Wittgenstein:
(Emphasis in bold is inserted by Shawver to enhance commentary.) |
Shawver commentary: | ||||
81. F. P. Ramsey once emphasized in conversation
with me that logic was a 'normative science'. I do not know exactly what
he had in mind, but it was doubtless closely related to what only dawned
on me later: namely, that in philosophy we often compare the use of words
with games and calculi which have fixed rules, but cannot say that someone
who is using language must be playing such a game. --But if you say
that our languages only approximate to such calculi you are standing on
the very brink of a misunderstanding. For then it may look as
if what we were talking about were an ideal language. As if our logic were,
so to speak, a logic for a vacuum. --Whereas logic does not treat of language
-- or of thought -- in the sense in which a natural science treats of a
natural phenomenon, and the most that can be said is that we construct
ideal languages. But here the word "ideal" is liable to mislead, for it
sounds as if these languages were better, more perfect, than our everyday
language; and as if it took the logician to shew people at last what a
proper sentence looked like.
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81. This is an important aphorism. Early
Wittgenstein, the Wittgenstein of the Tractatus, thought of language as
something like a calculus. The idea was that if you knew the rules
of language, you could apply the calculus to understand it.
For example, suppose you had the following four sentences: A. Mary went to the store
And suppose you also had four ways of connecting those sentences: v - meaning either or both
And suppose you could also modify any sentence by negating it and symbolizing that negation with a tilde like this: ~ And let's enrich this calculus. You can also use parentheses. Using the character names above to name the four sentences, couldn't you figure out the following statement like one would figure out a calculus? (A*B) * ~A It would mean
And, as you can see, this would not be possible because it is not true for Mary to have both gone to the store and not to have gone to the store. So, we can see that the symbolic phrase (A*B) * ~A is nonsense. because to be true it would requires A to be both true and false. Now, consider the following: [~(A*B) v (B>C)] v (D#B) Could this statement be true? You could figure this out using the same process that we used above and it would feel very much like performing a kind of mathematical calculus. This was the sort of vision of language that inspired early Wittgenstein (and the logical positivists), but now he is saying that it will not work. One might want to say that if it were a misunderstanding that language
worked as a calculus, then it was because language is defective in some
way. But Wittgensein is telling us that the failure of langauge to
conform to a calculus does not imply that it is defective.
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All this, however, can only appear in the right light when one has attained greater clarity about the concepts of understanding, meaning, and thinking. For it will then also become clear what can lead us (and did lead me) to think that if anyone utters a sentence and means or understands it he is operating a calculus according to definite rules. | And these concepts of understanding, meaning and
thinking are concepts Wittgenstein will explicate.
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82. What do I call 'the rule by which he proceeds'?
--The hypothesis that satisfactorily describes his use of words, which
we observe; or the rule which he looks up when he uses signs; or the one
which he gives us in reply if we ask him what his rule is? --But what if
observation does not enable us to see any clear rule, and the question
brings none to light? --For he did indeed give me a definition when I asked
him what he understood by "N", but he was prepared to withdraw and alter
it.-So how am I to determine the rule according to which he is playing?
He does not know it himself. --Or, to ask a better question: What meaning
is the expression "the rule by which he proceeds" supposed to have left
to it here?
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82. Suppose you are playing chess and you move your
knight. A child who does know how to play chess asks you how you
were able to move the piece in such an odd way. If you know chess,
the rule is probably clear in your mind and you can state it unambiguously.
You can say what the rule is that guides and constrains the movement of
the bishop, compared to the movement of the knight. There is no ambiguity
here.
But if you were asked the rule you used to decide if a sentence were a well formed sentence, or grammatically flawed, you might find that you do not know the answer immediately. You feel you have to think about it a bit. It may be that you can choose which sentence has a flaw, but not know immediately what the rule that this correct useage obeys. Similarly, you might know how to use a word in a sentence, and use it regularly and meaningfully, yet still not be know its useage well enough to give a definition spontaneously and easily. So, ask yourself, are you following a rule in the cases in which you cannot easily and spontaneously state the rule? In what sense are you following one? Are you subsequently just trying to discover a stated rule that wold capture the behavior you are engaging in without any sense of trying to conform to a defined rule? |
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83. Doesn't the analogy between language and games throw light here? We can easily imagine people amusing themselves in a field by playing with a ball so as to start various existing games, but playing many without finishing them and in between throwing the ball aimlessly into the air, chasing one another with the ball and bombarding one another for a joke and so on. And now someone says: The whole time they are playing a ball-game and following definite rules at every throw. | 83. See how far this new model of language
is from the model of language as a calculus? Yes, there are rules,
but the rules are not binding in the same way that they are in calculus.
