1.
Augustine, in describing his learning of language, says that
he was taught to speak by learning the names of things. It
is clear that whoever says this has in mind the way in which
a child learns such words as “man”, “sugar”, “table”, etc.
He does not primarily think of such words as “today”, “not”,
“but”, “perhaps”.

     

      Suppose a man described a game of chess, without mentioning
the existence and operations of the pawns. His description
of the game as a natural phenomenon will be incomplete. On
the other hand we may say that he has completely described a
simpler game. In this sense we can say that Augustine's des-
cription of learning the language was correct for a simpler
language than ours. Imagine this language:-
1).   Its function is the communication between a builder A &
his man B. B has to reach A building stones. There are cubes,
bricks, slabs, beams, columns. The language consists of the
words “cube”, “brick”, “slab”, “column”. A calls out one of
these words, upon which B brings a stone of a certain shape.
Let us imagine a society in which this is the only system of
language. The child learns this language from the grown-ups
by being trained to its use. I am using the word “trained”
in a way strictly analogous to that in which we talk of an anim-
al being trained to do certain things. It is done be means of
example, reward, punishment, and such like. Part of this train-
ing is that we point to a building stone, direct the attention
of the child towards it, & pronounce a word. I will call
this procedure demonstrative teaching of words. In the actual

2.
use of this language, one man calls out the words as orders,
the other acts according to them. But learning and teaching
this language will contain this procedure: The child just
“names” things, that is, he pronounces the words of the lan-
guage when the teacher points to the things. In fact, there
will be a still simpler exercise: The child repeats words which
the teacher pronounces.

     

      (Note: Objection: The word “brick” in language 1) has not
the meaning which it has in our language. — This is true if it
means that in our language there are usages of the word “brick!”
different from our usages of this word in language 1). But
don't we sometimes use the word “brick!” in just this way? Or
should we say that when we use it, it is an elliptical sentence,
a shorthand for “Bring me a brick”? Is it right to say that if
we say “brick!” we mean “Bring me a brick”? Why should I trans-
late the expression “brick!” into the expression, “Bring me a
brick”? And if they are synonymous, why shouldn't I say: If
he says “brick!” he means “brick!”…? Or: Why shouldn't he
be able to mean just “brick!” if he is able to mean “Bring me
a brick”, unless you wish to assert that while he says aloud
“brick!” he as a matter of fact always says in his mind, to
himself, “Bring me a brick”? But what reason could we have to
assert this? Suppose someone asked: If a man gives the order,
“Bring me a brick”, must he mean it as four words, or can't he
mean it as one composite word synonymous with the one word
“brick!”? One is tempted to answer: He means all four words if
in his language he uses that sentence in contrast with other

<…>3.
sentences in which these words are used, such as, for instance,
“Take these two bricks away”. But what if I asked, “But how
is his sentence contˇrasted with these others? Must he have
thought them simultaneously, or shortly before or after, or is
it sufficiaent that he should have one time learnt them, etc.?”
When we have asked ourselves this question, it appears that it
is irrelevant which of these alternatives is the case. And
we are inclined to say that all that is really relevant is
that these contrasts should exist in the system of language
which he is using, and that they need not in any sense be present
in his mind when he utters his sentence. Now compare this
conclusion with our original question. When we asked it, we
seemed to ask a question about the state of mind of the man who
says the sentence, whereas the idea of meaning which we arrived
at in the end was not that of a state of mind. We think of the
meaning of signs sometimes as states of mind of the man using
them, sometimes as the role which these signs are playing in a
system of language. ⇆ William James speaks of specific feelings
accompanying the use of such words as “&”, “if”, “or”. And
there is no doubt that at least certain gestures are often con-
nected with such words, as a collecting gesture with “and”, &
a dismissing gesture with “not”. And there obviously are
visual and muscular sensations connected with these gestures.
On the other hand it is clear enough that these sensations do
not accompany every use of the word “not”, and “&”. If in some
language the word “but” meant what “not” means in English, it
is clear that we should not compare the meanings of these two

3a.

      Insert:     The connection between these two ideas is that the
mental experiences which accompany the use of a sign undoubt-
edly are caused by our usage of the sign in a particular
system of language. ⇄

34.
words by comparing the sensations which they produce. Ask
yourself what means we have of finding out the feelings which
they produce in different people and on different occasions.
Ask yourself: “When I said, ‘Give me an apple & a pear, &
leave the room’, had I the same feeling when I pronounced the
two words ‘&’?” But we do not deny that the people who use the
word “but” as “not” is used in English will broadly speaking
have similar sensations accompanying the word “but” as the Eng-
lish have when they use “not”. And the word “but” in the two
languages will on the whole be accompanied by different sets of
experiences.)
2).   Let us now look at an extension of language 1). The
builder's man knows by heart the series of words from one to
ten. On being given the order, “Five slabs!”, he goes to
where the slabs are kept, says the words from one to five,
takes up a plate for each word, & carries them to the builder.
Here both the parties use the language by speaking the words.
Learning the numerals by heart will be one of the essential
features of learning this language. The use of the numerals
will again be taught demonstratively. But now the same word,
e.g., “three”, will be taught either by pointing to slabs, or
to bricks, or to columns, etc.. And on the other hand, different
numerals, will be taught by pointing to groups of stones of the
same shape.

     

      (Remark: We stressed the importance of learning the series
of numerals by heart because there was no feature comparable to
this in the learning of language 1). And this sh[e|o]ws us that by
introducing numerals we have introduced an entirely different

<…>5.
kind of instrument into our language. The difference of kind
is much more obvious when we contemplate such a simple example
than when we look at our ordinary language with innumerable
kinds of words all looking more or less alike when they stand
in the dictionary. —

     

      What have the demonstrative explanations of the numerals
in common with those of the words “slab”, “column”, etc. except
a gesture and pronouncing the words? The way such a gesture
is used in the two cases is different. This difference is
blurred if one says, “In one case we point to a shape, in the
other we point to a number”. The difference becomes obvious
and clear only when we contemplate a complete example (i.e.,
the example of a language completely worked out in detail).)
3).   Let us introduce a new instrument of communication, —
a proper name. This is given to a particular object (a par-
ticular building stone) by pointing to it and pronouncing the
name. If A calls the name, B brings the object. The demon-
strative teaching of a proper name is different again from the
demonstrative teaching in the cases 1 [(|)] & 2).

     

      (Remark: This difference does not lie, however, in the act
of pointing and pronouncing the word or in any mental act
(meaning) ? accompanying it, but in the role which the demonstrat-
ion (pointing & pronouncing) plays in the whole training and in
the use which is made of it in the practice of communication
by means of this language. One might think that the difference
could be described by saying that in the different cases we
point to different kinds of objects. But suppose I point with

6.
my hand to a blue jersey. How does pointing to its colour
differ from pointing to its shape? — We are inclined to say
the difference is that we mean something different in the two
cases. And “meaning” here is to be some sort of process tak-
ing place while we point. What particularly tempts us to this
view is that a man on being asked whether he pointed to the
colour or the shape is, at least in most cases, able to answer
this & to be certain that his answer is correct. If on the
other hand, we look for two such characteristic mental acts as
meaning the colour and meaning the shape, etc., we aren't able
to find any, or at least none which must always accompany point-
ing to colour, pointing to shape, respectively. We have only
a rough idea of what it means to concentrate one's attention
on the colour as opposed to the shape, or vice versa. The
difference one might say does not lie in the act of demonstrat-
ion, but rather in the surrounding of the that act in the use of the
language.)
4).   On being ordered “This slab!”, B brings the plate to which
A points. On being ordered, “Plate, there!”, he carries a
plate to the place indicated. Is the word “there” taught dem-
onstrativel[t|y]? Yes & no! When a person is trained in the use
of the word “there”, the teacher will in training him make the
pointing gesture and pronounce the word “there”. But should
we say that thereby he gives a place the name “there”? Rem-
ember that the pointing gesture in this case is part of the prac-
tice of communication itself.

     

      (Remark: It has been suggested that such words as “there”,

7.
“here”, “now”, “this” are the “real proper names” as opposed
to what in ordinary life we call proper names, & in the view I
am referring to, can only be called so crudely. There is a
widespread tendency to regard what in ordinary life is called
a proper name only as a rough approximation of what ideally
could be called so. Compare Russell's idea of the “individual”.
He talks of individuals as the ultimate costituents of reality,
but says that it is difficult to say which things are individ-
uals. The idea is that further analysis has to reveal this.
We, on the other hand, introduced the idea of a proper name in
a language in which it was applied to what in ordinary life we
call “objects”, “things” (“building stones”).

     

      — “What does the word ‘exactness’ mean? Is it real
exactness if your are supposed to come to tea at 4.30 and come
when a good clock strikes 4.30? Or would it only be exactness
if you began to open the door at the moment the clock begins to
strike? But how is this moment to be defined and how is “be-
ginning to open the door” to be defined? Would it be correct
to say, ‘It is difficult to say what real exactness is, for all
we know is only rough approximations’?”)
5).   Question and answer: A asks, “How many plates?” B counts
them and answers with the numeral.

     

      Systems of communication as for instance 1), 2), 3), 4),
5) we shall call “language-games”. They are more or less akin
to what in ordinary language we call games. Children are
taught their native language by means of such games, and here
they even have the entertaining character of games. We are not,

8.
however, regarding the language-games which we describe as
incomplete parts of a language, but as languages complete in
themselves, as complete systems of human communication. To
keep this point of view in mind, it very often is useful to
imagine such a simple language to be the entire system of comm-
unication of a tribe in a primitive state of society. Think
of primitive arithmetics of such tribes.

     

      When the boy or grown-up learns learns what one might call
special technical languages, e.g., the use of charts and diag-
rams, descriptive geometry, chemical symbolism, etc., he learns
more language-games. (Remark: The picture we have of the lan-
guage of the grown-up is that of a nebulous mass of language,
his mother tongue, surrounded by discreet and more or less
clear cut language games, the technical languages.)
6).   Asking for the name: we introduce new forms of building
stones. B points to one of them & asks, “What is this?”; A
answers, “This is a…”. Later on A calls out this new word,
say “arch”, & B brings the stone. The words, “This is a…”
together with the pointing gesture we shall call ostensive
explanation or ostensive definition. In case 6) a generic
name was explained, in actual fact, the name of a shape. But
we can ask analogously for the proper name of a particular ob-
ject, for the name of a colour, of a number numeral, of a direction.

     

      (Remark: Our use of expressions like “names of numbers”,
“names of colours”, “names of materials”, “names of nations” may
a) spring from two different sources. One is that we might imag-
ine the functions of proper names, numerals, words for colours,

9.
etc. to be much more alike than they actually are. If we do
so we are tempted to think that the function of every word is
more or less like the function of a proper name of a person,
or such generic names as “table”, “chair”, “door”, etc. The
b) second source is this, that if we see how fundamentally differ-
ent the functions of such words as “table”, “chair”, etc. are
from those of proper names, and how different from either the
functions of, say, the names of colours, we see no reason why
we shouldn't speak of names of numbers or names of directions
either, not by way of saying some such thing as “numbers and
directions are just different forms of objects”, but rather
by way of stressing the analogy which lies in the lack of ana-
logy between the functions of the words “chair” & “Jack” on
the one hand, & “east” and “Jack” on the other hand.)
7).   B has a table in which written signs are placed opposite
to pictures of objects (say, a table, a chair, a tea-cup, etc.).
A writes one of the signs, B looks for it in the table, looks or
points with his finger from the written sign to the picture
opposite, & fetches the object which the picture represents.

     

      Let us now look at the different kinds of signs which
we have introduced. First let us distinguish between sentences
and words. A sentence I will call every complete sign in a
language-game, its constituent signs are words. (This is
merely a rough and general remark about the way I will use the
words “proposition” and “word”). A proposition may consist of
only one word. In 1) the signs “brick!”, “column!” are the
sentences. In 2) a sentence consists of two words. Accord-


10.
ing to the role which propositions play in a language-game,
we distinguish between orders, questions, explanations, descrˇip-
tions, & so on.
8).   If in a language-game similar to 1) A calls out an order:
“slab, column, brick!” which is obeyed by B by bringing a slab,
a column & a brick, we might here talk of three propositions,
or of one only. If on the other hand,
9)   the order of words shews B the order in which to bring the
building stones, we shall say that A calls out a proposition
consisting of three words. If the command in this case took
the form, “Slab, then column, then brick!” we should say that
it consisted of four words (not of five). Amongst the words
we see groups of words with similar functions. We can easily
see a similarity in the use of the words “one”, “two”, “tree”,
etc. & again one in the use of “slab”, “column” & “brick”, etc.,
& thus we distinguish parts of speech. In 8) all words of
the proposition belonged to the same part of speech.
10).   The order in which B had to bring the stones in 9) could
have been indicated by the use of the ordinals thus: “Second,
column; first, slab; third, brick!”. Here we have a case in
which what was the function of the order of words in one lan-
guage-game is the function of particular words in another.

     

      Reflections such as the preceding will show us the infin-
ite variety of the functions of words in propositions, and it is
curious to compare what we see in our examples with the simple
& rigid rules which logicians give for the construction of prop-
ositions. If we group words together according to the simil-
arity of their functions, thus distinguishing parts of speech,

11.
it is easy to see that many different ways of classification
can be adopted. We could indeed easily imagine a reason for
not classing the word “one” together with “two”, “three”, etc.,
as follows:
11).   Consider this variation of our language-game 2). Ins-
tead of calling out, “One slab!”, “One cube!”, etc., A just
calls “slab!”, “cube!”, etc., the use of the other numerals
being as described in 2). Suppose that a man accustomed to
this form (11)) of communication was introduced to the use of
the word “one” as described in 2). We can easily imagine that
he would refuse to classify “one” with the numerals “2”, “3”,
etc..

     

      (Remark: Think of the reasons for and against classifying
“O” with the other cardinals. “Are black and white colours?”
In which cases would you be inclined to say so & which not? —
Words can in many ways be compared to chess men. Think of the
several ways of distinguishing different kind of pieces in the
game of chess (e.g., pawns &“officers”).
Remember the phrase, “two or more”.)

     

      It is natural for us to call geestures, as those employed
in 4), or pictures as in 7), elements or instruments of language.
(We talk sometimes of a language of gestures.) The pictures
in 7) & other instruments of language which have a similar
function I shall call patterns. (This explanation, as others
which we have given, is vague, and meant to be vague.) We
may say that words and patterns have different kinds of functions.
When we make use of a pattern we compare something with it, e.g.,

12.
q a chair with the picture of a chair. We did not compare a
slab with the word “slab”. In introducing the distinction,
“word, pattern”, the idea was not to set up a final logical
duality. We have only singled out two characteristic kinds
of instruments from the variety of instruments in our language.
We shall call “one”, “two”, “three”, etc. words. If instead
of these signs we used “-”, “--”, “---”, “----“, we might call
these patterns. Suppose in a language the numerals were “one”,
“one one”, “one one one”, etc., should we call “one” a word or
a pattern? The same element may in one place be used as word
& in another as pattern. A circle might be the name for an
ellipse, or on the other hand a pattern with which the ellipse
is to be compared by a particular method of projection. Con-
sider also these two systems of expression:
12).   <…> A gives B an order consisting of two written symbols,
the first an irregularly shaped patch of a geometrical figure, say
a circle. B brings an object of this outline and that colour,
say a circular green object.
13).   A gives B an order consisting of one symbol, a geomet-
rical figure painted a particular colour, say a green circle.
B brings him a green circular object. In 12) patterns corres-
pond to our names of colours and other patterns to our names of
shape. The symbols in 13) cannot be regarded as combinations
of two such elements. A word in inverted commas can be called
a pattern. Thus in the sentence, “He said, ‘Go to hell’”,
‘Go to hell’ is a pattern of what he said. Compare these cases:

13.
a) Someone says, “I whistled… (whistling a tune) „ ”; b) Some-
one writes, “I whistled ”. An onomatopoetic word like
“rustling” may be called a pattern. We call a very great
variety of processes “comparing an object w[e|i]th a pattern”.
We comprise many kinds of symbols under the name “pattern”.
In 7) B compares a picture in the table with the objects he has
before him. But what does comparing a picture with the object
consist in? Suppose the table shewed: a) a picture of a
hammer, of pincers, of a saw, of a chisel; b) on the other hand,
pictures of twenty different kinds of butterflies. Imagine
what the comparison in these cases would consist in, & note
the difference. Compare with these cases a third case c)
where the pictures in the table represent building stones drawn
to scale, & the comparing has to be done with ruler and comp-
asses. Suppose that B's task is to bring a piece of cloth of
the colour of the sample. How are the colours of sample and
cloth to be compared? Imagine a series of different cases:
14).   A shews the sample to B, upon which B goes and fetches
the material “from memory”.
15).   A gives B the sample,B looks from the sample to the
materials on the shelves from which he has to choose.
16).   B lays the sample on each bolt of material & chooses
that one which he can't distinguish from the sample, for which
the difference between the sample & the material seems to vanish.
17).   Imagine on the other hand that the order has been, “Bring
a material slightly darker than this sample”. In 14) I said
that B fetches the material “from memory”, which is using a

14.
common form of expression. But what might happen in such a
case of comparing “from memory” is of the greatest variety.
Imagine a few instances:
14a).   B has a memory image before his mind's eye when he goses
for the material. He alternately looks at materials and re-
calls his image. He goes through this process with, say, five
of the bolts, in some instances saying to himself, “Too dark”,
in some instances saying to himself, “Too light”. At the
fifth bolt he stops, says, “That's it”, & takes it from the
shelf.
14b).   No memory image is before B's eye. He looks at four
bolts, shaking his head each time, feeling some sort of mental
tension. On reaching the fifth bolt, this tension relaxes,
he nods his head, & takes the bolt down.
14c).   B goes to the shelf without a memory image, looks at
five bolts one after the other, takes the fifth bolt from the
shelf.
      “But this can't be all comparing consists in”.

