[lit-ideas] Re: Philosophical Investigations - text and comments II B
- From: Donal McEvoy <donalmcevoyuk@xxxxxxxxxxx>
- To: "lit-ideas@xxxxxxxxxxxxx" <lit-ideas@xxxxxxxxxxxxx>
- Date: Tue, 17 Apr 2012 21:13:51 +0100 (BST)
“143. Let us now examine the following kind of
language-game:
when A gives an order B has to write down series of
signs according
to a certain formation rule.
The first of these series is meant to be that of the
natural numbers in
decimal notation.—How does he get to understand this
notation?—
First of all series of numbers will be written down
for him and he will
be required to copy them. (Do not balk at the
expression "series of
numbers"; it is not being used wrongly here.) And
here already there
is a normal and an abnormal learner's reaction.—At
first perhaps we
guide his hand in writing out the series 0 to 9; but
then the possibility
of getting him to understand will depend on his going on to write
it down independently.—And here we can imagine, e.g.,
that he
does copy the figures independently, but not in the
right order:
he writes sometimes one sometimes another at random.
And then
communication stops at that point.—Or again, he
makes 'mistakes"
in the order.—The difference between this and the
first case will of
course be one of frequency.—Or he makes a systematic mistake; for
example, he copies every other number, or he copies
the series 0, 1, 2,
3, 4, 5, .... like this: 1, 0, 3, 2, 5, 4, . . . . .
Here we shall almost be
tempted to say that he has understood wrong.
Notice, however, that there is no sharp distinction
between a random
mistake and a systematic one. That is, between what
you are inclined
to call "random" and what
"systematic".
Perhaps it is possible to wean him from the systematic
mistake (as
from a bad habit). Or perhaps one accepts his way of
copying and
tries to teach him ours as an offshoot, a variant of
his.—And here too
our pupil's capacity to learn
may come to an end.”
Though it is not said by W, what is important here is the essential role of
showing in understanding
the sense of ‘what is said’. W is ‘pointing out’ that, where a person is being
instructed in a “series of numbers”, that
person may conceivably make what we regard as ‘mistakes’, and their ‘mistakes’
may even have a systematic character
so that we are “tempted to say that he has
understood wrong”.
While W does not here say it, it is
implicit that a person could not make such mistakes if the sense of the
“series” was said in ‘what is said’
here. Of course, we could try to explain their mistakes as arising because they
do not understand the sense of ‘what is said’ here [to instruct them in the
“series”]:- but if the sense is said in ‘what is said’ how can they not
understand it? How can they understand ‘what
is said’ at all [which they may do,
as their response may show some understanding that ‘what is said’ concerns what
we understand as a mathematical
series], and yet still be mistaken as to the sense of ‘what is said’ – if that
sense is said in ‘what is said’? The implicit
answer is that, for W, they can have some understanding of ‘what is said’, yet
also fail to understand its sense as we do, because the sense of ‘what is said’
is not said in ‘what is said’. Also
‘what is said’ may be understood in more than one sense, so a person may
understand the sense of ‘what is said’ correctly in certain respects but not in
others.
The ‘key tenet’ holds
that the sense of ‘what is said’ can only be shown. So when they make ‘mistakes’
in writing out the series, so that it is clear they do not understand the sense
of the series, we try to teach them by showing
them various things [not simply repeating ‘what is said’ as if this conveys
its own sense] – we try to show them the
sense so that they may understand it: and we can imagine various ways we
might try to show them. If they write
‘1,0,2,3,4,5’ etc. we might begin by repeating the correct order
‘0,1,2,3,4,5,’; but if this does not show them the correct sense of the
“series”, we might try to show them by shaking
our head at their series and then writing out other ‘wrong series’ [e.g.
‘0,2,1,3,5,4’, ‘0,5,2,4,3,1’ etc.] and shaking our head so as to show them
‘what is a wrong series’; and
then perhaps writing the correct series and nodding so as to show them ‘what is
the correct series’. Or we might link the writing of each number in the correct
series with a number of objects we consecutively place in a box: so after ‘0’
we point to an empty box, after ‘1’ we place one object in the box (and point
to show the link between the number in the series and the number of objects in
the box), and after ‘2’ we place another object in the box (and point to show
the link) etc. Or, if what this seeks
to show is not understood, we begin with the empty box then move to the number
‘0’ in the series, then put one object in the box and move to the number ‘1’ in
the series etc. And so on.
We
might exhaust all the ways we can think to show them the sense of the “series”.
But if all these ways fail to convey to them ‘what is a wrong series’ from
‘what is the correct series’ – if what can only be shown here is not understood
– there is nothing to be said so that
they may understand what they do not understand by what is shown (unless, of
course, something is ‘said’ that inspires understanding because the pupil
understands _‘what is shown’_ by ‘what is said’).