The rules of langauge do not confine every movement that is made.
In languge, one can stop, metaphorically speaking, to toss the ball up
into the air.
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And is there not also the case where we play and-make up the rules
as we go along? And there is even one where we alter them-as we go along.
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This is a particularly significant observation. In language we will find ourselves making up meanings for words as we go along. "What do you mean by that?" someone asks you. Then you say, "I mean..." and you give the word a definite sense, not a sense that is quite what it is in the dictionary, but a definite sense. You are making up the rules of this language game as you go along. | ||||
84. I said that the application of a word is not everywhere bounded by rules. But what does a game look like that is everywhere bounded by rules? whose rules never let a doubt creep in, but stop up all the cracks where it might? -- Can't we imagine a rule determining the application of a rule, and a doubt which it removes-and so on? | 84. Am I right that games are not completely bounded
by rules? Sure, there are gaps in the stated rules. But can't we
imagine some sort of implicit rule that guides us in the spaces between
the rules?
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But that is not to say that we are in doubt because it is possible for us to imagine a doubt. I can easily imagine someone always doubting before he opened his front door whether an abyss did not yawn behind it, and making sure about it before he went through the door (and he might on some occasion prove to be right)-but that does not make me doubt in the same case. | Sure, we can imagine such a thing, but we need not.
It is not a requirement of games that they be everywhere bounded by rules.
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85. A rule stands there like a sign-post.--Does the sign-post leave no doubt open about the way I have to go? Does it shew which direction I am to take when I have passed it; whether along the road or the footpath or cross-country? But where is it said which way I am to follow it; whether in the direction of its finger or (e.g.) in the opposite one? --And if there were, not a single sign-post, but a chain of adjacent ones or of chalk marks on the ground-- is there only one way of interpreting them?-- So I can say, the sign-post does after all leave no room for doubt. Or rather: it sometimes leaves room for doubt and sometimes not. And now this is no longer a philosophical proposition, but an empirical one. | 85. And even if we stated rules (like sign-posts)
every space, this would not leave us with some flexibility in how we played
the game. Even sign-posts have to be interpreted. Even if a
hand
points in a certain direction, where is the rule that says I must follow
it in the direction of the finger?
And even if we assume that the hand points towards the flag, is it pointing to the stripes or the stars? Or the flag as a whole? Or to the colors? Is there not room for interpretation here? Is everything completely bound by rules? And if we have this flexibility in pointing, is there not room for a similar flexibility in how we interpret the rules of a game?
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86. Imagine a language-game like (2) played with the help of a table. The signs given to B by A are now written ones. B has a table, in the first column are the signs used in the game, in the second pictures of building stones. A shews B such a written sign; B looks it up in the table, looks at the picture opposite, and so on. So the table is a rule which he follows in executing orders.-One learns to look the picture up in the table by receiving a training, and part of this training consists perhaps in ~e pupil's learning to pass with his finger horizontally from left to right; and so, as it were, to draw a series of horizontal lines on the table. |
Imagine the workers in a language-game like
(2)
having the following table to use to make their selection of stones.
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Suppose different ways of reading a table were now
introduced; one time, as above, according to the schema:
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If we did include arrows in our own culture, it would
likely look like this:
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another time like this:
or in some other way.
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For this kind of looking, however, we would need
arrows:
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--Such a schema is supplied with the table as the rule for its use. | But what Wittgensein had in mind for this tribe is
two tables. For exxample, imagine one being up on a wall, and the
other being in one's hand.
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However, if their mythology required a more complex, the rule might be: |
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Or, imagine things more complex,, still. Perhaps
this language game is not for the purpose of building but for the purpose
of assuaging the temper of the gods, and supppose, too, that the paths
the gods want their servants to take to read these tables requires them
to work through a maze of arrows such as this:
in order to read a table like this:
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Can we not now imagine further rules to explain this one? | Now, suppose the various rules in the network of
arrows was tied to a mythology so that each arrow represented a sacred
path that must be followed exactly. Not only did this sacred path
guide how one's eyes were to move, but also how one stood and the expression
one put on one's face:
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And, on the other hand, was that first table incomplete without the schema of arrows? And are other tables incomplete without their schemata? | The initial table seemed easy to us:
All these implicit rules seem to guide our behavor, and rules we can
no longer state, that no longer guide us in a concscious way. Do
we want to say that the table needed to include such rules in order to
be complete? If so, would any table ever be complete?