     

      When we call these three preceding cases cases of com-
paring from memory, we feel that their description is in a sense
unsatisfactory, or incomplete. We are inclined to say that the
description has left out the essential feature of such a pro-
cess & given us accessory features only. The essential feature
it seems would be what one might call a specific experience of
comparing & of recognizing. Now it is clear queer that on closely
looking at cases of comparing, it is very easy to see a great
number of activities and states of mind, all more or less charac-

15.
teristic of the act of comparing. This in fact is so, whether
we speak of comparing from memory or of comparing by means of
a sample before our eyes. We know a vast number of such proc-
esses, processes similar to each other in a vast number of dif-
ferent ways. We hold pieces whose colours we want to compare
together or near each other for a longer or shorter period,
look at them alternately or simultaneously, place them under
different lights, say different things while we do so, have mem-
ory images, feelings of tension & relaxation, satisfaction &
dissatisfaction, the various feelings of strain in and around
our eyes accompanying prolonged gazing at the same object, &
all possible combinations of these & many other experiences.
The more such cases we observe & the closer we look at them, the
more doubtful we feel about finding one particular mental exp-
erience characteristic of comparing. In fa[s|c]t, if after you
had scrutinized a number of such closely, I admitted that there
existed a peculiar mental experience which you might call the
experience of comparing, & that if you insisted, I should be
willing to adopt the word “comparing” only for cases in which
this peculiar feeling had occurred, you would now feel that the
assumption of such a peculiar experience had lost i[y|t]s point,
because this experience was placed side by side with a vast num-
ber of other experiences which after we have scrutinized the
cases seems to be that which really constitutes what connects all
the cases of comparing. For thise “specific experience” we had
been looking for was meant to have played the role which has
been assumed by the mass of experiences revealed to us by our

16.
scrutiny: We never wanted the specific experience to be just
one among a number of more or less characteristic experiences.
(One might say that there are two ways of looking at this mat-
ter, one as it were, at close quarters, the other as though
from a distance and through the medium of a particular peculiar atmos-
phere.) In fact we have found that the use which we really
make of the word “comparing” is different from that which look-
ing at it from far away we were led to expect. We find that
what connects all the cases of comparing is a vast number of
overlapping similarities, and as soon as we see this, we feel
no longer compelled to say that there must be some one feature
common to them all. What ties the ship to the wharf is a
rope, and the rope consists of fibres, but it does not get its
strength from any fibre which runs through it from one end to
the other, but from the fact that there is a vast number of
fibres overlapping.

     

      “But surely in case 14c) B acted entirely automatically.
If all that happened was really what was described there, he
did not know why he chose the bolt he did choose. He had no
reason for choosing it. If he chose the right one, he did it
as a machine might have done it”. Our first answer is that we
did not deny that B in case 14c) had what we should call a per-
sonal experience, for we did not say that he didn't see the mat-
erials from which he chose or that which he chose, nor that he
didn't have muscular and tactile sensations and such like while
he did it. Now what would such a reason which justified his
choice and made it non-automatic be like? (i.e. : What do we

17.
imagine it to be like?) I suppose we should say that the
opposite of automatic comparing, as it were, the ideal case of
conscious comparing, was that of having a clear memory image
before our mind's eye or of seeing a real sample & of having a
specific feeling of not being able to distinguish in a partic-
ular way between these samples and the material chosen. I
suppose that this peculiar sensation is the reason, the justif-
ication, for the choice. This specific feeling, one might say,
connects the two experiences of seeing the sample, on the one
hand, and the material on the other. But if so, what connects
this specific experience with either? We don't deny that such
an experience might intervene. But looking at it as we did
just now, the distinction between automatic and non-automatic
appears no longer clear-cut and final as it did at first. We
don't mean that this distinction loses its practical value in
particular cases, e.g., if asked under particular circumstances,
“Did you take this bolt from the shelf automatically, or did you
think about it?”, we may be justified in saying that we did
not act automatically and give as a reason explanation we had looked
at the material carefully, had tried to recall the memory image
of the pattern, & had uttered to ourselves doubts and decisions.
This may in the particular case be taken to distinguish automat-
ic from non-automatic. In another case however we may distin-
guish between an automatic & a non-automatic way of the appear-
ance of a memory image, and so on.

     

      If our case 14c) troubles you, you may be inclined to say:
“But why did he bring just this bolt of material? How has he

18.
recognized it as the right one? What by? — If you ask “why”,
do you ask for the cause or for the reason? If for the cause,
it is easy enough to think up a physiological or psychological
hypothesis which explains this choice under the given conditions.
It is the task of the experimental sciences to test such hypoth-
eses. If on the other hand you ask for a reason the answer is,
“There need not have been a reason for the choice. A reason
is a step preceding the step of the choice. But why should
every step be preceded by another one?”

     

      “But then B didn't really recognize the material as the
right one”. — You nee[e|d]n't reckon 14c) among the cases of recog-
nizing, but if you have become aware of the fact that the proc-
esses which we call processes of recognition form a vast family
with overlapping similarities, you will probably feel not dis-
inclined to include 14c) in this family, too. — “But doesn't B
in this case lack the criterion by which he can recognize the
material? In 14a), e.g., he had the memory image and he recog-
nized the material he looked for by its agreement with the image”.
— But had he also a picture of this agreement before him, a
picture with which he could compare the agreement between the
pattern and the bolt to see whether it was the right one? And,
on the other hand, couldn't he have been given such a picture?
Suppose, e.g., that A wished B to remember that what was wanted
was a bolt exactly like the sample, not, as perhaps in other
cases, a material slightly darker than the pattern. Couldn't
A in this case have given to B an example of the agreement
required by giving him two pieces of the same colour (e.g.,

19.
as a kind of reminder)? Is any such link between the order &
its execution necessarily the last one? — And if you say that
in 14b) at least he had the relaxing of the tension by which
to recognize the right material, had he to have an image of
this relaxation about him to recognize it as that by which the
right material was to be recognized? —

     

      “But supposing B brings the bolt, as in 14c), & on compar-
ing it with the pattern it turns out to be the wrong one?” —
But couldn't that have happened in all the other cases as well?
Suppose in 14a) the bolt which B brought back was found not to
match with the pattern. Wouldn't we in some such cases say
that his memory image had changed, in others that the pattern
or the material had changed, in others again that the light had
changed? It is not difficult to invent cases, imagine circ-
umstances, in which each of these judgements would be made. —
“But isn't there after all an essential difference between the
cases 14a) & 14c)?”— Certainly! Just that pointed out in the
description of these cases. —

     

      In 1) B learnt to bring a building stone on hearing the
word “column!” called out. We could imagine what happened in
such a case to be this: In B's mind the word called out brought
up an image of a column, say; the training had, as we should
say, established this association. B takes up that building
stone which conforms to his image. — But was this necessarily
what happened? If the training could bring it about that the
idea or image — automatically — arose in B's mind, why shouldn't
it bring about B's actions without the intervention of an image?

20.
This would only come to a slight variation of the associative
mechanism. Bear in mind that the image which is brought up by
the word is not arrived at by a rational process (but if it is,
this only pushes our argument further back), but that this case
is strictly comparable with that of a mechanism in which a but-
ton is pressed and an indicator plate appears. In fact this
sort of mechanism can be used instead of that of association.

     

      Mental images of colours, shapes, sounds, etc. etc., which
play a role in communication by means of language we put in the
same category with patches of colour actually seen, sounds
heard.
18[(|)].   The object of the training in the use of tables (as in
7)) may be not only to teach the use of one particular table,
but it may be enable the pupil to use or construct himself
tables with new coordinations of written signs & pictures.
Suppose the first table a person was trained to use contained
the four words “hammer”, “pincers”, “saw”, “chisel” & other
corresponding pictures. We might now add the picture of anoth-
er object which the pupil had before him, say of a plane, &
correlate with it the word “plane”. We shall make the correl-
ation between this new picture and word as similar as possible
to the correlations in the previous table. Thus we might add
the new word and picture on the same sheet, and place the new
word under the previous words and the new picture under the
previous pictures. The pupil will now be encouraged to make
use of the new picture and word without the special training
which we gave him when we taught him to use the first table.

21.
These acts of encouragement will be of various kinds, and many
such acts will only be possible if the pupil responds, and res-
ponds in a particular way. Imagine the gestures, sounds, etc.
of encouragement you use when you teach a dog to retrieve. ˇImagine
on the other hand, that you tried to teach a cat to retrieve. As
the cat will not respond to your encouragement, most of the acts
of encouragement which you performed when you trained the dog
are here out of the question.
19).   The pupil could also be trained to give things names of
his own invention and to bring the objects when the names are
called. He is, e.g., presented with a table on which he finds
pictures of objects around him on one side and blank spaces on
the other, and he plays the game by writing signs of his own
invention opposite the pictures and reacting in the previous way
when these signs are used as orders. Or else,
20).   the game may consist in B's constructing a table and
obeying orders given in terms of this table. When the use of
a table is taught, and the table consists, say, of two vertical
columns, the left hand one containing the names, the right hand
one the pictures, a name and a picture being correlated by
standing on a horizontal line, an important feature of the train-
ing may be that which makes the pupil slide his finger from left
to right, as it were the training to draw a series of horizon-
tal lines, one below the other. Such training may help to make
the transition from the first table to the new item.

     

      Tables, ostensive definitions, & similar instruments I
shall call rules, in accordance with ordinary usage. The use
of a rule can be explained by a further rule.

22.
21).   Consider this example: We introduce different ways of
reading tables. Each table consists of two columns of words &
pictures, as above. In some cases they are to be read horiz-
ontally from left to right, i.e., according to the scheme:

In others according to such schemes as:

Or:
etc.

Schemes of this kind can be adjoined to our tables, as rules
for reading them. Could not these rules again be explained
by further rules? Certainly. On the other hand, is a rule
incompletely explained if no rule for its usage has been given?

     

      We introduce into our language-games the endless series
of numerals. But how is this done? Obviously the analogy
between this process & that of introducing a series of twenty
numerals is not the same as that between introducing a series
of twenty numerals and introducing a series of ten numerals.
Suppose that our game was like 2) but played with the endless
series of numerals. The difference between it & 2) would not
be just that more numerals were used. That is to say, suppose
that as a matter of fact in playing the game we had actually
made use of, say, 155 numerals, the game we play would not be
that which could be described by saying that we played the game
2), only with 155 instead of 10 numerals. But what does the
difference consist in? (The difference would <…>seem to be almost

23.
one of the spirit in which the games are played.) The difference
between games can lie say in the number of the counters used,
in the number of squares of the playing board, or in the fact
that we use squares in one case & hexagons in the other, & such
like. Now the difference between the finite and infinite game
does not seem to lie in the material tools of the game; for we
should be inclined to say that infinity can't be expressed in
them, that is, that we can only conceive of it in our thoughts
& hence that it is in these thoughts that the finite and infin-
ite game must be distinguished. (It is queer though that these
thoughts should be capable of being expressed in signs.) Let
us consider two games. They are both played with cards carry-
ing numbers, and the highest number takes the trick.
22).   One game is played with a fixed number of such cards, say
32. In the other game we are under certain circumstances
allowed to increase the number of cards to as many as we like,
by cutting pieces of paper and writing numbers on them. We
will call the first of these games bounded, the second unbound-
ed. Suppose a hand of the second game was played & the number
of cards actually used was 32. What is the difference in this
case between playing a hand a) of the unbounded game & playing
a hand b) of the bounded game?

     

      The difference will not be that between a hand of a bound-
ed game with 32 cards and a hand of a bounded game with a great-
er number of cards. The number of cards used, was, we said,
the same. But there will be differences of another kind, e.g.,
the bounded game is played with a normal pack of cards, the
unbounded game with a large supply of blank cards & pencils.

24.
The unbounded game is opened with the question, “How high
shall we go?” If the players look up the rules of this game
in a book of rules, they will find the phrase “& so on” or
“& so on ad inf.” at the end of certain series of rules. So
the difference between the two hands a) & b) lies in the tools
we use, though admittedly not in the cards they are played
with. But this difference seems trivial and not the essential
difference between the games. We feel that there must be a
big & essential difference somewhere. But if you look closely
at what happens when the hands are played, you find that you
can only detect a number of differences in details, each of
which would seem inessential. The acts, e.g., of dealing &
playing the cards may in both cases be identical. In the
course of playing the hand a), the players may have considered
making up more cards, & again discarded the idea. But what
was it like to consider this? It could be some such process
as saying to themselves or aloud, “I wonder whether I should
make up another card”. Again, no such consideration may have
entered the minds of the players. It is possible that the
whole difference in the events of a hand of the bounded, and a
hand of the ˇunbounded game lay in what was said before the game
started, e.g., “Let's play the bounded game”

     

      “But isn't it correct to say that hands of the two diff-
erent games belong to two different systems?” Certainly.
Only the facts which we are referring to by saying that they
belong to different systems are much more complex than we might
expect them to be.

     

      Let us now compare language-games of which we should say

25.
that they are played with a limited set of numerals with lan-
guage-games of which we should say that they are played with
the endless series of numerals.
23).   Like 2) A orders B to bring him a number of building
stones. The numerals are the <…> signs “1”, “2”, etc.
… “9”, each written on a card. A has a set of these cards
and gives B the order by shewing him one of the set & calling
out one of the words, “slab”, “column”, etc.
24).   Like 23), only there is no set of indexed cards. The
series of numerals 1…9 is learned by heart. The numerals
are called out in the orders, & the child learns them by word
of mouth.
25).   An abacus is used. A sets the abacus, gives it to B,
B goes with it to where the slabs lie, etc..
26).   B is to count the slabs in a heap. He does it with an
abacus, the abacus has twenty beads. There are never more than
20 plates in a heap. B sets the abacus for the heap in quest-
ion & shews A the abacus thus set.
27).   Like 26). The abacus has 20 small beads & one large
one. If the heap contains more than 20 plates, the large bead
is moved. (So the large bead in some way corresponds to the
word “many”).
28).   Like 26). If the heap contains n plates, n being more
than 20 but less than 40, B moves n-20 beads, shews A the abacus
thus set, & claps his hand once.
29).   A & B use the numerals of the decimal system (written or
spoken) up to 20. The child learning this language learns these

26.
numerals by heart, etc., as in 2).
30).   A certain tribe has a language of the kind 2). The
numerals used are those of our decimal system. No one numeral
used can be observed to play the predominaˇnt role of the last
numeral in some of the above games (27), 28)). (One is tempted
to continue this sentence by saying, “although there is of
course a highest numeral actually used”). The children of the
tribe learn the numerals in this way: They are taught the signs
from 1 to 20 as in 2) and to count rows of beads of no more
than 20 on being ordered, “Count these”. When in counting the
pupil arrives at the numeral 20, one makes a gesture suggestive
of “Go on”, upon which the child says (in most cases at any
rate) “21”. Analogously, the children are made to count to 22
& to higher numbers, no particular number playing in these exer-
cises the predominant role of a last one. The last stage of
the training is that the child is ordered to count a group of
objects, well above 20, without the suggestive gesture being
used to help the child over the numeral 20. If a child does
not respond to the suggestive gesture, it is separated from the
others and treated as a lunatic.
31).   Another tribe. Its language is like that in 30). The
highest numeral observed in use is 159. In the life of this
tribe the numeral 159 plays a peculiar role. Supposing I said,
“They treat this number as their highest”, — but what does this
mean? Could we answer: “They just say that it is the highest”?
— They say certain words, but how do we know what they mean by
them? A criterion for what they mean would be the occasions

27.
on which the word we are inclined to translate into our word
“highest” is used, the role, we might say, which we observe this
word to play in the life of the tribe. In fact we could eas-
ily imagine the numeral 159 to be used on such occasions, in con-
nection with such gestures and forms of behaviour as would make
us say that this numeral plays the role of an unsurmountable
limit, even if the tribe had no word corresponding to our “high-
est”, and the criteria for numeral 1[3|5]9 being the highest numeral
did not consist of anything that was said about the numeral.
32).   A tribe has two systems of counting. People learned to
count with the alphabet from A to Z and also with the decimal
system as in 30). If a man is to count objects with the first
system, he is ordered to count “in the closed way”, in the sec-
ond case, “in the open way”; & the tribe uses the words “closed”
& “open” also for a closed and open door.

