자꾸 절 번호가 자동으로 매겨지는 바람에 42. 43. 45. 로 하는 대신 대괄호를 붙였어요.
[42] Let us consider very simple rules. Let the expression be a figure, say this one:
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and one follows the rule by drawing a straight sequence of such figures (perhaps as an ornament).
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Under what circumstances should we say: someone gives a rule by writing down such a figure? Under what circumstances: someone is following this rule when he draws that sequence? It is difficult to describe this.
If one of a pair of chimpanzees once scratched the figure | - - | in the earth and thereupon the other the series | - - | | - - | etc., the first would not have given a rule nor would the other be following it, whatever else went on at the same time in the mind of the two of them.
If however there were observed, e.g., the phenomenon of a kind of instruction, of shewing how and of imitation, of lucky and misfiring attempts, of reward and punishment and the like; if at length the one who had been so trained put figures which he had never seen before one after another in sequence as in the first example, then we should probably say that the one chimpanzee was writing rules down, and the other was following them.
[43] But suppose that already the first time the one chimpanzee had purposed to repeat this procedure? Only in a particular technique of
acting, speaking, thinking, can someone purpose something. (This 'can' is the grammatical 'can'.)
It is possible for me to invent a card-game today, which however never gets played. But it means nothing to say: in the history of mankind just once was a game invented, and that game was never played by anyone. That means nothing. Not because it contradicts psychological laws. Only in a quite definite surrounding do the words "invent a game" "play a game" make sense.
In the same way it cannot be said either that just once in the history of mankind did someone follow a sign-post. Whereas it can be said that just once in the history of mankind did some walk parallel with a board. And that first impossibility is again not a psychological one.
The words "language", "proposition", "order", "rule", "calculation", "experiment", "following a rule" relate to a technique, a custom.
A preliminary step towards acting according to a rule would be, say, pleasure in simple regularities such as the tapping out of simple rhythms or drawing or looking at simple ornaments. So one might train someone to obey the order: "draw something regular", "tap regularly". And here again one must imagine a particular technique.
You must ask yourself: under what special circumstances do we say that someone has "made a mere slip of the pen" or "he could perfectly well have gone on, but on purpose did not do so" or "he had meant to repeat the figure that he drew, but he happened not to do it".
The concept "regular tapping", "regular figure", is taught us in the same way as 'light- coloured' or 'dirty' or 'gaudy'.
[45] Suppose however there were a tribe whose people apparently had an understanding of a kind of regularity which I do not grasp. That is they would also have learning and instruction, quite analogous to that in § 42. If one watches them one would say that they follow rules, learn to follow rules. The instruction effects, e.g., agreement in actions on the part of pupil and teacher. But if we look at one of their series of figures we can see no regularity of any kind.
What should we say now? We might say: "They appear to be following a rule which escapes us," but also "Here we have a phenomenon of behaviour on the part of human beings, which we don't understand".
Instruction in acting according to the rule can be described without employing "and so on".
What can be described in this description is a gesture, a tone of voice, a sign which the teacher uses in a particular way in giving instruction, and which the pupils imitate. The effect of these expressions can also
be described, again without calling 'and so on' to our aid, i.e. finitely. The effect of "and so on" will be to produce agreement going beyond what is done in the lessons, with the result that we all or nearly all count the same and calculate the same.
It would be possible, though, to imagine the very instruction without any "and so on" in it. But on leaving school the people would still all calculate the same beyond the examples in the instruction they had had.
Suppose one day instruction no longer produced agreement?
Could there be arithmetic without agreement on the part of calculators?
Could there be only one human being that calculated? Could there be only one that followed a rule?
Are these questions like, say, this one: "Can one man alone engage in commerce?"
It only makes sense to say "and so on" when "and so on" is understood. I.e., when the other is as capable of going on as I am, i.e., does go on just as I do.
Could two people engage in trade with one another?