148* PHILOSOPHICAL INVESTIGATIONS I
that we mean different things by "one", that "one" has different
meanings?—Not at all.—Say e.g. such a sentence as "One yard is
occupied by one soldier, and so two yards are occupied by two
soldiers." Asked "Do you mean the same thing by both 'ones'?"
one would perhaps answer: "Of course I mean the same thing: one 1"
(Perhaps raising one ringer.)
553. Now has "i" a different meaning when it stands for a measure
and when it stands for a number? If the question is framed in this
way, one will answer in the affirmative.
\
5 5 4. We can easily imagine human beings with a 'more primitive'
logic, in which something corresponding to our negation is applied
only to certain sorts of sentence; perhaps to such as do not themselves
contain any negation. It would be possible to negate the proposition
"He is going into the house", but a negation of the negative proposi-
tion would be meaningless, or would count only as a repetition of the
negation. Think of means of expressing negation different from ours:
by the pitch of one's voice, for instance. What would a double negation
be like there?
555. The question whether negation had the same meaning to these
people as to us would be analogous to the question whether the figure
"5" meant the same to people whose numbers ended at 5 as to us.
556. Imagine a language with two different words for negation,
"X" and "Y". Doubling "X" yields an affirmative, doubling "Y"
a strengthened negative. For the rest the two words are used alike.—
Now have "X" and "Y" the same meaning in sentences where they
occur without being repeated?—We could give various answers to
this.
(a) The two words have different uses. So they have different
meanings. But sentences in which they occur without being repeated
and which for the rest are the same make the same sense.
(b) The two words have the same function in language-games,
except for this one difference, which is just a trivial convention. The
use of the two words is taught in the same way, by means of the same
actions, gestures, pictures and so on; and in explanations of the words
the difference in the ways they are used is appended as something
incidental, as one of the capricious features of the language. For this
reason we shall say that "X" and "Y" have the same meaning.
(c) We connect different images with the two negatives. "X" as it
PHILOSOPHICAL INVESTIGATIONS I i49e
were turns the sense through 180°. And that is why two such negatives
restore the sense to its former position. "Y" is like a shake of the
head. And just as one does not annul a shake of the head by shaking
it again, so also one doesn't cancel one "Y" by a second one. And so
even if, practically speaking, sentences with the two signs of negation
come to the same thing, still "X" and "Y" express different ideas.
5 5 7. Now, when I uttered the double negation, what constituted my
meaning it as a strengthened negative and not as an affirmative?
There is no answer running: "It consisted in the fact that ....."
In certain circumstances instead of saying "This duplication is meant
as a strengthening," I can pronounce it as a strengthening. Instead of
saying "The duplication of the negative is meant to cancel it" I can
e.g. put brackets.—"Yes, but after all these brackets may themselves
have various roles; for who says that they are to be taken as brackets'?"
No one does. And haven't you explained your own conception in
turn by means of words? The meaning of the brackets lies in the
technique of applying them. The question is: under what circumstances
does it make sense to say "I meant . . . .", and what circumstances
justify me in saying "He meant . . . ."?
558. What does it mean to say that the "is" in "The rose is red"
has a different meaning from the "is" in "twice two is four"? If it is
answered that it means that different rules are valid for these two
words, we can say that we have only one word here.—And if all I am
attending to is grammatical rules, these do allow the use of the word
"is" in both connexions.—But the rule which shews that the word
"is" has different meanings in these sentences is the one allowing us
to replace the word "is" in the second sentence by the sign of equality,
and forbidding this substitution in the first sentence.
559. One would like to speak of the function of a word in this
sentence. As if the sentence wrere a mechanism in which the word
had a particular function. But what does this function consist in?
How does it come to light? For there isn't anything hidden—don't
we see the whole sentence? The function must come out in operat-
ing with the word. ((Meaning-body.))
560. "The meaning of a word is what is explained by the explana-
tion of the meaning." I.e.: if you want to understand the use of the
word "meaning", look for what are called "explanations of meaning".

2OO* PHILOSOPHICAL INVESTIGATIONS Hxi
The concept of 'seeing' makes a tangled impression. Well, it is
tangled.—I look at the landscape, my gaze ranges over it, I see
all sorts of distinct and indistinct movement; this impresses itself
sharply on me, that is quite hazy. After all, how completely ragged
what we see can appear 1 And now look at all that can be meant by
"description of what is seen".—But this just is what is called descrip-
tion of what is seen. There is not one genuine proper case of such
description—the rest being just vague, something which awaits
clarification, or which must just be swept aside as rubbish.
Here we are in enormous danger of wanting to make fine distinc-
tions.—It is the same when one tries to define the concept of a material
object in terms of 'what is really seen'.—What we have rather to do is
to accept the everyday language-game, and to note false accounts of
the matter as false. The primitive language-game which children are
taught needs no justification; attempts at justification need to be
rejected.
Take as an example the aspects of a triangle. This triangle
can be seen as a triangular hole, as a solid, as a geometrical drawing;
as standing on its base, as hanging from its apex; as a mountain,
as a wedge, as an arrow or pointer, as an overturned object which is
meant to stand on the shorter side of the right angle, as a half parallel-
ogram, and as various other things.
"You can think now of this now of this as you look at it, can regard
it now as this now as this, and then you will see it now this way, now
/j-." — What way? There is no further qualification.
But how is it possible to see an object according to an interpretation? —
The question represents it as a queer fact; as if something were being
forced into a form it did not really fit. But no squeezing, no forcing
took place here.
When it looks as if there were no room for such a form between
other ones you have to look for it in another dimension. If there is
no room here, there is room in another dimension.
PHILOSOPHICAL INVESTIGATIONS Hxi 201*
(It is in this sense too that there is no room for imaginary numbers
in the continuum of real numbers. But what this means is: the applica-
tion of the concept of imaginary numbers is less like that of real
numbers than appears from the look of the calculations. It is necessary
to get down to the application, and then the concept finds a different
place, one which, so to speak, one never dreamed of.)
How would the following account do: "What I can see something
asy is what it can be a picture of"?
What this means is: the aspects in a change of aspects are those
ones which the figure might sometimes have permanently in a picture.
A triangle can really be standing up in one picture, be hanging in
another, and can in a third be something that has fallen over.—That is,
I who am looking at it say, not "It may also be something that has
fallen over", but "That glass has fallen over and is lying there in
fragments". This is how we react to the picture.
Could I say what a picture must be like to produce this effect?
No. There are, for example, styles of painting which do not convey
anything to me in this immediate way, but do to other people. I
think custom and upbringing have a hand in this.
What does it mean to say that I 'see the sphere floating in the air' in a
picture?
Is it enough that this description is the first to hand, is the matter-
of-course one? No, for it might be so for various reasons. This might,
for instance, simply be the conventional description.
What is the expression of my not merely understanding the picture in
this way, for instance, (knowing what it is supposed to be), but seeing
it in this way?—It is expressed by: "The sphere seems to float", "You
see it floating", or again, in a special tone of voice, "It floats!"
This, then, is the expression of taking something for something.
But not being used as such.
Here we are not asking ourselves what are the causes and what
produces this impression in a particular case.
And is it a special impression?—"Surely I see something different
when I see the sphere floating from when I merely see it lying there."—
This really means: This expression is justified!—(For taken literally
it is no more than a repetition.)