     

      (Remarks: 23) is limited in an obvious way by the set of
cards. 24): Note analogy and lack of analogy between the lim-
ited supply of cards in 23) & of words in our memory in 24).
Observe that the limitation in 26) on the one hand lies in the
tool (the abacus of 20 beads) & its usage in our game, on the
other hand (in a totally different way) in the fact that in the
actual practice of playing the game no more than 20 objects are
ever to be counted. In 27) that latter kind of limitation was
absent, but the large bead rather stressed the limitation of our
means. Is 28) a limited or an unlimited game? The practice
we have described gives the limit 40. We are inclined to say
this game “has it in it” to be continued indefinitely, but rem-

28.
ember that we could also have construed the pre[d|c]eding games
as beginnings of a system. In 29) the systematic aspect of
the numerals used is even more conspicuous than in 28). One
might say that there was no limitation imposed by the tools of
this game, if it were not for the remark that the numerals up
to 20 are learnt by heart. This suggests the idea that the
child is not taught to “understand” the system which we see in
the decimal notation. Of the tribe in 30) we should certainly
say that they are trained to construct numerals indefinitely,
that the arithmetic of their language is not a finite one, that
their series of numbers has no end. (It is just in such a
case when numerals are constructed “indefinitely” that we say
that people have the infinite series of numbers.) 31) might
show you what a vast variety of cases can be imagined in which
we should be inclined to say that the arithmetic of the tribe
deals with a finite series of numbers, even in spite of the use of
numerals suggests no upper limit. In 32) the terms “closed” &
“open” (which could by a slight variation of the example be
replaced by “limited” and “unlimited”) are introduced into the
language of the tribe itself. Introduced in that simple and
clearly circumscribed game, there is of course nothing myster-
ious about the use of the word “open”. But this word corres-
ponds to our “infinite”, & the games we play with the latter
differ from 31) only by being vastly more complicated. In other
words, our use of the word “infinite” is just as straight forward
32? as that of “open” in 31), and our idea that its meaning is

29.
“transcendent” rests on a misunderstanding.)

     

      We might say roughly that the unlimited cases are charac-
terized by this: that they are not played with a definite supply
of numerals, but instead with a system for constructing numer-
als (indefinitely). When we say that someone has been supplied
with a system for constructing numerals, we generally think of
either of three things: a) of giving him a training similar to
that described in 30), which, experience teaches us, will make
him pass tests of the kind mentioned there; b) of creating a
disposition in the same man's mind, or brain, to react in that
way; c) of supplying him with a general rule for the constˇruction
of numerals.

     

      What do we call a rule? Consider this example:
33).   B moves about according to rules which A gives him. B
is supplied with the following table:

A gives an order made up of the letters in the table, say:
“aacaddd”. B looks up the arrow corresponding to each letter
of the order and moves accordingly; in our example thus:

The table 33) we should call a rule (or else “the expression of
a rule”. Why I give these synonymous expressions will appear
later.) We shan't be inclined to call the sentence “aacaddd”
itself a rule. It is of course the description of the way B
has to take. On the other hand, such a description would under
certain circumstances be called a rule, e.g., in the following
case:
34). B is to draw various ornamental

30.
34).   B is to draw various ornamental linear designs. Each
design is a repetition of one element which A gives him.
Thus if A gives the order “cada”, B draws a line thus:

     

      In this case I think we should say that “cada” is the
rule for drawing the design. Roughly speaking, it characteriz-
es what we call a rule to be applied repeatedly, in an indef-
inite number of instances. Cf., e.g., the following case with
34):
35).   A game played with pieces of various shapes on a chess
board. The way each piece is allowed to move is laid down by
a rule. Thus the rule for a particular piece is “ac”, for
another piece “acaa”, & so on. The first piece then can make
a move like this: , the second, like this: . Both
a formula like “ac” or a diagram like that corresponding to
such a formula might here be called a rule.
36).   Suppose that after playing the game 33[(|)] several times as
described above, it was played with this variation: that B no
longer looked at the table, but reading A's order the letters
call up the images of the arrows (by association), & B acts <…>
according to these imagined arrows.
37).   After playing it like this for several times, B moves
about according to the written order as he would have done had
he looked up or imagined the arrows, but actually without any
such picture intervening. Imagine even this variation:
38).   B in being trained to follow a written order, is shewn
the table of 33) once, upon which he obeys A's orders without
further intervention of the table in the same way in which B in

31.
33) does with the help of the table on each occasion.

     

      In each of these cases, we might say that the table 33)
is a rule of the game. But in each one this rule plays a dif-
ferent role. In 33) the table is an instrument used in what
we should call the practice of the game. It is replaced in
36) by the working of association. In 37) even this shadow of
the table has dropped out of the practice of the game, and in
38) the table is admittedly an instrument for the training of B
only.

     

      But imagine this further case:
39).   A certain system of communication is used by a tribe.
I will describe it by saying that it is similar to our game 38)
except that no table is used in the training. The training
might have consisted in several times leading the pupil by the
hand along the path one wanted him to go. But we could also
imagine a case:
40).   where even this training is not necessary, where, as we
should say, the look of the letters abcd naturally produced an
urge to move in the way described. This cause at first sight
looks puzzling. We seem to be assuming a most unusual working
of the mind. Or we may ask perhaps we ask, “How on earth is he to know which
way to move if the letter a is shewn him”? But isn't B's
reaction in this case the very reaction described in 37) & 38),
& in fact our usual reaction when for instance we hear and obey
an order? For, the fact that the training in 38) & 39) preced-
ed the carrying out of the order does not change the process of
carrying out. In other words the “curious mental mechanism”
assumed in 40) is no other than that which we assumed to be

32.
created by the training in 37) and 38). “But could such a
mechanism be born with you?” But did you find any difficulty
in assuming that that mechanism was born with B, which enabled
him to respond to the training in the way he<…> did? And remem-
ber that the rule or explanation given in table 33) of the signs
abcd was not essentially the last one, and that we might have
given a table for the use of such tables, and so on. (Cf. 21)).

     

      How does one explain to a man how he should carry out the
order, “Go this way!” (pointing with an arrow the way he should
go)? Couldn't this mean going the direction which we should
call the opposite of that of the arrow? Isn't every explanat-
ion of how he should follow the arrow in the position of another
arrow? What would you<…> say to this explanation: A man says,
“If I point this way (pointing with his right hand) I mean you
to go like this” (pointing with his left hand the same way)?
 This just shews you the extremes between which the uses of signs
vary.

     

      Let us return to 39). Someone visits the tribe and ob-
serves the use of the signs in their<…> language. He describes
the language by saying that its sentences consist of the letters
abcd used according to the table: (of 33)). We see that the
expression, “A game is played according to the rule so-and-so”
is used not only in the variety of cases exemplified by 36), 37),
& 38), but even in cases where the rule is neither an instrument
of the training nor of the practice of the game, but stands in
the relation to it in which our table stands to the practice of
our game 39). One might in this case call the table a natural

33.
law describing the behaviour of the people of this tribe.
Or we might say that the table is a record belonging to the
natural history of the tribe.

     

      Note that in the game 33) I distinguished sharply between
the order to be carried out and the rule employed. In 34) on
the other hand, we called the sentence “cada” a rule, & it was
the order. Imagine also this variation:
41).   The game is similar to 33), but the pupil is not just
trained to use a single table; but the training aims at making
the pupil use any table correlating letters with arrows. Now
by this I mean no more than that the training is of a peculiar
kind, roughly speaking one analogous to that described in 30).
I will refer to a training more or less similar to that in 30)
as a “general training”. General trainings form a family
whose members differ greatly from one another. The kind of
thing I'm thinking of now mainly consists: 9) a) of a training
in a limited range of actions, b) of giving the pupil a lead to
extend this range, & c) of random exercises and tests. After
the general training the order is now to consist in giving him
a sign of this kind:

He carries out the order by moving thus: . Here I
suppose we should say the table, the rule, is part of the order.

     

      Note, we are not saying “what a rule is” but just giving
different applications of the word “rule”; & we certainly do
this by giving applications of the words “expression of a rule”.

     

      Note also that in 41) there is no clear case against call-

34.
ing the whole symbol given the sentence, though we might
distinguish in it between the sentence and the table. What
in this case more particularly tempts us to this distinction
is the linear writing of the part outside the table. Though
from ceratin certain points of view we should call the linear character
of the sentence merely external and inessential, this charac-
ter and similar ones play a great role in what as logicians we
are inclined to say about sentences and propositions. And
therefore if we conceive of the symbol in 41) as a unit, this
may make us realise what a sentence can look like.

     

      Let us now consider these two games:
42).   A gives orders to B: they are written signs consisting of
dots and dashes and B executes them by doing a figure in danc-
ing with a particular step. Th[i|u]s the order “-.” is to be car-
ried out by taking a step and a hop alternately; the <…>
order “..---” by alternately taking two hops and three steps,
etc. The training in this game is “general” in the sense
explained in 41); and I should like to say, “the orders given
don't move in a limited range. They comprise combinations of
any number of dots and dashes”. — But what does it mean to say
that the orders don't move in a limited range? Isn't this
nonsense? Whatever orders are given in the practice of the
game constitute the limited range. — Well, what I meant to say
by “the orders don't move in a limited range” was that neither
in the teaching of the game nor in the practice of it a limit-
ation of the range plays a “predominant” role (see 30)) or, as
we might say, the range of the game (it is superfluous to say

35.
limited) is just the extent of its actual (“accidental”)
practice. (Our game is in this way like 30)) Cf.with this
game the following:
43).   The orders and their execution as in 42); but only
these three signs are used: “-.”, “-..”, “.--”. We say that
in 42) B in executing the order is guided by the sign given to
him. But if we ask ourselves whether the three signs in 43)
guide B in executing the orders, it seems that we can say both
yes and no according to the way we look at the execution of the
orders.

     

      If we try to decide whether B in 43) is guided by the
signs or not, we are inclined to give such answers as the fol-
lowing: a) B is guided if he doesn't just look at an order, say
“.--” as a whole and then act, but if he reads it “word by
word” (the words used in our language being “.” “-”) and acts
according to the words he has read.

     

      We could make these cases clearer if we imagine that the
“reading word by word” consisted in pointing to each word of
the sentence in turn with one's finger as opposed to pointing
at the whole sentence at once, say by pointing to the beginning
of the sentence. And the “acting according to the words” we
shall for the sake of simplicity imagine to consist in acting
(stepping or hopping) after each word of the sentence in turn.
— b) B is guided if he goes through a conscious process which
makes a connection between the pointing to a word and the act
of hopping and stepping. Such a connection could be imagined
in many different ways. E.g., B has a table in which a dash

36.
is correlated to the picture of a man making a step and a dot
to a picture of a man hopping. Then the conscious acts conn-
ecting reading the order and carrying it out might consist
in consulting the table, or in consulting a memory image of it
“with one's mind's eye”. c) B is guided if he does not just
react to looking at each word of the order, but experiences the
peculiar strain of “trying to remember what the sign means”,
& further, the relaxing of this strain when the meaning, the
right action, comes before his mind.

     

      All these <…> explanations seem in a particular peculiar way unsat-
isfactory, and it is the limitation of our game which makes
them unsatisfactory. This is expressed by the explanation that
B is guided by the particular combination of words in one of
our three sentences if he could also have carried out orders
consisting in other combinations of dots and dashes. And if
we say this, it seems to us that the “ability” to carry out
other orders is a particular state of the person carrying out
the orders of 42). And at the same time we can't in this case
find anything which we should call such a state.

     

      Let us see what role the words “can” or “to be able to”
play in our language. Consider these examples:
44).   Imagine that for some purpose or other people use a kind
of instrument or tool; this consists of a board with a slot in
it guiding the movement of a peg. The man using the tool
slides the peg along the slot. There are such boards with
straight slots, circular slots, elliptic slots, etc. The lan-
guage of the people using this instrument has expressions for

37.
describing the activity of moving the pe[h|g] in the slot. They
talk of moving it in a c[o|i]rcle, in a straight line, etc. They
also have a means of describing the board used. They do it
in this form: “This is a board in which the peg can be moved in
a circle”. One could in this case call the word “can” an
operator by means of which the form of expression describing an
action is transformed into a description of the instrument.
45).   Imagine a people in whose language there is no such form
of sentence as “the book is in the drawer” or “water is in the
glass”, but wherever we should use these forms they say, “The
book can be taken out of the drawer”, “The water can be taken
out of the glass”.
46).   An activity of the men of a certain tribe is to test
sticks as to their hardness. They do it by trying to bend the
sticks with their hands. In their language they have express-
ions of the form, “This stick can be bent easily” or “This stick
can be bent with difficulty”. They use these expressions as
we use “This stick is soft” or “This stick is hard”. I mean to
say that they don't use the expression, “This stick can be bent
easily” as we should use the sentence “I am bending the stick
with ease”. Rather they use their expression in a way which
would make us say that they are describing a state of the
stick. I.e., they use such sentences as, “This hut is built
of sticks that can be bent easily”. (Think of the way in which
we form adjectives out of verbs by means of the ending “-able”,
e.g., “deformable”.)

     

      Now we might say that in the last three cases the sent-

38.
ences of the form “so-and-so can happen” described the state of
objects, but there are great differences between these examples.
In 44) we saw the state described before our eyes. We saw
that the board had a circular or a straight slot, etc. In
45), in some instances at least this was the case, we could see
the objects in the box, the water in the glass, etc. In such
cases we use the expression “state of an object” in such a way
that there corresponds to it what one might call a stationary
sense experience.

     

      When on the other hand, we talk of the state of a stick
in 46), observe that to this “state” there does not correspond
a particular sense experience which lasts while the state lasts.
[i|I]nstead of that, the defining criterion for something being in
this state consists in certain tests.

     

      We may say that a car travels 20 miles an hour even if it
only travels for half an hour. We can explain our form of
expression by saying that the car travels with a speed which
enables it to make 20 miles an hour. And here also we are in-
clined to talk of the velocity of the car as of a state of its
motion. I think we should not use this expression if we had
no other “experiences of motion” than those of a body being in a
particular place at a certain time and in another place at an-
other time; if, e.g., our experience<s> of motion were of the
kind which we have when we see the hour hand of the clock has
moved from one point of the dial to the other.
47).   A tribe has in its language commands for the execution of
certain actions of men in warfare, something like “Shoot!”,

39.
“Run!”, “Crawl!”, etc. They also have a way of describing a
man's build. Such a description has the form “He can run fast”,
“He can throw the spear far”. What justifies me in saying
that these sentences are descriptions of the man's build is the
use which they make of sentences of this form. Thus if they
see a man with bulging leg muscles but who as we should say has
not the use of his legs for some reason or other, they say he
is a man who can run fast. The drawn image of a man which
shews large biceps they describe as representing a man “who
can throw a spear far”.
48).   The men of a tribe are subjected to a kind of medical
examination before going into war. The examiner puts the men
through a set of standard[s|i]sed tests. He lets them lift certain
weights, swing their arms, skip, etc. The examiner then gives
his verdict in the form “So-and-so can throw a spear” or “can
throw a boomerang” or “is fit to pursue the enemy”, etc. There
are no special expressions in the language of this tribe for
the activities performed in the tests; but these are referred
to only as the tests for certain activities in warfare.

     

      It is an important remark concerning this example and
others which we give that one may object to the description
which we give of the language of a tribe, that in the specimens
we give of their language we let them speak English, thereby
already presupposing the whole background of the English lan-
guage, that is, our usual meanings of the words. Thus if I
say that in a certain language there is no special verb for
“skipping”, but that this language uses instead the form “making

40.
the test for throwing the boomerang”, one may ask how I have
characterized the use of the expressions, “make a test for” &
“throwing the boomerang”, to be justified in substituting these
English expressions for whatever their actual words may be.
To this we must answer that we have only given a very sketchy
description of the practices of our fictitious languages, in
some cases only hints, but that one can easily make these des-
criptions more complete. Thus in 48) I could have said that
the examiner uses orders for making the men go through the tests.
These orders all begin with one particular expression which I
could translate into the English words, “Go through the test”.
And this expression is followed by one which in actual warfare
is used for certain actions. Thus there is a command upon which
men throw their boomerangs and which therefore I should trans-
late into, “Throw the boomerangs”. Further, if a man gives an
account of the battle to his chief, he again uses the expression
I have translated into “Throw a boomerang”, this time in a des-
cription. Now what characterizes an order as such or a descr-
iption as such or a question as such, etc., is — as we have
said — the role which the utterance of these signs plays in
the whole practice of the language. That is to say, whether a
word of the language of our tribe is rightly translated into a
word of the English language depends upon the role this word
plays in the whole life of the tribe; the occasions on which it
is used, the expressions of emotions by which it is generally
accompanied, the ideas which it generally awakens or which prompt
its saying, etc. etc. As an exercise ask yourself: in which

41.
cases would you say that a certain word uttered by the people
of the tribe was a greeting? In which cases should we say it
corresponded to our “Goodbye”, in which to our “Hello”? In
which cases would you say that a word of a foreign language
corresponded to our “perhaps”? — to our expressions of doubt,
trust, certainty? You will find that the justifications for
calling something an expression of doubt, conviction, etc.
largely, though of course not wholly, consist in descriptions
of gestures, the play of facial expressions, and even the tone
of voice. Remember at this point that the personal experiences
of an emotion must in part be strictly localized experiences;
for if I frown in anger I feel the muscular tension of the frown
in my forehead, & if I weep, the sensations around my eyes are
obviously part, and an important part, of what I feel. This is,
I think, what William James meant when he said that a man doesn't
cry because he is sad but that he is sad because he cries. The
reason why this point is often not understood is that we think
of the utterance of an emotion as though it were some artificial
device to let others know that we have it. Now there is no
sharp line between such “artificial devices” and what one might
call the natural expressions of emotion. Cf. in this respect:
a) weeping, b) raising one's voice when one is angry, c) writ-
ing an angry letter, d) ringing the bell for a servant you wish
to scold.

