to think that very thing will happen which hasn't yet happened.

159

(1)

However many steps I insert between the thought and its application, each intermediate step always follows the previous one without any intermediate link, and so too the application follows the last intermediate step. -- We can't cross the bridge to the execution (of an order) until we are there.

160

(1)

It is the calculus of thought that connects with extra-mental reality. From expectation to fulfilment is a step in a calculation.

160

(1)

We are -- as it were -- surprised, not at anyone's knowing the future, but at his being able to prophesy at all (right or wrong).

161

(2)

Is the pictorial character of thought an agreement with reality? In what sense can I say that a proposition is a picture?

163

(1)

The sense of a proposition and the sense of a picture. The different grammar of the expressions:

``This picture shows people at a village inn.''

``This picture shows the coronation of Napoleon.''

164

(1)

A picture's telling me something will consist in my recognizing in it objects in some sort of characteristic arrangement. --

What does ``this object is familiar to me'' mean?

165

(1)

``I see what I see.'' I say that because I don't want to give a name to what I see. -- I want to exclude from my consideration of familiarity everything that is `historical'. -- The multiplicity of familiarity is that of feeling at home in what I see.

165

(1)

Understanding a genre picture: don't we recognize the painted people as people and the painted trees as trees, etc.?

A picture of a human face is a no less familiar object than the human face itself. But there is no question of recognition here.

166

(1)

The false concept that recognizing always consists in comparing two impressions with one another. --

``We couldn't use words at all if we didn't recognize them and the objects they denote.'' Have we any sort of check on this recognition?

167

(1)

This shape I see is not simply a shape, but is one of the shapes I know. -- But it is not as if I were comparing the object with a picture set beside it, but as if the object coincided with the picture. I see only one thing, not two.

168

(1)

``This face has a quite particular expression.'' We perhaps look for words and feel that everyday language is here too crude.

169

(1)

That a picture tells me something consists in its own form and colours. Or it narrates something to me: it uses words so to speak, and I am comparing the picture with a combination of linguistic forms. -- That a series of signs tells me something isn't constituted by its now making this impression on me. ``It's only in a language that something is a proposition.''

169

(1)

`Language' is languages. -- Languages are systems.

It is units of languages that I call ``propositions''.

170

(1)

Certainly, I read a story and don't give a hang about any system of language, any more than if it was a story in pictures. Suppose we were to say at this point ``something is a picture only in a picture-language.''?

171

(1)

We might imagine a language in whose use the impression made on us by the signs played no part.

What I call a ``proposition'' is a position in the game of language.

Thinking is an activity, like calculating.

171

(1)

A puzzle picture. What does it amount to to say that after the solution the picture means something to us, whereas it meant nothing before?

172

(2)

The impression is one thing, and the impression's being determinate is another thing. The impression of familiarity is perhaps the characteristics of the determinacy that every strong impression has.

174

(1)

Can I think away the impression of individual familiarity where it exists; and think it into a situation where it does not? The difficulty is not a psychological one. We have not determined what that is to mean.

Can I look at a printed English word and see it as if I hadn't learnt to read?

I can ascribe meaning to a meaningless shape.

175

(1)

We can read courage into a face and say ``now once more courage fits this face''. This is related to ``an attributive adjective agrees with the subject''.

What do I do if I take a smile now as a kind one, now as malicious? This is connected with the contrast between saying and meaning.

176

(2)

A friendly mouth, friendly eyes, the wagging of a dog's tail are primary symbols of friendliness: they are parts of the phenomena that are called friendliness. If we want to imagine further appearances as expressions of friendliness, we read these symbols into them. It is not that I can imagine that this man's face might change so that it looked courageous, but that there is a quite definite way in which it can change into a courageous face.

Think of the multifariousness of what we call ``language'': word-language, picture-language, gesture-language, sound-language.

178

(1)

``This object is familiar to me' is like saying `this object is portrayed in my catalogue'.'' We are making the assumption that the picture in our catalogue is itself familiar.

The sheath in my mind as a ``form of imagining''. -- The pattern is no longer presented as an object, which means that it didn't make sense to talk of a pattern at all.

``Familiarity: an object's fitting into a sheath'' -- that's not quite the same as our comparing what is seen with a copy.

The question is ``What do I recognize as what?'' For ``to recognize a thing as itself'' is meaningless.

179

(2)

The comparison between memory and a notebook.

How did I read off from the memory image that I stood thus at the window yesterday? What made you so certain when you spoke those words? Nothing; I was certain.

How do I react to a memory?

181

(1)

Operating with written signs and operating with ``imagination pictures''.

An attitude to a picture (to a thought) is what connects it with reality.

182

(2)

Grammatical rules determine a meaning and are not answerable to any meaning that they could contradict.

Why don't I call cookery rules arbitrary, and why am I tempted to call the rules of grammar arbitrary?

I don't call an argument good just because it has the consequences I want.

The rules of grammar are arbitrary in the same sense as the choice of a unit of measurement.

184

(1)

Doesn't grammar put the primary colours together because there is a kind of similarity between them? Or colours, anyway, in contrast to shapes or notes?

The rules of grammar cannot be justified by shewing that their application makes a representation agree with reality.

The analogy between grammar and games.

185

(2)

Langauge considered as a part of a psychological mechanism.

I do not use ``this is the sign for sugar'' in the same way as the sentence ``if I press this button, I get a piece of sugar''.