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87. Suppose I give this explanation:
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87. LW is going to try to show us (or remind
us) how difficult it can be to tie down the meaning of even an apparently
simple sentence. This may seem to you like a change in subject, because
we are no longer talking about tables and arrows, but the subject is much
the same. We are noticing how many gaps there are in the rules we
might use to interpret things, how much of our understanding takes place
without our noticing how it all works.
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But similar doubts to those about "Moses" are possible about the words of this explanation (what are you calling "Egypt", whom the "Israelites" etc.?). Nor would these questions come to an end when we got down to words like "red", "dark", "sweet". | As soon as you try to pin down these words, you can see how hard it is to make sure the person in history that we talk about refers to "Moses." Maybe the real person had a different name and maybe his story has been modified through the years. Has it been so modified that the person we think of as "Moses" is no longer congruent with the historical figure? It is possible to doubt all of these things. | ||||
"But then how does an explanation help me to understand, if after
all it is not the final one? In that case the explanation is never completed;
so I still don't understand what he means, and never shall!" --
As though an explanation as it were hung in the air unless supported by another one. |
This is Wittgenstein's questioning voice, voice of
aporia,
wondering. If I can't tie these things down with an explanation,
I not only fail to understand who Moses is, but I fail in all similar attempts.
Exaplanations cannot help me understand! (or so it seems to the aporetic
voice).
It seems (when in this apoetic mood) that we must be able
to use explanations to tie down all the ambiguities, or else nothing will
ever be known.
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Whereas an explanation may indeed rest on another one that has been given, but none stands in need of another -- -unless we require it to prevent a misunderstanding. | That is, we may be able to use one explanation to explain another -- but no additional explanation is needed except to prevent misunderstanding. You do not need an explanation for the statement "The chair I am sitting in is uncomfortable," unless you don't understand it (and you might not, for example, if it looked o you that I was not sitting at all.) | ||||
One might say: an explanation serves to remove or to avert a misunderstanding -- one, that is, that would occur but for the explanation not every one that I can imagine. | The confusion comes about because we imagine that explanations contain a complete rule that require no training to interpret. Explanations canavert misunderstandings but only for those whose training is sufficient to understand the explanation. And, we cannot find sufficient explnations to replace that history of training. | ||||
88. If I tell someone "Stand roughly here"-may not this explanation work perfectly? And cannot every other one fail too? | |||||
But isn't it an inexact explanation? -Yes; why shouldn't we call
it "inexact"? Only let us understand what "inexact" means. For it does
not mean "unusable". And let us consider what we call an "exact" explanation
in contrast with this one. Perhaps something like drawing a chalk line
round an area? Here it strikes us at once that the line has breadth.
So a colour-edge would be more exact. But has this exactness still got
a function here: isn't the engine idling? And remember too that we have
not yet defined what is to count as overstepping this exact boundary; how,
with what instruments, it is to be established. And so on.
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We understand what it means to set a pocket watch
to the exact time or to regulate it to be exact. But what if it were asked:
is this exactness ideal exactness, or how nearly does it approach the ideal?-Of
course, we can speak of measurements of time in which there is a different
and as we
should say a greater, exactness than in the measurement of time by
a pocket-watch; in which the words "to set the clock to the exact time"
have a different, though related meaning, and 'to tell the time' is a different
process and so on.-Now, if I tell someone: "You should come to dinner more
punctually; you know it begins at one o'clock exactly"-is there really
no question of exactness here? because it is possible to say: "Think of
the determination of time in the laboratory or the observatory; there you
see what 'exactness' means"?
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"Inexact" is really a reproach, and "exact" is praise. And that is to say that what is inexact attains its goal less perfectly than what is more exact. Thus the point here is what we call "the goal". Am I inexact when I do not give our distance from the sun to the nearest foot, or tell a joiner the width of a table to the nearest thousandth of an inch? | |||||
88-5
No single ideal of exactness has been laid down; we do not know what we should be supposed to imagine under this head-unless you yourself lay down what is to be so called. But you will kind it difficult to hit upon such a convention; at least any that satisfies you. |
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