     
49).   Imagine a tribe in whose language there is an expression
corresponding to our “He has done so-and-so” and another expres-
sion corresponding to our “He can do so-and-so”, this latter

42.
expression, however, being only used where its use is justified
by the same fact which would also justify the former expression.
Now what can make me say this? They have a form of communic-
ation which we should call narration of past events because of
the circumstances under which it is employed.. There are also
circumstances under which we should ask and answer such questions
as “Can so-and-so do this?”. Such circumstances can be descr-
ibed, e.g., by saying that a chief picks men suitable for a
certain action, say crossing a river, climbing a mountain, etc.
As the defining criteria of “the chief picking men suitable
for this action”, I will not take what he says but only the
other features of the situation. The chief under these circ-
umstances asks a question which, as far as its practical con-
sequences go, would have to be translated by our “Can so-and-so
swim across this river?” This question, however, is only
answered affirmatively by those who actually have swum across
this river. Th[u|i]s answer is not given in the same words in
which under the circumstances characterizing narration he would
say that he has swum across this river, but it is given in the
terms of the question asked by the chief. On the other hand,
this answer is not given in cases in which we should certainly
give the answer, “I can swim across this river”, if, e.g., I
had performed more difficult feats of swimming though not just
that of swimming across this particular river.

     

      By the way, have the two phrases, “He has done so-&-so”
and “He can do so-&-so” the same meaning in this language or
have they different meanings? If you think about it, something

43.
will tempt you to say the one, something to say the other.
This only shows that the question has here no clearly defined
meaning. All I can say is: If the fact that they only say,
“He can…” if he has done… is your criterion for the same
meaning, then the two expressions have the same meaning. If
the circumstances under which an expression is used make its
meaning, the meanings are different. The use which is made of
the word “can” — the expression of possibility in 49) — can
throw a light upon the idea that what can happen must have hap-
pened before (Nietzsche). It will also be interesting to
look, in the light of our examples, on the statement that what
happens can happen.

     

      Before we go on with our consideration of the use of “the
expression of possibility”, let us get clearer about that dep-
artment of our language in which things are said about past &
future, that is, about the use of sentences containing such
expressions as “yesterday”, “a year ago”, “in five minutes”,
“before I did this”, etc. Consider this example:
50).   Imagine how a child might be trained in the practice of
“narration of past events”. He was first trained in asking for
certain things (as it were, in giving orders. See 1).) Part
of this training was the exercise of “naming the things”. He
has thus learnt to name (& ask for) a dozen of his toys. Say
now that he has played with three of them (e.g., a ball, a stick,
and a rattle), then they are taken away from him, and now the
grown-up says such a phrase as, “He's had a ball, a stick, and
a rattle”. On a similar occasion he stops short in the enum-

44.
eration and induces the child to complete it. On another
occasion, perhaps, he only says, “He's had…” and leaves
the child to give the whole enumeration. Now the way of “in-
ducing the child to go on” can be this: He stops short in his
enumeration with a facial expression and a raised tone of voice
which we should call one of expectancy. All then depends on
whether the child will react to this “inducement” or not. Now
there is a queer misunderstanding we are most liable to fall
into, which consists in regarding the “outward means” the teach-
er uses to induce the child to go on as what we might call an
indirect means of making himself understood to the child. We
treat regard the case as though the child already possessed a language
in which it thought and that the teacher's job is to induce it
to guess his meaning in the realm of meanings before the child's
mind, as though the child could in his own private language
ask himself such a question as, “Does he want me to continue,
or repeat what he said, or something else?” (Cf. with 30)).
51).   Another example of a primitive kind of narration of past
events: we live in a landscape with characteristic natural
landmarks against the horizon. It is therefore easy to rem-
ember the place at which the sun rises at a particular season,
or the place above which it stands when at its highest point,
or the place at which it sets. We have some characteristic
pictures of the sun in different positions in our landscape.
Let us call this series of pictures the sun series. We have
also some characteristic pictures of the activities of a child,
lying in bed, getting up, dressing, lunching, etc. This set

45.
I'll call the life pictures. I imagine that the child can
frequently see the position of the sun while about the day's
activities. We draw the child's attention to the sun's stand-
ing in a certain place while the child is occupied in a part-
icular way. We then let it look both at a picture representing
its occupation and at a picture showing the sun in its position
at that time. We can thus roughly tell the story of the child's
day by laying out a row of the life pictures, and above it what
I called the sun series, the two rows in the proper correlation.
We shall then proceed to let the child supplement such a pic-
ture story, which we leave incomplete. And I wish to say at
this point that this form of training (see 50) and 30)) is one
of the big characteristic features in the use of language, or
in thinking.
52).   A variation of 51). There is a big clock in the nurs-
ery, for simplicity's sake imagine it with an hour hand only.
The story of the child's day is narrated as above, but there is
no sun series; instead we write one of the digits numbers of the dial
against each life picture.

     
53).   Note that there would have been a similar game in which
also, as we might say, time was involved, that of just laying
out a series of life pictures. We might play this game with
the help of words which would correspond to our “before” and
“after”. In this sense we may say that 53) involves the ideas
of before and after, but not the idea of a measurement of time.
I needn't say that an easy step would lead us from the narrations
in 51), 52), & 53) to narrations in words. Possibly someone

46.
considering such forms of narration might think that in them
the real idea of time isn't yet involved at all, but only some
crude substitute for it, the position of a clock hand and such
like. Now if a man claimed that there is an idea of “five
o'clock” which does not bring in a clock, that the clock is
only the coarse instrument indicating when it is five o'clock
or that there is an idea of an hour which does not bring in an
instrument for measuring the time, I will not contradict him,
but I will ask him to explain to me what his use of the term
“an hour” or “five o'clock” is. And if it is not that involv-
ing a clock, it is a different one; and then I will ask him why
he uses the term “five o'clock”, “an hour”, “a long time”, “a
short time”, etc., in one case in connection with a clock, in
the other independent of one; it will be because of certain ana-
logies holding between the two uses, but we have now two uses
of these terms, and no reason to say that one of them is less
real and pure than the other. This might get clearer by con-
sidering the following example:
54).   If we give a person the order, “Say a number, any one
which comes into your mind”, he can generally comply with it
at once. Suppose it were found that the numbers thus said
on request increased — with every normal person — as the day
went on; a man starts out with some small number every morning
and reaches the highest number before falling asleep at night.
Consider what could tempt one to call the reactions described
“a means of measuring time” or even to say that they are the
real milestones in the passage of time, the sun clocks, etc.

47.
being only indirect markers. indicators. (Examine the statement that the
human heart is the real clock behind all the other clocks).

     

      Let us now consider further language-games into which
temporal expressions enter.
55).   This arises out of 1). If an order like “Slab!”,
“Column!”, etc. is called out, B is trained to carry it out
immediately. We now introduce a clock into this game, an order
is given, and we train the child not to carry it out until the
hand of our clock reaches a point indicated before w[a|i]th the
finger. (This might, e.g., be done in this way: You first
trained the child to carry out the order immediately. You
then give the order, but hold the child back, releasing it only
when the hand of the clock has reached the point of the dial to
which we point with our fingers.)

     

      We could at this stage introduce such a word as “now”.
We have two kinds of orders in this game, the orders used in
1), or and orders consisting of these together with a gesture indic-
ating a point of the clock dial. In order to make the distin-
ction between these two kinds more explicit, we may affix a
particular sign to the orders of the first kind and e.g., say:
“slab, now!”.

     

      It would be easy now to describe language-games in such
expressions as “in five minutes”, “half an hour ago”.
56).   Let us now have the case of a description of the future,
a forecast. One might, e.g., awaken the tension of expectation
in a child by keeping his attention for a considerable time
on some traffic lights changing their colour periodically. We
also have a red, a green, and a yellow disc before us and alter-

48.
nately point to one of these discs by way of forecasting the
colour which will appear next. It is easy to imagine further
developements of this game.

     

      Looking at these language-games, we don't come across
the ideas of the past, the future, and the present in their
problematic and almost mysterious aspect. What this aspect is
and how it comes about that it appears can be most characterist-
ically exemplified if we look at the question, “Where does the
present go when it becomes past, and where is the past?” —
under what circumstances has this question an allurement for
us? For under certain circumstances it hasn't, and we should
wave it away as nonsense.

     

      It is clear that this question most easily arises if we
are preoccupied with cases in which there are things flowing by
us, — as logs of wood float down a river. In such a case we
can say the logs which have passed us are all down towards the
left and the logs which will pass us are all up towards the
right. We then use this situation as a simile for all happen-
ing in time and even embody the simile in our language, as when
we say that “the present event passes by” (a log passes by),
“the future event is to come” (a log is to come). We talk
about the flow of events; but also about the flow of time —
the river on which the logs travel.

     

      Here is one of the most fertile sources of philosophic
puzzlement: We talk of the future event of something coming
into my room, and also of the future coming of this event.

     

      We say, “Something will happen”, and also, “Something

49.
comes towards me”; we refer to the log as to “something”, but
also to the log's coming towards me.

     

      Thus it can come about that we aren't able to rid ourselves
of the implications of our symbolism, which seems to admit of
a question like, “where does the flame of a candle go to when
it's blown out?”, “Where does the light go to?”, “Where does the
past go to?”. We have become obsessed with our symbolism.
We may say that we are led into puzzlement by an analogy which
irresistibly drags us on.— And this also happens when the
meaning of the word “now” appears to us in a mysterious light.
In our example 55) it appears that the function of “now” is in
no way comparable to the function of an expression like “five
o'clock”, “midday”, “the time when the sun sets”, etc. This
latter group of expressions I might call “specifications “determinations of
times”. But our ordinary language uses the word “now” and
determinations of time in similar contexts. Thus we say “The
sun sets now”. “The
sun sets at six o' clock”. We are inclined to say that both
“now” and “six o'clock” “refer to points of time”. This use
of words produces a puzzlement which one might express in the
question, “What is the ‘now’? — for it is a moment of time and
yet it can't be said to be either the ‘moment at which I speak’
or the ‘moment at which the clock strikes’ etc., etc.”— Our
answer is: The function of the word “now” is entirely different
from that of a specification of time.— This can easily be
seen if we look at the role this word really plays in our usage
of language, but it is obscured when instead of looking at the
whole language-game, we only look at the contexts, the phrases

50.
of language in which the word is used. (The word “today” is
not a date, but it isn't anything like it either. It doesn't
differ from a date as a hammer differs from a mallet, but as a
hammer differs from a nail; and surely we may say there is both
a connection between a hammer and a mallet and between a hammer
and a nail.)

     

      One has been tempted to say that “now” is the name of an
instant of time, and this, of course, would be like saying that
“here” is the name of a place, “[T|t]his” the name of a thing, and
“I” the name of a man. (One could of course also have said
“a year ago” was the name of a time, “over there” the name of a
place, and “you” the name of a person.) But nothing is more
unlike than the use of the word “this” and the use of a proper
name, — I mean the games played with these words, not the phrases
in which they are used. For we do say, “This is short” and
“Jack is short”; but remember that “This is short” without the
pointing gesture and without the thing we are pointing to would
be meaningless. — What can be compared with a name is not the
word “this” but, if you like, the symbol consisting of this
word, the gesture, and the sample. We might say: Nothing is
more characteristic of a proper name A than that we can use it
in such a phrase as, “This is A”; & it makes no sense to say,
“This is this” or “Now is now” or “Here is here”.

     

      The idea of a proposition saying something about what will
happen in the future is even more liable to puzzle us than the
idea of a proposition about the past. For comparing future
events with past events, one may almost be inclined to say that

51.
though the past events do not really exist in the full light of
day, they exist in an underworld into which they have passed
out of the real life; whereas the future events do not even
have this shadowy existence. We could, of cou[s|r]se, imagine a
realm of the unborn, future events, whence they come into real-
ity and pass into the realm of the past; and, thinking if we think in terms
of this metaphor, we may be surprised that the future should
appear less existent than the past. Remember, however, that
the grammar <…> of our temporal expressions is not symmetrical
with respect to an origin corresponding with the present moment.
Thus the grammar of the expressions relating to memory does
not reappear “with opposite sign” in the grammar of the future
tense. //Thus there is nothing in the grammar of the future
tense corresponding to the grammar of the word “memory”. This
part of the grammar of the past tense does not recur “with its
sign changed” on the future side.// This is the reason why
it has been said that propositions concerning future events are
not really propositions. And to say this, is all right as long
as it isn't meant to be more than a decision about the use of
the term “proposition”; a decision which, though not agreeing
with the common usage of the word “proposition”, may come natur-
al to human beings under certain circumstances. If a philos-
opher says that propositions about the future are not real prop-
ositions, it is because he has been struck by the asymmetry in
the grammar of temporal expressions. The danger is, however,
that he imagines he has made a kind of scientific statement
about “the nature of the future”.

52.
57).   A game is played in this way: A man throws a die, and
before throwing he draws on a piece of paper some one of the
six faces of the die. If, after having thrown, the face of
the die turning up is the one he has drawn, he fe[l|e]ls (expresses)
satisfaction. If a different face turns up, he is dissatis-
fied. Or, let there be two partners and every time one guesses
correctly what he will throw his partner pays him a penny, and
if incorrectly, he pays his partner. Drawing the face of the
die will be under the circumstances of this game be called
“making a guess” or a “conjecture”.
58).   In a certain tribe contests are held in running, putting
the weight, etc. and the spectators stake money possessions on the compet-
itors. The pictures of all the competitors are placed in a
row, and what I called the spec[a|t]ators' staking property on one
of the competitors consists in laying this property (pieces of
gold) under one of the pictures. If a man has placed his gold
under the picture of the winner in the competition he gets back
his stake doubled. Otherwise he loses his stake. Such a
custom we should undoubtedly call betting, even if we observed
it in a society whose language held no scheme for stating “de-
grees of probability”, “chances” and the like. I assume that
the behaviour of the spectators expresses great keenness and
excitement before and after the result outcome of the bet is known. I
further imagine that on <…> examining the placing of the
bets I can understand “why” they were thus placed. I mean:
In a competition between two wrestlers, mostly the bigger man is
the favorite; or if the smaller, I find that he has shown great-

53.
er strength on previous occasions, or that the bigger had recent-
ly been ill, or had neglected his training, etc. Now this may
be so although the language of the tribe does not express reas-
ons for the placing of the bets. That is to say, nothing in
their language corresponds to our saying, e.g., “I bet on this
man because he has kept fit, whereas the other has neglected
his training”, and such like. I might describe this state of
affairs by saying that my observation has taught me certain
causes for their placing their bets as they do, but that the
bettors had used no reasons for ac[y|t]ing as they did. %

     

      The tribe may, on the other hand, have a language which
comprises “giving reasons”. Now this game of giving the reason
why one acts in a particular way does not involve finding the
causes of one's actions (by frequent observations of the con-
ditions under which they arise). Let us imagine this:
59).   If a man of our tribe has lost his bet and upon this is
chaffed or scolded, he points out, possibley exaggerating, cert-
ain features of the man on whom he has laid his bet. One can
imagine a discussion of pros and cons going on in this way: two
people pointing out alternately certain features of the two
competitors whose chances, as we should say, they are discussing;
A pointing with a gesture to the great height of the one, B in
answer to this shrugging his shoulders and pointing to the size
of the other's biceps, and so on. I could easily add more
details which would make us say that A and B are giving reasons
for laying a bet on one person rather than on the other.

     

      Now one might say suggest that giving reasons in this way for

54.
laying their bets certainly presupposes that they have observed
causal connections between the result of a fight, say, and cert-
ain features of the bodies of the fighters, or of their train-
ing. But this is an assumption which, whether reasonable or
not, I certainly have not made in the description of our case.
(Nor have I made the assumption that the bettors give reasons
for their reasons.) We should in a case like that just describ-
ed not be surprised if the language of the tribe contained what
we should call expressions of degrees of belief, conviction,
certainty. These expressions we could imagine to consist in
the use of a particular word spoken with different intonations,
or a series of words. (I am not thinking however of the use
of a scale of probabilities.) — It is also easy to imagine that
the people of our tribe accompany their betting by verbal ex-
pressions which we translate into, “I believe that
so-and-so can beat so-and-so in wrestling”, etc.
60).   Imagine in a similar way conjectures being made as to
whether a certain load of gunpowd/er will be sufficient to
blast a certain rock, and the conjecture to be expressed in a
phrase of the form, “This quantity of gunpowder can blast this
rock”.
61).   Compare with 60) the case in which the expression, “I
shall be able to lift this weight”, is used as an abbreviation
for the conjecture, “My hand holding this weight will rise if
I go through the process (experience) of ‘making an effort to
lift it’”. In the last two cases the word “can” characterized
what we should call the expression of a conjecture. (Of course

55.
I don't mean that we call the sentence a conjecture because it
contains the word “can”; but in calling a sentence a conjecture
we referred to the role which the sentence played in the lan-
guage-game; and we translate a word our tribe uses by “can” if
“can” is the word we should use under the circumstances des-
cribed). Now it is clear that the use of “can” in 59), 60),
61) is closely related to the use of “can” in 46) to 49); dif-
fering, however in this, that in 46) to 49) the sentences say-
ing that something could can happen were not expressions of con-
jecture. Now one might object to this by saying: Surely we are
only willing to use the word “can” in such cases as 46) to 49)
because it is reasonable to conjecture in these cases what a
man will do in the future from the tests he has passed or from
the state he is in.