If ‘showing’ fails to convey the sense of ‘what is said’, there is no further
recourse to ‘what is said’ for explanation of its sense, for ‘what is said’
does not say its own sense (185: “Or suppose
he pointed to the series and said: "But I went on in the same way." —
It would now be no use to say: "But can't you see . . . . ?" — and
repeat the old examples and explanations.”). As grasping the sense
depends on the pupil grasping what can only be shown, if we exhaust our ways of
showing them the sense and still they
do not understand then, in this way, “our
pupil's capacity to learn may come to an end.”Why? Because we have nothing left
to show them and there is nothing to be said that can convey the sense
by ‘saying’ the sense.
In the next numbered section, W remarks on the role of
showing here, and to show that what he is doing is also showing [not saying]:
“144. What do I
mean when I say "the pupil's capacity to learn may
come to an end here"? Do I say this from my own
experience? Of
course not. (Even if I have had such experience.) Then
what am I
doing with that proposition? Well, I should like you
to say: "Yes,
it's true, you can imagine that too, that might happen
too!"—But was
I trying to draw someone's attention to the fact that
he is capable of
imagining that?——I wanted to put that picture before
him, and his
acceptance of
the picture consists in his now being inclined to regard a
given case differently: that is, to compare it with this rather than that
set of pictures. I have changed his way of looking
at things. (Indian
mathematicians: "Look at
this.")”
How can
W change our way of looking at things [or, as W asks, what is W doing with the
proposition “"the pupil's capacity to learn may come to an
end here"?”]? By showing how ‘what can only be shown’
plays a fundamental role in understanding sense and “the capacity to learn”
sense. This role is often invisible to us because we often do understand ‘what
can only be shown’ unproblematically – perhaps without any need to
conspicuously show it. But it does not matter that in our normal experience the
pupil understands the series ‘0,1,2,3’ etc.
without our having to try to conspicuously show
the sense of ‘what is said’ when we state such a series. The point is that
if we ‘imagine’ how we would teach a pupil who did not understand, we see the
inescapable and fundamental role of ‘what can only be shown’ in conveying and
explaining sense. We see that the sense of ‘what is said’ is not said in ‘what
is said’.
W’s
view, that the sense of ‘what is said’ is not said in ‘what is said’, was
previously illustrated by W pointing out that ‘what is said’ is always
compatible
with more than one sense. At 152 W ‘shows’ that a formula does not say its own
sense because a person could be
aware there is such a formula – a ‘what is said’ – without understanding its
sense:-
152. But are the processes which I have described here understanding!
"B understands the principle of the series"
surely doesn't mean
simply: the formula "an = . . . . " occurs to B. For it is perfectly
imaginable that the formula should occur to him and
that he should
nevertheless not understand. "He
understands" must have more in it
than: the formula occurs to him. And equally, more
than any of those
more or less characteristic accompaniments or
manifestations of understanding.
As is
illustrated before and subsequent to this:- this “more in it” than ‘what is
said’ reflects the ‘key tenet’, and is a “more in it” than can only be shown
not said.
“S185. Let us
return to our example (143). Now—judged by the
usual criteria—the pupil has mastered the series of
natural numbers.
Next we teach him to write down other series of
cardinal numbers and
get him to the point of writing down series of the
form
o, n, 2n, 3n, etc.
at an order of the form "+n"; so at the
order "+1" he writes
down the series of natural numbers. — Let us suppose
we have done
exercises and given him tests up to 1000.
Now we get the pupil to continue a series (say +2)
beyond 1000 —
and he writes 1000, 1004, 1008, 1012.
We say to him: "Look what you've done!" — He
doesn't understand.
We say: "You were meant to add two: look
how you began the series!"
— He answers: "Yes, isn't it right? I thought
that was how I was
meant to do
it." —— Or suppose he pointed to the series and said:
"But I went on in the same way." — It would
now be no use to say:
"But can't you see . . . . ?" — and repeat
the old examples and explanations.
— In such a case we might say, perhaps: It comes
natural to this
person to understand our order with our explanations
as we should
understand the order: "Add 2 up to 1000, 4 up to
2000, 6 up to 3000
and so on."
Such a case would present similarities with one in
which a person
naturally reacted to the gesture of pointing with the
hand by looking
in the direction of the line from finger-tip to wrist,
not from wrist to
finger-tip.”
This
last remark is like a philosophical joke but the point is serious: if attempts
to show the sense of ‘what is said’ are to succeed, the person being taught
must understand ‘what we seek to show’ in the same sense as we understand ‘what
we seek to show’. Failure to convey a given sense by ‘showing’ could occur if
they can make no sense of ‘what we seek to show’. But failure can also occur if
they take ‘what we seek to show’ and make sense of it but different to the
sense we take it to convey. Then ‘what is shown’ by us, as we understand it,
will
not teach them the sense we want to convey. But implicit here is the ‘key
tenet’ that the sense of ‘what is said’ is not said in ‘what is said’ but can
only
be shown. For when a person applies a formula ‘wrongly’ – ‘wrongly’ according
to our understanding – there is nothing said in the formula that we can point
to
in order to correct them – we can only try to show they have not understood the
sense of the formula correctly,
perhaps by showing them the correct
sense.
contd. at III C
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