187

(1)

Suppose we compare grammar to a keyboard which I can use to direct a man by pressing different combinations of keys. What corresponds in this case to the grammar of language?

If the utterance of a `nonsensical' combination of words has the effect that the other person stares at me, I don't on that account call it the order to stare.

188

(1)

Language is not defined for us as an arrangement fulfilling a definite purpose.

189

(1)

Grammar consists of conventions -- say in a chart. This might be a part of a mechanism. But it is the connection and not the effect which determines the meaning.

Can one speak of a grammar in the case where a language is taught to a person by a mere drill?

190

(1)

I do not scruple to invent causal connections in the mechanism of language.

To invent a keyboard might mean to invent something that had the desired effect; or else to devise new forms which were similar to the old ones in various ways.

``It is always for living beings that signs exist.''

191

(1)

Inventing a language -- inventing an instrument -- inventing a game.

If we imagine a goal for chess -- say entertainment -- then the rules are not arbitrary. So too for the choice of a unit of measurement.

We can't say ``without language we couldn't communicate with one another''. The concept of language is contained in the concept of communication.

192

(1)

Philosophy is philosophical problems. Their common element extends as far as the common element in different regions of our language.

Something that at first sight looks like a proposition and is not one. Something that looks like a design for a steamroller and is not one.

193

(1)

Are we willing to call a series of independent signals ``a language''?

Imagine a diary kept with signals. Are explanations given so that the signals are connected to another language?

A language consisting of commands. We wouldn't say that a series of such signals alone would enable me to derive a picture of the movement of a man obeying them unless in addition to the signal there is something that might be called a general rule for translating into drawing.

The grammar explains the meaning of the signs and thus makes the language pictorial.

194

(5)

Appendix

Complex and Fact.

199

(3)

Concept and Object, Property and Substrate.

202

(6)

Objects.

208

(2)

Elementary propositions.

210

(5)

Is time essential to propositions? Comparison between time and truth-functions.

215

(4)

The nature of hypotheses.

219

(5)

Probability.

224

(12)

The concept ``about''. The problem of the heap.

236

(7)

Part II On Logic and Mathematics

Logical Inference

Is it because we understand the propositions that we know that q entails p? Does a sense give rise to the entailment?

243

(4)

``If p follows from q, then thinking that q must involve thinking that p.''

247

(3)

The case of infinitely many propositions following from a single one.

250

(5)

Can an experience show that one proposition follows from another?

255

(2)

Generality

The proposition ``The circle is in the square'' is in a certain sense independent of the assignment of a particular position. (In a certain sense it is totally unconnected.)

257

(4)

The proposition ``The circle is in the square'' is not a disjunction of cases.

261

(4)

The inadequacy of the Frege-Russell notation for generality.

265

(3)

Criticism of my former view of generality.

268

(2)

The explanation of generality by examples.

270

(10)

The law of a series. ``And so on''.

280

(9)

The Foundations of Mathematics

The comparison between Mathematics and a game.

289

(7)

There is no metamathematics.

296

(3)

Proofs of relevance.

299

(4)

Consistency proofs

303

(3)

Justifying arithmetic and preparing it for its application (Russell, Ramsey).

306

(9)

Ramsey's theory of identity.

315

(4)

The concept of the application of arithmetic (mathematics)

319

(2)

On Cardinal Numbers

Kinds of cardinal number

321

(11)

2 + 2 = 4.

332

(16)

Statements of number within mathematics.

348

(3)

Sameness of number and sameness of length.

351

(8)

Mathematical Proof

In other cases, if I am looking for something, then even before it is found I can describe what finding is; not so, if I am looking for the solution of a mathematical problem.

Mathematical expeditions and Polar expeditions.

359

(7)

Proof and the truth and falsehood of mathematical propositions.

366

(3)

If you want to know what is proved, look at the proof.

369

(8)

Mathematical problems. Kinds of problems. Search. ``Projects'' in mathematics.

377

(6)

Euler's Proof.

383

(4)

The trisection of an angle etc.

387

(6)

Searching and trying.

393

(2)

Inductive Proofs and Periodicity

How far is a proof by induction a proof of a proposition?

395

(2)

Recursive proof and the concept of proposition. Is the proof a proof that a proposition is true and its contradictory false?

397

(3)

Induction, (x). φx and (Ex). φx. Does the induction prove the general proposition true and an existential proposition false?

400

(5)

Is there a further step from writing the recursive proof to the generalization? Doesn't the recursion schema already say all that is to be said?

405

(3)

How far does a recursive proof deserve the name of ``proof''. How far is a step in accordance with the paradigm A justified by the proof of B?

408

(17)

The recursive proof does not reduce the number of fundamental laws.

425

(2)

Recurring decimals 1:3 = 0.3.

427

(3)

The recursive proof as a series of proofs.

430

(7)

Seeing or viewing a sign in a particular manner. Discovering an aspect of a mathematical expression. ``Seeing an expression in a particular way.'' Marks of emphasis.

437

(11)

Proof by induction, arithmetic and algebra.

448

(3)

Infinity in Mathematics

Generality in arithmetic.

451

(9)

On set theory.

460

(11)

The extensional conception of the real numbers.

471

(4)

Kinds of irrational number (π'P,F).

475

(8)

Irregular infinite decimals.

483

(4)

Note in Editing.

487

(4)

Translator's note.

491

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Philosophical Grammar

Summary

Table of Contents

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