     

      Now it is true that I have deliberately made up the cases
46) to 49) so as to make a conjecture of this kind seem reason-
able. But I have also deliberately made them up so as not to
contain a conjecture. We can, if we like, make the hypothesis
that the tribe woul[s|d] never use such a form of expression as
that used in 49), etc. if experience had not shown them that…
etc. But this is an assumption which, though possibly correct,
is in no way presupposed in the games 46) to 49) as I have act-
ually described them.
62).   Let the game be this: A writes down a row of numbers.
B watches him and tries to find a system in the sequence of
these numbers. When he has done so he says: “Now I can go on”.
This example is particularly instructive because “being able to

56.
go on” here seems to be something setting in suddenly in the
form of a clearly outlined event. — Suppose then that A had
written down the row 1,5,11,19,29. At thath point B shouts,
“Now I can go on”. What was it that happened when suddenly he
saw how to go on? A great many different things might have
happened. Let us assume then that in the present case while
A wrote one number after the other B busied himself with try-
ing out several algebraic formulae to see whether they fitted.
When A had written “19” B had been led to try the formula
<…> an = n2 + n - 1. A's writing 29 confirms his guess.
63).   Or, no formula came into B's mind. After looking at
the growing row of numbers A was is writing, possibly with a feeling
of tension and with hazy ideas floating in his mind, he said to
himself the words, “He's squaring and always adding one more”;
then he made up the next number of the sequence and found it
to agree with the numbers A then wrote down. —
64).   Or the row A wrote down was 2, 4, 6, 8. B looks at it,
and says, “Of course I can go on”, and continues the series of
even numbers. Or he says nothing, and just goes on. Perhaps
when looking at the row 2, 4, 6, 8 which A had written down,
he had some sensation, or sensations, often accompanying such
words as, “That's easy!” A sensation of this kind is for ins-
tance, the experience of a slight, quick intake of breath,
what one might call a slight start.

     

      Now, should we say that the proposition, “B can continue
the series”, means that one of the occurrences just described
takes place? Isn't it clear that the statement, “B can contin-

57.
ue…” is not the same as the statement that the formula
an = n2 + n - 1 comes into B's mind? This occurrence might have
been all that actually took place. (It is clear, by the way,
that it can make no difference to us here whether B has the
experience of this formula appearing before his mind's eye, or
the experience of writing or speaking the formula, or of pick-
ing it out with his eyes from amongst several formulae written
down beforehand.) If a parro[y|t] had uttered the formula, <…>
we should not have said that he could continue the series. —
Therefore, we are inclined to say “to be able to…” must mean
more than just uttering the formula, — and in fact more than
any one of the occurrences we have described. And this, we go
on, shows that saying the formula was only a symptom of B's being
able to go on, and that it was not the ability of going on it-
self. Now what is misleading in this is that we seem to intim-
ate that there is one peculiar activity, process, or state called
“being able to go on” which somehow is hidden from our eyes
but manifests itself in these occurrents which we call symptoms
(as an inflammation of the mucous membranes of the nose prod-
uces the symptom of sneezing). This is the way talking of
symptoms, in this case, misleads us. When we say, “Surely
there must be something else behind the mere uttering of the
formula, as this alone we should not call ‘being able to…’”,
the word “behind” here is certainly used metaphorically, and
“behind” the utterance of the formula may be the circumstances
under which it is uttered. It is true, “B can continue…”
is not the same as to say, “B says the formula…”, but it does

58.
doesn't follow from this that the expression, “B can continue…”
refers to an activity other than that of saying the formula,
in the way in which “B says the formula” refers to the well-
known activity. The error we are in is analogous to this:
Someone is told the word “chair” does not mean this particular
chair I am pointing to, upon which he looks round the room for
the object which the word “chair” does denote. (The case
would be even more a striking illustration if he tried to look
inside the chair in order to find the real meaning of the word
<…> “chair”.) It is clear that when with reference to the
act of writing or speaking the formula etc., we use the sentence,
“He can continue the series”, this must be because of some con-
nection between writing down a formula and actually continuing
the series. And the connection in experience of these two
processes or activities is clear enough. But this connection
tempts us to suggest that the sentence, “B can continue…”
means something like, “B does something which, experience has
shown us, generally leads to his continuing the series.” But
does B, when he says, “Now I can go on” really mean, “Now I am
doing something which, as experience has shown us, etc., etc.”?
Do you mean that he had this phrase in his mind or that he would
have been prepared to give it as an explanation of what he had
said?! To say the phrase, “B can continue…” is correctly
used when prompted by such occurrences as described in 62), 63),
64) but that these occurrences justify its use only under cert-
ain circumstances (e.g. when experience has shown certain con-
nections) is not to say that the sentence, “B can continue…”

59.
is short for the sentence which describes all these circum-
stances, i.e. the whole situation which is the background of
our game.

     

      On the other hand we should under certain circumstances
be ready to substitute “B knows the formula”, “B has said the
formula” for “B can continue the series”. As when we ask a
doctor, “Can the patient walk?”, we shall sometimes be ready to
substitute for this, “Is his leg healed?” — “Can he speak?”
under certain circumstances means, “Is his throat all right?”,
under others ([E|e].g. if he is a small child) it means, “Has he
learned to speak?” — To the question, “Can the patient walk?”,
the doctor's answer may be, “His leg is all right”. — We use
the phrase, “He can walk, as far as the state of his leg is con-
cerned”, especially when we wish to oppose this condition for
his walking to some other condition, say the state of his spine.
Here we must beware of thinking that there is in the nature of
the case something which we might call a the complete set of con-
ditions, e.g. for his walking; so that the patient, as it were,
must walk can't help walking if all these conditions are fulfilled.

     

      We can say: The expression, “B can continue the series”,
is used under different circumstances to make different distinct-
ions. Thus it may distinguish a) between the case when a man
knows the formula and the case when he doesn't; or b) between
the case when a man knows the formula and hasn't forgotten how
to write the numerals of the decimal system, and the case when
he knows the formula and has forgotten how to write the numerals;
or c) (as perhaps in 64)) between the case when a man is feel-

60.
ing his normal self and the case when he is still in a condition
of shell shock; or d) between the case of a man who has done
this kind of exercise before and the case of a man who is new
at it. These are only a few of a large family of cases.

     

      The question whether “He can continue…” means the same
as “He knows the formula” can be answered in several different
ways: We can say, “They don't mean the same, i.e., they are not
in general used as synonyms as, e.g., the phrases, ‘I am well’
and ‘I am in good health’”; or we may say, “Under certain circ-
umstances” ‘He can continue…’ means he knows the formula”.
Imagine the case of a language (somewhat analogous to 49)) in
which two forms of expression, two different sentences, are
used to say that a person's legs are in working order. The one
form of expression is exclusively used under circumstances
when preparations are going on for an expedition, a walking
tour, or the like; the other is used in cases when there is no
question of such preparations. We shall here be doubtful
whether to say the two sentences have the same meaning or dif-
ferent meanings. In any case the true state of affairs can
only be seen when we look into the detail of the usage of our
expressions. — And it is clear that if in our present case we
should decide on saying to say that the two expressions have different
meanings, we shall certainly not be able to say that the dif-
ference is that the fact which makes the second sentence true
is a different one from the fact which makes the first sentence
true.

     

      We are justified in saying that the sentence, “He can

61.
continue…” has a different meaning from that, “He knows the
formula”. But we mustn't imagine that we can find a particul-
ar state of affˇairs “which the first sentence refers to”, as it
were on in a plane above that on in which the special occurrences
(like knowing the formula, imagining certain further terms, etc.)
take place.

     

      Let us ask the following question: Suppose that, on one
ground or another, B has said, “I can continue the series”, but
on being asked to continue it he had shown himself unable to do
so, — should we say that this proved that his statement, that
he could continue, was wrong, or should we say that he was able
to continue when he said he was? Would B himself say, “I see
I was wrong”, or “What I said was true, I could do it then but
I can't now”? — There are cases in which he would correctly say
the one and cases in which he would correctly say the other.
Suppose a) when he said he could continue he saw the formula
before his mind, but when he was asked to continue he found he
had forgotten it; — or, b) when he said he could continue he
had said to himself the next five terms of the series, but now
finds that they don't come into his mind; — or c) before, he
had continued the series calculating five more places, now he
still remembers these five numbers but has forgotten how he had
calculated them; — or d) he says, “Then I felt I could continue,
now I can't”; — or e), “When I said I could lift the weight my
arm didn't hurt, now it does”; etc.

     

      On the other hand we say, “I thought I could lift this
weight, but I see I can't”, “I thought I could say this piece

62.
by heart, but I see I was mistaken”.

     

      These illustrations of the our use of the word “can” should
be supplemented by illustrations showing the variety of uses
we make of the terms “forgetting” and “trying”, for these uses
are closely connected with those of the word “can”. Consider Contemplate
these cases: a) Before, B had said to himself the formula, now,
“He finds a complete blank there”. b) Before, he had said to
himself the formula, now, for a moment he isn't sure “whether
it was 2ⁿ or 3ⁿ”. c) He has forgotten a name and it is “on
the tip of his tongue”. Or d), he is not certain whether he
has ever known the name or has forgotten it.

     

      Now look at the way in which we use the word “trying”:
a) A man is trying to open a door by pulling as hard as he can.
b) He is trying to open the door of a safe by trying to find
the combination. c) He is trying to find the combination by
trying to remember it, or d) by turning the knobs and listening
with a stethoscope. Consider the various processes we call
“trying to remember”. Compare e) trying to move your finger
against a resistance (e.g. when someone is holding it), and f)
when you have intertwined the fingers of both hands in a part-
icular way and feel “You don't know what to do in order to make
a particular finger move”.

     

      (Consider also the class of cases in which we say, “I can
do so-and-so but I won't”: “I could if I tried” — e.g. lift
100 pounds; “I could if I wished” — e.g. say the alphabet.)

     

      One might perhaps suggest that the only case in which it
is correct to say, without restriction, that I can do a certain

63.
thing, is that in which while saying that I can do it, I
actually do it, and that otherwise I ought to say, “I can do
it as far as… is concerned”. One may be inclined to think
that only in the above case has a person given a real proof of
being able to so a thing.
65).   But if we look at a language-game in which the phrase
“I can…” is used in this way (e.g., a game in which doing a
thing is taken as the only justification for saying that one is
able to do it), we see that there is not the metaphysical dif-
ference between this game and one in which other justifications
are accepted for saying “I can do so-and-so”. A game of the
kind 65), by the way, shows us the real use of the phrase, “If
something happens it certainly can happen”; an almost useless
phrase in our language. It sounds as though it had some very
clear and deep meaning, but like most of the general philosoph-
ical propositions it is meaningless except in very special cases.
66).   Make this clear to yourself by imagining a language
(similar to 49)) which has two expressions for such sentences
as, “I am lifting a fifty pound weight”; one expression is used
whenever the action is performed as a test (say, before an
athletic competition), the other expression is used when the
action is not performed as a test.

     

      We see that a vast net of family likenesses connects the
cases in which the expressions of possibility, “can”, “to be
able to”, etc. are used. Certain characteristic features, we
may say, appear in these cases in different combinations: there
is, e.g., the element of conjecture (that something will behave

64.
in a certain way in the future); the description of the state
of something (as a condition for its behaving in a certain way
in the future); the account of certain tests someone or some-
thing has passed. —

     

      There are, on the other hand, various reasons which in-
cline us to look at the fact of something being possible,
someone being able to do something, etc., as the fact that he
or it [a|i]s in a particular peculiar state. Roughly speaking, this comes
to saying that “A is in the state of being able to do something”
is the form of representation we are most strongly tempted to
adopt, or, as one could also put it, we are strongly inclined
to use the metaphor of something being in a peculiar state for
saying that something can behave in a particular way. And
this way of representation, or this metaphor, is embodied in
the expressions, “He is capable of…”, “He is able to multiply
large numbers in his head”, “He can play chess”: in these
sentences the verb is used in the present tense, suggesting that
the phrases are descriptions of states which exist at the moment
when we speak.

     

      The same tendency shows itself in our calling the ability
of solving a mathematical problem, the ability to enjoy a piece
of music, etc., certain states of the mind; we don't mean by
this expression “conscious mental phenomena”. Rather, a state
of the mind in this sense is the state of a hypothetical mech-
anism, a mind model meant to explain the conscious mental phen-
omena. (Such things as unconscious or subconscious mental
states are features of the mind model.) In this way also we

65.
can hardly help conceiving of memory as of a kind of store-
house. Note also how sure people are that to the ability of
adding or multiplying or to that of saying a poem by heart,
etc., there must correspond a peculiar state of the person's
brain, although on the other hand they know next to nothing
about such psycho-physiological correspondences. We have an
overwhelmingly strong tendency to conceive of the phenomena
which in such these cases we actually observe by the symbol of a mech-
anism whose manifestations these phenomena are; //We regard these
phenomena as manifestations of this mechanism.// and their
possibility is the particular construction of the mechanism
itself.

     

      Now looking back to our discussion of 43), we see that
it was no final real explanation of B's being guided by the signs
when we said that B was guided if he could also have carried
out orders consisting in other combinations of dots and dashes
than those of 43). In fact, when we considered the question
whether B in 43) was guided by the signs, we were all the time
inclined to say some such thing as that we could only decide
this question with certainty if we could look into the actual
mechanism connecting seeing the signs with acting according to
them. For we have a definite picture of what in a mechanism
we should call certain parts being guided by others. In fact,
the mechanism which immediately suggests itself when we wish to
show what in such a case as 43) we should call “being guided by
the signs” is a mechanism of the type of a pianola. Here, in
the working of the pianola we have a clear case of certain act-

66.
ions, those of the hammers of the piano, being guided by the
pattern of holes in the pianola roll. We could use the expres-
sion, “The pianola is reading off the record made by the perf-
orations in the roll”, and we might call patterns of such perf-
orations complex signs or sentences, opposing their function in
a pianola to the function which similar devices have in mechan-
isms of a different type, e.g., the combination of notches and
teeth which form a key bit. The bolt of a lock is caused to
slide by this particular combination, but we should not say
that the movement of the bolt was guided by the way in which we
combined teeth and notches, i.e., we should not say that the
bolt moved according to the pattern of the key bit. You see
here the connection between the idea of being guided and the
idea of being able to read new combinations of signs: for we
should say that the pianola can read any pattern of perforat-
ions, of a particular kind, it is not built for one particular
tune or set of tunes (like a musical box), — whereas the bolt
of the lock reacts to that pattern of the key bit only which is
predetermined in by the construction of the lock. We could say
that the notches and teeth forming a key bit are not comparable
to the words making up a sentence but to the letters making up
a word, and that the pattern of the key bit in this sense did
not correspond to a complex sign, to a sentence, but to a word.

     

      It is clear that although we might use the ideas of such
mechanisms as similes for describing the way in which B acts in
the games 42) and 43), no such mechanisms are actually involved
in these games. We shall have to say that the use which we

67.
made of the expression “to be guided” in our examples of the
pianola and of the lock is only one use within a family of us-
ages, though these examples may serve as metaphors, ways of
representation, for other usages.

     

      Let us study the use of the expression, “to be guided”,
by studying the use of the word “reading”. By “reading” I
here mean the activity of translating script into sounds, also
of writing according to dictation or of copying in writing a
page of print, and such like; reading in this sense does not
involve any such thing as understanding what you read. The use
of the word “reading” is, of course, extremely familiar to us
in the circumstances of our ordinary life (it would be extremely
difficult to describe these circumstances even roughly). A
person, say an Englishman, has as a child gone through one of
the normal ways of training in school or at home, he has learned
to read his language, later on he reads books, newspapers, let-
ters, etc. What happens when he reads the newspaper? — His
eyes glide along the printed words, he pronounces them aloud or
to himself, but he pronounces certain words just taking their
pattern in as a whole, other words which he pronounces after
having seen their first few letters only, others again he reads
out letter by letter. We should also say that he had read a
sentence if while letting his eyes glide along it he had said
nothing aloud or to himself, but on being asked afterwards what
he had read he was able to reproduce the sentence verbatim or
in slightly different words. He may also act as what we might
call a mere reading machine, I mean, paying no attention to

68.
what he spoke, perhaps concentrating his attention on something
totally different. We should in this case sa[t|y] that he read if
he acted faultlessly like a reliable machine. — Compare with
this case the case of a beginner. He reads the words by spell-
ing them out painfully. Some of the words however, he just
guesses from their contexts, or possibly he knows the piece by
heart. The teacher then says that he is pretending to read the
words, or just that he is not really reading them. If, looking
at this example, we asked ourselves what reading was, we should
be inclined to say that it was a particular conscious mental
act. This is the case in which we say, “Only he knows whether
he is reading; nobody else can really know it”. Yet we must
admit that as far as the reading of a particular word goes,
exactly the same thing might have happened in the beginner's
mind when he “pretended” to read as what happened in the mind
of the fluent reader when he read the word. We are using the
word “reading” in a different way when we talk about the accom-
plished reader on the one hand and the beginner on the other
hand. What in the one case we call an instance of reading we
don't call an instance of reading in the other. — Of course we
are inclined to say that what happened in the accomplished
reader and in the beginner when they pronounced the word could
not have been the same. The difference lying, if not in their
minds, or in their brains. We here imagine two mechanisms,
the internal working of which we can see, and this internal
working is the real criterion for a person's reading or not

69.
reading. But in fact no such mechanisms are known to us in
these cases. Look at it in this way:

     
67).   Imagine that human beings or animals were used as read-
ing machines, assume that in order to become reading machines
they need a particular training. The man who trains them says
of some of them that they already can read, of others that they
can't. Take a case of one who has so far not responded to the
training. If you put before him a printed word he will some-
times make sounds, and every now and then it happens “accident-
ally” that these sounds more or less agree with correspond to the printed word.
A third person hears the pupil creature under training uttering the right
sound on looking at the word “table”. The third person says,
“He reads”, but the teacher answers, “No, he doesn't, it is mere
accident”. But supposing now that the pupil on being shown
other words and sentences goes on reading them correctly. After
a time the teacher says, “Now he can read”. — But what about
the first word “table”? Should the teacher say, “I was wrong;
he read that, too”<…>, or should he say, “No, he only started
reading later”? When did he really begin to read, or: Which
was the first word, or the first letter, which he read? It
is clear that this question here makes no sense unless I give
an “artificial” explanation such as: “The first word which he
reads = the first word of the first hundred consecutive words
he reads correctly”. — Suppose on the other hand that we used
the word “reading” to distinguish between the case when a part-
icular conscious process of spelling out the words takes place
in a person's mind from the case in which this does not happen:

70.
— Then, at least the person who is reading could say that
such-and-such a word was the first which he actually read. —
Also, in the different case of a reading machine which is a
mechanism connecting signs with the reactions to these signs,
e.g., a pianola, we could say, “only after such-and-such a
thing has been done to the machine, e.g., certain parts had
been connected by wires, the machine actually read; the first
letter which it read was a d”. —

     

      In the case 67), by calling certain creatures “reading
machines” we meant only that they react in a particular way to
seeing printed signs. No connection between seeing and react-
ing, no internal mechanism enters into this case. It would be
absurd if the trainer had answered to the question whether he
read the word “table” or not, “Perhaps he read it”, for there
is no doubt in this case about what he actually did. The
change which took place was one which we might call a change in
the general behaviour of the pupil, and we have in this case
not given a meaning to the expression, “The first word in the
new era”. (Compare with this the following case:

In our figure a row of dots with large intervals succeeds a row
of dots with small intervals. Which is the last dot in the
first sequence and which the first dot in the second? Imagine
our dots were holes in the revolving disc of a siren. Then we
should hear a tone of low pitch following a tone of high pitch
(or vice versa). Ask yourself: At which moment does the tone
of low pitch begin and the other end?)

     

71.

      There is a great temptation on the other hand to regard
the conscious mental act as the only real criterion disting-
uishing reading from not reading. For we are inclined to say,
“Surely a man always knows whether he is reading or pretending
to read”, or “Surely a man always knows when he is really read-
ing”. If A tries to make B believe that he is able to read
Cyrillic script, cheating him by learning a Russian sentence
by heart and then saying it <…> while looking at the printed
sentence, we may certainly say that A knows that he is pretend-
ing and that he is not reading in this case is characterized by
a particular personal experience, namely, that of saying the
sentence by heart. Also, if A makes a slip in saying it by
heart, this experience will be different from that which a pers-
on has who makes a slip in reading.
68).   But supposing now that a man who could read fluently and
who was made to read sentences which he had never read before
read these sentences, but all the time with the peculiar feel-
ing of knowing the sequence of words by heart. Should we in
this case say that he was not reading, i.e., should we regard
his personal experience as the criterion distinguishing between
reading and not reading?
69).   Or imagine this case: A man under the influence of a
certain drug is shown a group of five signs, not letters of an
existing alphabet; and looking at them with all the outward signs
and personal experiences of spelling out a word, pronounces the
word “ABOVE”. (This sort of thing happens in dreams. After
waking up we then say, “It seemed to me that I was reading these

72.
signs though they weren't really signs at all”.) In such a
case some people might be inclined to say that he is reading,
others that he isn't. We could imagine that after he had spelt
out the word “above” we showed him other combinations of the
five signs and that he read them consistently with his reading
of the first permutation of signs shown to him. By a series
of similar tests we might find that he used what we might call
an imaginary alphabet. If this was so, we should be more
ready to say, “He reads” than “He imagines that he reads, but he
doesn't really”.

     

      Note also that there is a continuous series of intermed-
iary cases between the case when a person knows by heart what is
in print before him and the case in which he spells out the
letters of every word without any such help as guessing from
the context, knowing by heart, and such like.

     

      Do this: Say by heart the series of cardinals from one to
twelve, — Now look at the dial of your watch and read this
sequence of numbers. Ask yourself what in this case you called
reading, that is, what did you do to make it reading?

     

      Let us try this explanation: A person reads if he derives
the copy which he is producing from the model which he is copy-
ing. (I will use the word “model” to mean that which he is
reading off, e.g., the printed sentences which he is reading or
copying in writing, or such signs as “--..-” in 42) and 43)
which he is “reading” by his movements, or the scores which a
pianist plays off, etc. The word “copy” I use for the sentence
spoken or written from the printed one, for the movements made

73.
according to such signs as “--..-”, for the movements of the
pianist's fingers or the tune which he plays from the scores,
etc.) Thus if we had taught a person the Cyrillic alphabet
and had taught him how each letter was pronounced, if then we
gave him a piece printed in the Cyrillic script and he spelt it
out according to the pronunciation of each letter as we had
taught it, we should undoubtedly say that he was deriving the
sound of every word from the written and spoken alphabet taught
him. And this also would be a clear case of reading. (We
might use the expression, “We have taught him the rule of the
alphabet”.)

     

      But, let us see, what made us say that he derived the
spoken words from the printed by means of the rule of the alph-
abet? Isn't all we know that we told him that this letter was
pronounced this way, that letter that way, etc., and that he
afterwards read out words in the Cyrillic script? What sug-
gests itself to us as an answer is that he must have shown
somehow that he did actually make the transition from the printed
to the spoken words by means of the rule of the alphabet which
we had given him. And what we mean by his showing this will
certainly get clearer if we alter our example and
70)   assume that he reads off a text by transcribing it, say,
from block letters into cursive script. For in this case we
can assume the rule of the alphabet to have been given in the
form of a table which shows the block alphabet and the cursive
alphabet in parallel columns. Then the deriving the copy from
the text we should imagine this way: The person who copies looks

74.
up the table for each letter at frequent intervals, or he says
to himself such things as, “Now what's a small a like?”, or he
tries to visualize the table, refraining from actually looking
at it. —

     
71).   But what if, doing all this, he then transcribed an “A”
into a “b”, a “B” into a “c”, and so on? Should we not call
this “reading” “deriving” too? We might in this case describe
his procedure by saying that he used the table as we should
have used it had we not looked straight from left to right like
this: but like this: though he actually when looking
up the table passed with his<…> eyes or finger horizontally from
left to right. — But let us suppose now
72)   that going through the normal processes “looking up”, he
transcribed an “A” into an “n”, a “B” into an “x”, in short,
acted, as we might say, according to a scheme of arrows which
showed no simple regularity. Couldn't we call this “deriving”
too? — But suppose that
73)   he didn't stick to this way of transcribing. In fact he
changed it, but according to a simple rule: After having trans-
cribed “A” into “n”, he transcribed the next “A” into “o”, and
the next “A” into “p”, and so on. But where is the sharp line
between this procedure and that of producing a transcription
without any system at all? Now you might object to this by
saying, “In the case 71), you obviously assumed that he under-
stood the table differently; he didn't understand it in the
normal way”. But what do we call “understanding the table in

75.
a particular way?” But whatever process you imagine this
“understanding” to be, it is only another link interposed
between the outward and inward processes of deriving derivation I have des-
cribed and the actual transcription. In fact this process of
understanding could obviously be described by means of a schema
of the kind used in 71), and we could then say that in a part-
icular case he looked up the table like this: ; underst-
ood the table like this: ; and transcribed it like this:
. But does this mean that the word “deriving” (or
“understanding”) has really no meaning, as by following up its
meaning this seems to trail off into nothing? In case 70) the
meaning of “deriving” stood out quite clearly, but we told our-
selves that this was only one special case of deriving. It
seemed to us that the essence of the process of deriving was
here presented in a particular dress and that by stripping it
of this we should get at the essence. Now in 71), 72), 73) we
tried to strip our case of what had seemed but its peculiar
<…>costume only to find that what had seemed mere costumes were the
essential features of the case. (We acted as though we had
tried to find the real artichoke by stripping it of its leaves.)
The use of the word “deriving” is indeed exhibited in 70), i.e.,
this example showed us one of the family of cases in which this
word is used. And the explanation of the use of this word, as
that of the use of the word “reading” or “being guided by sym-
bols”, essentially consists in describing a selection of examples
exhibiting characteristic features, some examples showing these

76.
features in exaggeration, others showing transitions, exaggerated forˇm, others in transitional phases, certain
series of examples showing the trailing off of such features.
Imagine that someone wished to give you an idea of the facial
characteristics of a certain family, the So-and-so's, he would
do it by showing you a set of family portraits and by drawing
your attention to certain characteristic features, and his main
task would consist in the proper arrangement of these pictures,
which, e.g., would enable you to see how certain influences
gradually changed the features, in what characteristic ways the
members of the family aged, what features appeared more strongly
as they did so.

     

      It was not the function of our examples to show us the
essence of “deriving”, “reading”, and so forth through a veil of
inessential features; they the examples were not descriptions of an outside
letting us guess at an inside which for some reason or other
could not be shown in its nakedness. We are tempted to think
that our examples are indirect means for producing a certain
image or idea in a person's mind, — that they hint at something
which they cannot show. This would be so in some such case as
this: Suppose I wish to produce in someone a mental image of the
inside of a particular 18th century room which he is prevented
from entering. I therefore adopt this method: I show him the
house from the outside, pointing out the windows of the room in
question, I further lead him into other rooms of the same period.—

     

      Our method is purely descriptive; the descriptions we give
are not hints of explanations.

77.

     

        ((Interval. Vacation after Michaelmas Term.))

     

          Do we have a feeling of familiarity whenever we look at
familiar objects? Or do we have it usually?

     

          When do we actually have it?

     

          It helps us to ask: What do we contrast the feeling of
familiarity with?

     

          One thing we contrast it with is surprise.

     

          One could say: “Unfamiliarity is much more of an experience
than familiarity”.

     

          We say: A shows B a series of objects. B is to tell A
whether the object is familiar to him or not. a) The question
may be, “Does B know what the objects are?” or b) “Does he rec-
ognize the particular object?”
1).   Take the case that B is shown a series of apparatus, —
a balance, a thermometer, a spectroscope, etc.
2).   B is shown a pencil, a pen, an inkpot, and a pebble. Or:
3)   Besides familiar objects he is shown an object of which he
says, “That looks as though it served some purpose, but I don't
know what purpose”.

     

          What happens when B recognizes a pencil something as a pencil?

     

          Suppose A had shown him an object looking like a stick.
B handles this object, suddenly it comes apart, one of the
parts being a cap, the other a pencil. B says, “Oh, this is a
pencil”. He has recognized the object as a pencil.
4).   We could say, “B always knew what a pencil looked like;
he could e.g., have drawn one on being asked to. He didn't
know that the object he was given contained a pencil which he

78.
could have drawn any time”.

     

      Compare with this case 5).
5).   B is shewn a word written on a piece of paper held upside
down. He does not recogn[o|i]ze the word. The paper is gradually
turned round until B says, “Now I see what it is. It is ‘pen-
cil’”.

     

      We might say, “He always knew what the word ‘pencil’
looked like. He di[s|d] not know that the word he was shewn
would when turned round look like ‘pencil’”.

     

      In both cases 4) and 5) you might say something was hid-
den. But note the different application of “hidden”.
6).   Compare with this: You read a letter and can't read one
of its words. You guess what it must be from the context,
and now can read it. You recognize this scratch as an e, the
second as an a, the third as a t. This is different from the
case where the word “eat” was covered by a blotch of ink, and
you only guessed that the word “eat” must have been in this
place.
7).   Compare: You see a word and can't read it. Someone
alters it slightly by adding a dash, lengthening a stroke, or
suchlike. Now you can read it. Compare this alteration
with the turning in 5), and note that there<…> is a sense in
which while the word was turned round you saw that it was no[y|t]
altered. I.e., there is a case in which you say, “I looked
at the word while it was turned, and I know that it is the same
now as it was when I didn't recognize it”.
8).   Suppose the game between A and B just consisted in this,

79.
that B should say whether he knows the object or not but does
not say what it is. Suppose he was shewn an ordinary pencil,
after having been shewn a hygrometer which he had never seen
before. On being shewn the hygrometer he said that he was not
familiar with it, on being shewn the pencil, that he knew it.
What happened when he recognized it? Must he have told him-
self, though he didn't tell A, that what he saw was a pencil?
Why should we assume this?

     

      Then, when he recognized the pencil, what did he recognize
it as?
9).   Suppose even that he had said to himself, “Oh, this is a
pencil”, could you compare this case with 4) or 5)? In these
cases one might have said, “He recognized this as that” (point-
ing, e.g., for “this” to the covered up pencil and for “that”
to an ordinary pencil, and similarly in <…> 5)).

     

      In 8) the pencil underwent no change and the words, “Oh,
this is a pencil” did not refer to a paradigm, the similarity
of which with the pencil shewn B had recognized.

     

      Asked, “What is a pencil?”, B would not have pointed to
another object as the paradigm or sample, but could straight
away have pointed to the pencil shewn to him.

     

      “But when he said, ‘Oh, this is a pencil’, how did he know
that it was if he didn't recognize it as something?” — This
really comes to saying, “How did he recognize ‘pencil’ as the <…>
name of this sort of thing?” Well, how did he recognize it?
He just reacted in this particular way by saying this word.
10).   Suppose someone shews you colours and asks you to name

80.
them. Pointing to a certain object you say, “This is red”.
What would you answer if you were asked, “How do you know that
this is red?”?

     

      Of course there is the case in which a general explanation
was given to B, say, “We shall call ‘pencil’ anything that one
can easily write with on a wax tablet”. Then A shews B amongst
other objects a small pointed object, and B says, “Oh, this is
a pencil”, after having thought, “One could write with this
quite easily”. In this case, we may say, a derivation takes
place. In 8), 9), 10) there is no derivation. In 4) we
might say that B derived that the object shewn to him was a
pencil by means of a paradigm, or else no such derivation might
have taken place.

     

      Now <…> should we say that B on seeing the pencil after seeing
instruments which he didn't know had a feeling of familiarity?
Let us imagine what really might have happened. He saw a pen-
cil, smiled, felt relieved, and the name of the object which he
saw came into his mind or mouth.

     

      Now isn't the feeling of relief just that which character-
izes the experience of passing from unfamiliar to familiar
things?

     

      We say we experience tension and relaxation, relief, strain
and rest in cases as different as these: a man holds a weight
with outstretched arm; his arm, his whole body is in a state of
tension. We let him put down the weight, the tension relaxes.
A man runs, then rests. He thinks hard about the solution of
a problem in Euclid, then finds it, and relaxes. He tries to
remember a name, and relaxes on finding it.

81.

     

      What if we asked, <…> “What do all these cases have in com-
mon that makes us say that they are cases of strain and relax-
ation?”

     

      What makes us use the expression, “seeking in our memory”,
when we try to remember a word?

     

      Let us ask the question, “What is the similarity between
looking for a word in your memory and looking for my friend in
the park?” What would be the answer to such a question?

     

      One kind of answer certainly would consist in describing a
series of intermediate cases. One might say that the case
which looking in your memory for something is most similar to
is not that of looking for my friend in the park, but, say, that
of looking up the spelling of a word in the dictionary. And
one might go on interpolating cases. Another way of pointing
out the similarity would be to say, e.g., “In both these cases
at first we can't write down the word and then we can”. This
is what we call pointing out a common feature.

     

      Now it is important to note that we needn't be aware of
such similarities thus pointed out when we<…> are prompted to use
the words “seeking”, “looking for”, etc. in the case of trying
to remember.

     

      One might be inclined to say, “Surely a similarity must
strike us, or we shouldn't be { inclined driven moved to use the same word”. —
Compare this statement with that: “A similarity between these
cases must strike us in order that we should be inclined to use
the same picture to represent both”. This says that some act
must precede the act of using this picture. But why shouldn't

82.
what we call “the similarity striking us” consist partially or
wholly in our using the same picture? And why shouldn't it
consist partially or wholly in our being prompted to use the
same phrase?

     

      We say: “This picture (or this phrase) suggests itself to
us irresistibly”. Well, isn't this an experience?

     

      We are treating here of cases in which, as one might roughly
put it, the grammar of a word seems to suggest the “necessity”
of a certain intermediary step stage, although in fact the word is
used in cases in which there<…> is no such intermediary step.
Thus we are inclined to say, “A man must understand an order
before he obeys it”, “He must know where his pain is before he
can point to it”, “He must know the tune before he can sing it”,
& such like.)

     

      Let us ask the question: Suppose I had explained to someone
the word “red” (or the meaning of the word “red”) by having
pointed to various red objects and given the ostensive explan-
ation. — What does it mean to say, “Now if he has understood
the meaning, he will bring me a red object if I ask him to”?
This seems to say: If he has really got hold of what is in com-
mon between to all the objects I have shewn him, he will be in the
position to follow my order. But what is it that is in common
to these objects?

     

      Could you tell me what is in common between a light red and
a dark red? Compare with this the following case: I shew you
two pictures of two different landscapes. In both pictures,
amongst many other objects, there is the picture of a bush,
and it is exactly alike in both. I ask you, “Point to what

83.
these two pictures have in common”, and as answer you point to
this bush.

     

      Now consider this explanation: I give someone two boxes
containing various things, and say, “The object which both these
boxes have in common is called a toasting fork”. The person I
give this explanation to has to sort out the objects in the two
boxes until he finds the one they have in common, and thereby
we may say, he arrives at the ostensive explanation. Or, this
explanation: “In these two pictures you see patches of many
colours; the one colour which you find in both is called ‘mauve’”.
— In this case it makes a clear sense to say, “If he has seen
(or found) what is in common between these two pictures, he can
now bring me a mauve object.”

     

      There is this case game: I say to someone, “I shall explain to
you the word ‘w’ by shewing you various objects. What's in
common to them all is what ‘w’ means.” I first shew him two
books, and he ask[d|s] himself, “Does ‘w’ mean ‘book’?” I then
point to a brick, and he says to himself, “Perhaps ‘w’ means
‘parallelepiped’”. Finally I point to glowing coal, and he
says to himself, “Oh, it's ‘red’ he means, for all these objects
had something red about them.” It would be interesting to con-
sider another form of this game where the person has at each
stage to draw or paint what he thinks I mean. The interest of
this version lies in this, that in some cases it would be quite
obvious what he has got to draw, say, when he sees that all the
objects I have shewn him so far bear a certain trademark (; he'd
draw the trademark). — What, on the other hand, should he paint
if he recognizes that there is something red on each object?

84.
A red patch? And of what shape and shade? Here a convention
would have to be laid down, say, that of painting a red patch
with ragged edges does not mean that the objects have that red
patch with ragged e[g|d]ges in common, but something red.

     

      If, pointing to patches of various shades of red, you asked
a man, “What have these in common that makes you call them
red?”, he'd be inclined to answer, “Don't you see?” And this
of course would not be pointing out a common element.

     

      There are cases where experience teaches us that a person
is not able to carry out an order, say, of the form, “Bring me
x” if he did not see what was in common between the various
objects to which I pointed as an explanation of “x”. And
“seeing what they have in common” in some cases consisted in
pointing to it, in letting one's glance rest on a coloured patch
after a process of scrutiny and comparing, in saying to oneself,
“Oh, it's red he means,” and perhaps at the same time glancing
at all the red patches on the various objects, and so on. <…>
— There are cases, on the other hand, in which no process takes
place comparable with this intermediary “seeing what's in common”,
and where we still use this phrase, though this time we ought
to say, “If after shewing him these things he brings me another
red object, then I shall say that he has seen the common feature
of the objects I shewed him.” Carrying out the order is now
the criterion for his having understood.

     

      ((Having now made a start, Wittgenstein resumes formal
dictation.))

     

      “Why do you call ‘strain’ all these different experiences?” —
“Because they have some element in common.” — “What is it

85.
that bodily and mental strain have in common?” — “I don't know,
but obviously there is some similarity.”

     

      Then why did you say the experiences had something in com-
mon? Didn't this expression just compare the present case
with those cases in which we primarily say that two experiences
have something in common? (Thus we might say that some exper-
iences of joy and of fear have the feleling of heart beat in
common.) But when you said that the two experiences of strain
had something in common, these were only different words for
saying that they were similar: It was then no explanation to
say that the similarity consisted in the occurrence of a common
element.

     

      Also, shall we say that you had a feeling of similarity
when you compared the two experiences, and that this made you
use the same word for both? If you say you have a feeling of
similarity, let us ask a few questions about it:
     Could you say the feeling was located here or there?

     

      When did you actually have this feeling? For, what we
call comparing the two experiences is quite a complicated act-
ivity: perhaps you called the two experiences before your mind,
and imagining a bodily strain, and imagining a mental strain,
was each in itself imagining a process and not a state [i|u]niform
through time. Then ask yourself at what time during all this
you had the feeling of similarity.

     

      “But surely I wouldn't say they are similar if I had no
experience of their similarity.” — But must this experience
be anything you should call a feeling? Suppose for a moment

86.
it were the experience that the word “similar” suggested itself
to you. Would you call this a feeling?

     

      “But is there no feeling of similarity?” — I think there
are feelings which one might call feelings of similarity. But
you don't always have any such feeling if you “notice similar-
ity”. Consider some of the different experiences which you
have if you do so.

     

      a)  There is a kind of experience which one might call being
hardly able to distinguish. You see, e.g., two lengths, two
colours, almost exactly alike. But if I ask myself, “Does this
experience consist in having a peculiar feeling?”, I should
have to say that it certainly isn't characterized by any such
feeling alone, that a most important part of the experience is
that of letting my glance oscillate between the two objects,
fixing it intently, now on the one, now on the other, perhaps
saying words expressive of doubt, shaking my head, etc. etc.
There is, one might say, hardly any room left for a feeling of
similarity between these manifold experiences.

     

      b)  Compare with this the case in which it is impossible
to have any difficulty of distinguishing the two objects.
Supposing I say, “I like to have the two kinds of flowers in
this bed of similar colours to avoid a strong contrast.” The
experience here<…> might be one which one may describe as an easy
sliding of the glance from one to the other.

     

      c)   I listen to a variation on a theme and say, “I don't
see yet how this is a variation of the theme, but I see a cert-
ain similarity.” What happened was that at certain points of

87.
the variation, at certain turning points of the key, I had an
experience of “knowing where I was in the theme”. And this
experiences might again have consisted in imagining certain
figures of the theme, or in seeing them written before my mind
or in actually pointing to them in the score, etc.

     

      “But when two colours are similar, the experience of sim-
ilarity should surely consist in noticing the similarity which
there is between them.” — But is a bluish green similar to a
yellowish green or not? In certain cases we should say they
are similar and in others that they are most dissimilar.
Would it be correct to say that in the two cases we noticed
different relations between them? Suppose I observed a proc-
ess in which a bluish green gradually changed into a pure green,
into a yellowish green, into yellow, and into orange. I say,
“It only takes a short time from bluish green to yellowish green,
because these colours are similar.” — But mustn't you have had
some experience of similarity to be able to say this? — The
experience may be this, of seeing the two colours and saying
that they are both green. Or it may be this, of seeing a band
whose colour changes from one end to the other in the way des-
cribed, and having some one of the experiences which one may
call noticing how close to each other bluish green and yellowish
green are, compared to bluish green and orange.

     

      We use the word “similar” in a huge [g|f]amily of cases.

     

      There is something remarkable about saying that we use the
word “strain” for both mental and physical strain because there
is a similarity between them. Should you say we use the word
“blue” both for light blue and dark blue because there is a sim-

88.
ilarity between them? If you were asked, “Why do you call this
‘blue’ also?”, you would say, “Because this is blue, too”.

     

      One might suggest that the explanation is that in this
case you call “blue” what is in common between the two colours,
and that, if you called “strain” what was in common between the
two experiences of strain, it would have been wrong to say, “I
called them both ‘strain’ because they had a certain similarity”,
but that you would have had to say, “I used the word ‘strain’
in both cases because there is a strain present in both.”

     

      Now what should we answer to the question, “What do light
blue and dark blue have in common?”? At first sight the ans-
wer seems obvious: “They are both shades of blue.” But this
is really a tautology. So let us ask, “What do these colours
I am pointing to have in common?” (Suppose one is light blue,
the other dark blue.) The answer to this really ought to be,
“I don't know what game you are playing.” And it depends upon
this game whether I should say they had anything in common, and
what I should say they had in common.

     

      Imagine this game: A shews B different patches of colours
and asks him what they have in common. B is to answer by
pointing to a particular primary pure colour. Thus if A points to
pink and orange, B is to point to pure red. If A points to
two shades of greenish blue, B is to point to pure green and
pure blue, etc. If in this game A shewed B a light blue and
a dark blue and asked what they had in common, there would be
no doubt about the answer. If then he pointed to pure red and
pure green, the answer would be that these have nothing in com-
mon. But I could easily imagine circumstances under which

89.
we should say that they had something in common and would not
not hesitate to say what it was: Imagine a use of language (a
culture) in which there was a common name for green and red on
the one hand, and yellow and blue on the other. Suppose, e.g.,
that there were two castes, one the patrician caste, wearing red
and green garments, the other, the plebeian, wearing blue and
yellow garments. Both yellow and blue would always be referred
to as plebeian colours, green and red as patrician colours.
Asked what a red patch and a green patch have in common, a man
of our tribe would not hesitate to say they were both patrician.

     

      We could also easily imagine a language (and that means
again a culture) in which there existed no common expressions
for light blue and dark blue, in which the former, say, was
called “Cambridge”, the latter “Oxford”. If you ask a man of
this tribe what Cambridge and Oxford have in common, he'd be
inclined to say, “Nothing”.

     

      Compare this game with    ). B is shewn certain pictures,
combinations of coloured patches. On being asked what these
pictures have in common, he is to point to a sample of red, say,
if there is a red patch in both, to green if there is a green
patch in both, etc. This shews you in what different ways this
same answer may be used.

     

      Consider such a proposition an explanation as, “I mean by ‘blue’ what
these two colours have in common.” — Now isn't it possible that
someone should understand this explanation? He would, e.g.,
on being ordered to bring another blue object, carry out this
order satisfactorily. But perhaps he will bring a red object
and we shall be inclined to say: “He seems to notice some sort

90.
of similarity between samples we shewed him and that red thing.

     

      Note: Some people when asked to sing a note which we strik
for them on the piano, regularly sing the fifth of that note.
That makes it easy to imagine that a language might have one
name only for a certain note and its fifth. On the other hand
we should be embarrassed to answer the question: What do a
note and its fifth have in common? For of course it is no
answer to say: “They have a certain affinity.”

     

      It is one of our tasks here to give a picture of the gram-
mar (the use) of the word “a certain.”

     

      To say that we use the word “blue” to mean “what all these
shades of colour have in common” by itself says nothing more
than that we uses the word “blue” in all these cases.

     

      And the phrase, “He sees what all these shades have in
common,” may refer to all sorts of different phenomena, i.e.,
all sorts of phenomena are used as criteria for “his seeing
that…” Or all that happens may be that on being asked to
bring another shade of blue he carries out our order satisfact-
orily. Or a patch of pure blue may appear before his mind's
eye when we shew him the different samples of blue: or he may
instinctively turn his head towards some other shade of blue
which we haven't shewn him for sample, etc. etc.

     

      Now should we say that a mental strain and a bodily strain
were “strains” in the same sense of the word or in different
(or “slightly different”) senses of the word? — There are cases
of this sort in which we should not be doubtful about the ans-
wer.

     

      Consider this case: We have taught someone the use of the

91.
words “darker” and “lighter”. He could, e.g., carry out such
an order as, “Paint me a patch of colour darker than the one I
am shewing you.” Suppose now I said to him: “Listen to the
five vowels a, e, i, o, u and arrange them in order of their
darkness.” He may just look puzzled and do nothing, but he
may (and some people will) now arrange the vowels in a certain
order (mostly i, e, a, o, u,). Now one might imagine that arr-
anging the vowels in order of darkness presupposed that when a
vowel was sounded a certain colour came before a man's mind,
that he then arranged these colours in their order of darkness
and told you the corresponding arrangement of the vowels. But
this actually need not happen. A person will comply to the
order: “Arrange the vowels in their order of darkness”, without
seeing any colours before his mind's eye.

     

      Now if such a person was asked whether u was “really”
darker than e, he would almost certainly answer some such thing
as, “It isn't really darker, but it somehow gives me a darker
impression.”

     

      But what if we asked him, “What made you use the word
‘darker’ ˇin this case at all?”?

     

      Again we might be inclined to say, “He must have seen some-
thing that was in common both to the relation between two col-
ours and to the relation between two vowels.” But if he isn't
capa<…>ble of specifying what this common element was, this leaves
us just with the fact that he was prompted to use the words
“darker”, “lighter” [o|i]n both these cases.

     

      For, note the word “must” in “He m[i|u]st have seen something
…” When you said that, you didn't mean that from past

92.
experience you conclude that he probably did see something,
and that's just why this sentence adds nothing to what we know
and in fact only suggests a different form of words to describe
it.

     

      If someone said: “I do see a certain similarity, only I
can't describe it”, I should say: “This itself “Saying this also characterizes
your experience.”

     

      Suppose you look at two faces and say, “They are similar,
but I don't know what it is that's similar about them.” And
suppose that after a while you said: “Now I know; their eyes
have the same shape”, I should say, “Now your experience of thei
similarity is different from what it was when you saw similar-
ity and didn't know what it consisted in.” Now to the question
“What made you use the word ‘darker’…?” the answer may be,
“Nothing made me use the word ‘darker’, — that is, if you ask
me for a reason why I use it. I just used it, and what is more
I used it with the same intonation of voice, and perhaps with
the same facial expression and gesture which I should in cert-
ain cases be inclined to use when applying the word to colours.”
— It is easier to see this when we speak of ˇa deep sorrow, a deep sound, a
deep well. Some people are able to distinguish between fat
and lean days of the week. And their experience when they con-
ceive a day as a fat one consists in applying this word together
perhaps with a gesture expressive of fatness and a certain
comfort.

     

      But you may be tempted to say: This use of the word and
gesture is not their primary experience. First of all they

93.
have to conceive the day as fat and then they express this con-
ception by word and or gesture.

     

      But why do you use the expression, “They have to”? Do
you know of an experience in this case which you call “the con-
ception, etc.”? For if you don't, isn't it just what one might
call a linguistic prejudice that made you say, “He had to have
a conception before, etc.”?

     

      Rather, you can learn from this example and from others
that there are cases in which we may call a particular exper-
ience “noticing, seeing, conceiving that so & so is the case”,
before expressing it by word or gestures, and that there are
other cases in which if we talk of an experience of conceiving
at all, we have to apply this word to the experience of using
certain words, gestures, etc.

     

      When the man said, “u isn't really darker than e…”, it
was essential that he meant to say that the word “darker” was
used in different senses when one talked of one colour being
darker that another and, on the other hand, or one vowel being
darker than another.

     

      Consider this example: Suppose we had taught a man to use
the words “green”, “red”, “blue” by pointing to patches of these
colours. We had taught him to fetch us objects of a certain
colour on being ordered, “Bring me something red!”, to sort out
objects of various colours from a heap, and such like. Sup-
pose we now shew him a heap of leaves, some of which are a slight-
ly reddish brown, [i|o]thers a slightly greenish yellow, and give
him the order, “Put the red leaves and the green leaves on sep-
arate heaps.” It is quite likely that he will upon this

94.
separate the greenish yellow leaves from the reddish brown ones.
Now should we say that we had here used the words “red” and
“green” in the same sense as in the previous cases, or did we
use them in different but similar senses? What reasons would
one give for adopting the latter view? One could point out
that on being asked to paint a red patch, one should certainly
not have painted a slightly reddish brown one, and therefore
one might say “red” means something different in the two cases.
But why shouldn't I say that it had one meaning only but was,
of course, used according to the circumstances?

     

      The question is: Do we supplement our statement that the
word has two meanings by statement saying that in one case it
had this, in the other that meaning? As the criterion for a
word's having two meanings, we may use the fact of there being
two explanations given for a word. Thus we say the word “bank”
has two meanings; for in one case it means this sort of thing,
(pointing, say, to a river bank) in the other case that sort of thing, (pointing to the Bank of England). Now what I point to here
are paradigms for the use of the words. One could not say:
“The word ‘red’ has two meanings because in one case it means
this (pointing to a light red), in the other that (pointing to
a dark red)”, if, that is to say, there had been only one osten-
sive definition for the word “red” used in our game. One could,
on the other hand, imagine a language-game in which two words,
say “red” and “reddish”, were explained by two ostensive defin-
itions, the first shewing a dark red object, the second a light
red one. Whether two such definitions explanations were given or only one
might depend on the natural reactions of the people using the

95.
language. We might find that a person to whom we give the
ostensive definition, “This is called ‘red’” (pointing to one
red object) thereupon fetches any red object of whatever shade
of red on being ordered: “Bring me something red!” Another
person might not do so, but bring objects of a certain range of
shades only in the neighborhood of the shade pointed out to him
in the explanation. We might say that this person “does not
see what is in common between all the different shades of red”.
But remember please that our only criterion for that is the
behaviour we have described.

     

      Consider the following case: B has been taught a use of the
words “lighter” and “darker”. He has been shewn object of
various colours and has been taught that one calls this a darker
colour than that, trained to bring an object on being ordered,
“Bring something darker than this”, and to describe the colour
of an object by saying that it is darker or lighter than a cert-
ain sample, etc., etc. Now he is given the order to put down
a series of objects, arranging them in the order of their dark-
ness. He does this by laying out a row of books, writing down
a series of names of animals, and by writing down the five vow-
els in the order u, o, a, e, i. We ask him why he put down
that latter series, and he says, “Well o is lighter than u, and
e lighter than o.” — We shall be ast[i|o]nished at his attitude,
and at the same time admit that there is something in what he
says. Perhaps we shall say: “But look, surely e isn't lighter
than o in the way this book is lighter than that.” — But he
may shrug his shoulders and say, “I don't know, but e is lighter
than o, isn't it?”

96.

     

      We may be inclined to treat this case as some kind of
abnormality, and to say, “B must have a different sense, with
the help of which he arranges both coloured objects and vowels.”
And if we <…> tried to make this idea of ours (quite) explicit,
it would come to this: The normal person registers lightness and
darkness of visual objects on one instrument, and, what one
might call the lightness and darkness of sounds (vowels) on
another, in the sense in which one might say that we record
rays of a certain wave length with the eyes, and rays of another
range of wave length by with our sense of temperature. B on the other
hand, we wish to say, arranges both sounds and colours by the
readings of one instrument (sense organ) only (in the sense in
which a photographic plate might record rays of a range which
we could only cover with two of our senses).

     

      This roughly is the picture standing behind our idea that
B must have “understood” the word “darker” differently from the
normal person. On the other hand let us put side by side with
this picture the fact that there is in our case no evidence for
<…>“another sense”. — And in fact the use of the word “must”
when we say, “B must have understood the word differently”,
already shews us that this sentence (really) expresses our
determination to look at the phenomena we have observed after
the picture outlined in this sentence.

     

      “But surely he used ‘lighter’ in a different sense when he
said e was lighter than u”. — What does this mean? Are you
distinguishing between the sense in which he used the word and
his usage of the word? That is, do you wish to say that if
someone uses the word as he does, some other difference, say in

97.
his mind, must go along with the difference in usage? Or is
all you want to say that surely the usage of “lighter” was a
different one when he applied it to vowels?

     

      Now is the fact that the usages differ anything over and
above what you describe when you point out the particular dif-
ferences?

     

      What if somebody said, pointing to two patches which I had
called red, “Surely [t|y]ou are using the word ‘red’ in two differ-
ent ways.” — I should say, “This is light<…> red and the other
dark red,” — but why should I have to talk of two different
usages?ˇ”—

     

      It certainly is easy to point out differences between that
part of the game in which we applied “lighter” and “darker” to
coloured objects and that part in which we applied these words
to vowels. In the first part there was comparison of two
objects by laying them side by side and looking from one to the
other, there was painting a darker or lighter shade than a
certain sample given; in the second there was no comparison by
the eye, no painting, etc. But when these differences are
pointed out, we are still free to speak of two parts of the same
game (as we have done just now) or of two different games.

     

      “But don't I perceive that the relation between a lighter
and a darker bit of material is a different one than tha[n|t]
between the vowels e and u, — as on the other hand I perceive
that the relation between u and e is the same as that between
e and i?” — Under certain circumstances we shall in these cases
be inclined to talk of different relations, under certain others
to talk of the same relation. One might say, “It depends how

98.
one compares them.”

     

      Let us ask the question, “Should we say that the arrows
and point in the same direction or in different
directions?” — At first sight you might be inclined to say,
“Of course, in different directions.” But look at it this
way: If I look into a looking glass and see the reflection of
my face, I can take this as a criterion for seeing my own head.
If on the other hand, I saw in it the back of a head I might
say, “It can't be my own head I am seeing, but a head looking in
the opposite direction.” Now this could lead me on to say
that an arrow and the reflection of an arrow in a glass have the
same direction when they point at towards each other, and opposite dir-
ections when the head of the one points to the tail end of the
other. Imagine the case that a man had been taught the ordin-
ary use of the word “the same” in the cases of “the same colour”,
& “the same shape”, “the same length.” He had also been taught
the use of the word “to point to” in such contexts as, “The
arrow points to the tree.” Now we shew him two arrows facing
each other, and two arrows one following the other, and ask
him in which of these two cases he'd apply the phrase, “The
arrows point the same way.” Isn't it easy to imagine that if
certain applications were uppermost in his mind, he would be
inclined to say that the arrows point “the same way”?

     

      When we hear the diatonic scale we are inclined to say that
after every seven notes the same note recurs, and, asked why we
call it the same note again one might answer, “Well it's a c
again.” But this isn't the explanation I want, for I should
ask, “What made one call it a c again?” And the answer to this

99.
would seem to be, “Well, don't you hear that it's the same tone
only an octave higher?” — Here too we could imagine that a
man had been taught our use of the word “the same” when applied
to colours, lengths, directions, etc., and that we now played
the diatonic scale for him and asked him whether he'd say that
he heard the same notes again and again at certain intervals,
and we could easily imagine several answers, in particular for
instance, this, that he heard the same note alternately after
every four or three notes (he calls the tonic, the dominant,
and the octave the same tone).

     

      If we had made this experiment with two people A and B,
and A had applied the expression “the same tone” to the octave
only, B to the dominant and octave, should we have a right to
say that the two hear different things when we play to them the
diatonic scale? — If we say they do, let us be clear whether
we wish to assert that there must be some other difference be-
tween the two cases besides the one we have observed, or whether
we wish to make no such statement.

     

      All the questions considered here link up with this prob-
lem: Suppose you had taught someone to write down series of num-
bers according to rules of the form: Always write down a number
n greater than the preceding. (This rule is abbreviated to
“Add n”). The numerals in this game are to be groups of dashes
-, --, ---, etc. What I call teaching this game of course
consisted in giving general explanations and doing examples. —
These examples are taken from the range, say, between 1 and 85.
We now give the pupil the order, “Add 1”. After some time we
observe that after passing 100 he did what we should call

100.
adding 2; after passing 300 he does what we should call adding
3. We have him up for this: “Didn't I tell you always to add
<…> 1? Look what you have done before you got to 100!” —
Suppose the pupil said, pointing to the numbers 102, 104, etc.
“Well, didn't I do the same here? I thought this was what you
wanted me to do”. — You see that it would get us no further
here again to say, “But don't you see…?”, pointing out to
him again the rules and examples we had given to him. We might
in such a case, say that this person naturally understands
(interprets) the rule (and examples) we have given as we should
understand the rule (and examples) telling us: “Add 1 up to
100, then 2 up to 200, etc.”

     

      (This would be similar to the case of a man who did not
naturally follow an order given by a pointing gesture by mov-
ing in the direction shoulder to hand, but in the opposite
direction. And understanding here means the same as reacting.)

     

      “I suppose what you say comes to this, that in order to
follow the rule “Add 1” correctly a new insight, intuition,
is needed at every step.” — But what does it mean to follow the
rule correctly? How and when is it to be decided which at a
particular point is that which is in accordance with the
rule as it was meant, intended.” //… with the meaning, intention,
of the rule.”// — I suppose the idea is this: When you gave the
rule, “Add 1”, and meant it, you meant him to write 101 after
100, 199 after 198, 1041 after 1040, and so on. But how did
you do all these acts of meaning (I suppose an infinite number
of them) when you gave him the rule? Or is this misrepresenting

101.
it? And would you say that there was only one act of meaning,
from which, however, all these others, or any one of them,
followed in turn? But isn't the point just: “what does follow
from the general rule?” You might say, “Surely I knew when I
gave him the rule that I meant him to follow up 100 by 101.”
But here you are misled by the grammar of the word “to know”.
Was knowing this some mental act by which you at the time made
the transition from 100 to 101, e.g., some act like saying to
yourself: “I want him to write 101 after 100”? In this case
ask yourself how many such acts you performed when you gave him
the rule. Or do you mean by knowing some kind of disposition,
— then only experience can teach us what it was a disposition
for. — “But surely if one had asked me which number he should
write after 1568, I should have answered ‘1569’.” — I dare- you would, but how can you be sure of it? Your idea really
is that somehow in the mysterious act of meaning the rule you
made the transitions without really making them. You crossed
all the bridges before you were there. — This queer idea is
connected with a peculiar use of the word “to mean”. Suppose
our man got the number 100 and followed it up by 102. We
should then say, “I meant you to write 101.” Now the past
tense in the word “to mean” suggests that a particular act of
meaning had been performed when the rule was given, though as a
matter of fact this expression alludes to no such act. The
past tense could be explained by putting the sentence into the
form, “Had you asked me before what I wanted you to do at this
stage, I should have said…” But it is a hypothesis that you
would have said that.

     

102.

      To get this clearer, think of this example: Someone says,
“Napoleon was crowned in 1804.” I ask him, “Did you mean the
man who won the battle of Austerlitz?” He says, “Yes, I meant
him.” — Does this mean that when he “meant him” he in some way
thought of Napoleon's winning the battle of Austerlitz? —

     

      The expression, “The rule meant him to follow up 100 by
101,” makes it appear that this rule, as it was meant, foreshad-
owed all the transitions which were to be made according to it.
But the assumption of a shadow of a transition does not get us
any further, because it does not bridge the gulf between it and
the transition itself. real transition. If the mere words of the rule could not
anticipate a future transition, no more could any mental act
accompanying these words.

     

      We meet again and again with this curious superstition, as
one might be inclined to call it, that the mental act is capable
of crossing a bridge before we've got to it. This trouble
crops up whenever we try to think about the ideas of thinking,
wishing, expecting, believing, knowing, trying to solve a math-
ematical problem, mathematical induction, and so forth.

     

      It is no act of insight, intuition, which makes us use the
rule as we do at the particular stage // point of the series //.
It would be less confusing to call it an act of decision, though
this too is misleading, for nothing like an act of descision
must take place, but possibly just an act of writing or speaking.
And the mistake which we here and in a thousand similar cases are
inclined to make is labelled by the word “to make” as we have
used it in the sentence, “It is no act of insight which makes
us use the rule as we do,” because there is an idea that

103.
“something must make us” do what we do. And this again joins
on to the confusion between cause and reason. We need have no
reason [f|t]o follow the rule as we do. The chain of reasons has
an end.

     

      Now compare these sentences: “Surely it is using the rule
‘Add 1’ in a different way if after 100 you go on to 102, 104,
etc.” and “Surely it is using the word ‘darker’ in a new different way
if after applying it to coloured patches we apply it to the
vowels.” — I should say: “That depends on what you call a
‘different way’”. —

     

      But I should certainly say that I would should call the applicat-
ion of “lighter” and “darker” to vowels “another usage of the
words”; and I also should carry on the series „ “Add 1” in the
way 101, 102, etc., but not — or not necessarily — because of
some other justifying mental act.

     

      There is a kind of general disease of thinking which
always looks for (and finds) a mental state // what would be
called a mental state // from which all our act spring as from
a reservoir. Thus one says, “The fashion changes because the
taste of people changes.” The taste is the mental reservoir.
But if a tailor today designs a cut of dress different from that
which he designed a year ago, can't what is called his change
of taste have consisted, partly or wholly, in doing just this?

     

      And here we say, “But surely designing a new shape isn't
in itself changing one's taste, — and saying a word isn't
meaning it, — and saying that I believe isn't believing; there
must be feelings, mental acts, going along with these lines
and these words.” — And the reason we give for saying this is

104.
that a man certainly could design a new shape without having
changed his taste, say that he believes something without be-
lieving it, etc. And this obviously is true. But it doesn't
follow that what distinguishes a case of having changed one's
taste from a case of not having done so isn't under certain
circumstances just designing what one hasn't designed before.
Nor does it follow that in cases in which designing a new shape
is not the criterion for a change of taste, the criterion must
be a change in some particular region of our mind.

     

      That is to say, we don't use the word “taste” as the name
of a feeling. To think that we do is to imagine represent the structure practice
of our language in undue simplification. This, of course, is
the way in which philosophical puzzles generally arise; and our
case is quite analogous to that of thinking that wherever we
make a predicative statement we state that the subject has a
certain ingredient (as we really do in the case, “Beer is alc-
oholic.”)

     

      It is advantageous in treating our problems to consider
parallel with the feeling or feelings characteristic for having
a certain taste, changing one's taste, meaning what one says,
etc. etc. the facial expression (gestures or tone of voice)
characteristic for the same states or events. If someone should
object, saying that feelings and facial expressions can't be
compared, as the former are experiences and the latter aren't,
let him consider the muscular, kinaesthetic and tactile exper-
iences bound up with gestures and facial expressions.

     

      Let us then consider the proposition, “Believing something
can not merely consist in saying that you believe it, you must

105.
say it with a particular facial expression, gesture, and tone
of voice.” Now it cannot be doubted that we regard certain
facial expressions, gestures, etc. as characteristic for the
expression of belief. We speak of a “tone of conviction”.
And yet it is clear that this tone of conviction isn't always
present whenever we rightly speak of conviction // wherever we
should say there was conviction //. “Just so”, you might say,
“this shews that there is something else, something behind these
gestures, etc. which is the real belief as opposed to mere ex-
pressions of belief.” — “Not at all”, I should say, “many dif-
ferent criteria distinguish, under different circumstances,
cases of believing what you say from those of not believing what
you say.” There may be cases where the presence of a sensation
other than those bound up with gestures, tone of voice, etc.
distinguishes meaning what you say from not meaning it. But
sometimes what distinguishes these two is nothing that happens
while we speak, but a variety of actions and experiences of dif-
ferent kinds before and after.

     

      To understand this family of cases it will again be help-
ful to consider an analogous case drawn from facial expressions.
There is a family of friendly facial expressions. Suppose we
had asked, “What feature is it that characterizes a friendly
face?” At first one might think that there are certain friend-
ly traits which one might call friendly traits, each of which
makes the face look friendly to a certain degree, and which when
present in a large number constitute the friendly expression.
This idea would seem to be borne out by our common speech, talk-

106.
ing of “friendly eyes”, “friendly mouth”, etc. But it is easy
to see that the same eyes of which we say they make a face look
friendly, do not look friendly, or even ˇlook unfriendly, with certain
other wrinkles of the forehead, lines round the mouth, etc.
Why then do we ever say that it is these eyes which look friend-
ly? Isn't it wrong to say that they characterize the face as
friendly, for if we say they do so “under certain circumstances”
(these circumstances being the other features of the face) why
did we single out the one feature from amongst the others?
The answer is that in the wide family of friendly faces there
is what one might call a main branch characterized by a certain
kind of eyes, another by a certain kind of mouth, etc.; although
in the large family of unfriendly faces we meet these same eyes
when they don't mitigate the unfriendliness of the expression.
— There is further the fact that when we notice the friendly
expression of a face, our attention, our gaze, is drawn to a
particular feature in the face, the “friendly eyes” or the
“friendly mouth”, etc., and that it does not rest on other feat-
ures although these too are responsible for the friendly expres-
sion.

     

      “But is there no difference between saying something and
meaning it, and saying it without meaning it?” — There needn't
be a difference while he says it, and if there is, this differ-
ence may be of all sorts of different kinds according to the
surrounding circumstances. It does not follow from the fact
that there is what we call a friendly and an unfriendly expres-
sion of the eye that there must be a difference between the eye

107.
of a friendly and the eye of an unfriendly face.

     

      One might be tempted to say, “This trait can't be said to
make the face look friendly, as it may be belied by another
trait.” And this is like saying, “Saying something with the
tone of conviction can't be the characteristic of conviction,
as it may be belied by experiences going along with it.” But
neither of these sentences is correct. It is true that other
traits in this face could take away the friendly character of
this eye, and yet in this face it is the eye which is the out-
standing friendly feature.

     

      It is such phrases as, “He said it and meant it”, which
are most liable to mislead us. — Compare meaning “I shall be
delighted to see you” with meaning “The train leaves at 3.30”.
Suppose you had said the first sentence to someone and were
asked afterwards, “Did you mean it?”, you would then probably
think of the feelings, the experiences, which you had while you
said it. And accordingly you would in this case be inclined
to say, “Didn't you see that I meant it?” Suppose that on the
other hand, after having given someone the information, “The
train leaves at 3.30”, he asked you, “Did you mean it?”, you
might be inclined to answer, “Certainly. Why shouldn't I have
meant it?”

     

      In the first case we shall be inclined to speak of a feel-
ing characteristic of meaning what we said, but not in the
second. Compare also lying in both these cases. In the first
case we should be inclined to say that lying consisted in say-
ing what we did but without the appropriate feelings or even
with the opposite feelings. If we lied in giving the inform-

108.
ation about the train, we would be likely to have different
experiences while we gave it than those which we have in giving
truthful information, but the difference here would not consist
in the absence of a characteristic feeling, but perhaps just in
the presence of a feeling of discomfort.

     

      It is even possible while lying to have quite a strong
experience of what might be called the characteristic for meaning
what one says, — and yet under certain circumstamces, and per-
haps under the ordinary circumstances ones, one refers to just this
experience in saying, “I meant what I said”, because the cases
in which something might give the lie to these experiences do
not come into the question. In many cases therefore we are
inclined to say, “Meaning what I say” means having such-and-
such experiences while I say it.

     

      If by “believing” we mean an activity, a process, taking
place while we say that we believe, we may say that believing is
something similar to or the same as expressing a belief.

     

      It is interesting to consider an objection to this: What
if I said, “I believe it will rain” (meaning what I say) and
someone wanted to explain to a Frenchman who doesn't understand
English what it was I believed. Then, you might say, if all
that happened when I believed what I did was that I said the
sentence, the Frenchman ought ought to know what I believe if you tell
him the exact words I used, or say, “Il croit ‘It will rain’”.
Now it is clear that this will not tell him what I believe and
consequently, you might say, we failed to convey just that to
him which was essential, my real mental act of believing. —
But the answer is that even if my words had been accompanied by

109.
all sorts of experiences, and if we could have transmitted
these experiences to the Frenchman, he would still not have
known what I believed. For “knowing what I believe” just
doesn't mean: feel what I do just while I say it; just as know-
ing what I intend with this move in our game of chess doesn't
mean knowing my exact state of mind while I'm making the move.
Though, at the same time, in certain cases, knowing this state
of mind might furnish you with very exact information about my
intention.

     

      We should say that we had told the Frenchman what I believ-
ed if we translated my words for him into French. And it
might be that thereby we told him nothing — even indirectly —
about what happened “in me” when I uttered my belief. Rather,
we pointed out to him a sentence which in his language holds a
similar position to my sentence in the English language. —
Again one might say that, at least in certain cases, we could
have told him much more exactly what I believed if he had been
at home in the English language, because then, he would have
known exactly what happened within me when I spoke.

     

      We use the words “meaning”, “believing”, “intending” in
such a way that they refer to certain acts, states of mind given
certain circumstances; as by the expression “checkmating some-
body” we refer to the act of taking his king. If on the other
hand someone, say a child, playing about with chessmen, placed
a few of them on a chess board and went through the motions of
taking a king, we should not say the child had checkmated any-
one.— And here too one might think that what distinguished this

110.
case from real checkmating was what happened in the child's
mind.