Rule Following Flashcards
§85-87 (rules as signposts)
§85: a rule is like a signpost- it does not leave definite and precise instructions, or even say that one has to follow it in the direction of its finger as opposed to some other direction. There is no one way of interpreting them, and they do sometimes leave room for doubt.
§86: if we add to LG.2 a chart for which witten signs mean which building stones should be brought, we might misinterpret which signs are meant to apply to which stones. Even if we added a written rule to the chart to say that is is the stone parallel to the sign that is denoted, we could require further rules to explain this one, and so on. There is no meaningful way to talk about a complete chart here.
§87: We shouldn’t think that an explanation hangs in the air unless supported by another one- they can rest upon other ones, but these extra explanations will only be needed to prevent a misunderstanding that would arise were it not for the explanation. the signpost is in order if, under normal circumstances, it fulfils its purpose.
139-41 (understanding and mental pictures)
139 Must the whole use of a word [e.g., ‘cube’] come before us when we understand? “What really comes before our mind when we /understand/ a word?—isn’t it something like a picture? Can’t it /be/ a picture?”
But if we suppose that a picture does come before my mind when I think of the word cube, this would suggest a certain use to us but it would always be possible to use it differently. If we were to take the picture of a cube and point to a triangular prism as an example, we could still imagine a method of projection according to which the picture did fit after all.
140- We might be inclined to say that we were under a psychological, rather than a logical, compulsion.
The essential point here is that we can have the same thing in our minds when we hear the word and yet imagine multiple possible applications- we would deny that the word had the same meaning in both cases.
141- could we imagine a method of application as well as the picture? -This could still be interpreted in multiple ways. But could the application actually /come before my mind/?
142 (the dependence of the normative on the natural)
142 “It is only in normal cases that the use of a word is clearly prescribed: we know, are in no doubt, what to say in this or that case. The more abnormal the case, the more doubtful it becomes what we are to say….The procedure of putting a lump of cheese on a balance and fixing the price by the turn of the scale would lose its point if it frequently happened for such lumps to suddenly grow or shrink for no obvious reason.”
[dependence of the normal on the natural]
143-150 (learning decimal notation, conditions for understanding)
143 Getting someone to understand a new language-game: decimal notation. “Notice…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’.”
-146 Does one have to have the whole system in view to understand? “Isn’t one thinking of the derivation of a series from its algebraic formula? Or at least of something analogous?—But this is where we were before. The point is, we can think of more than one application of an algebraic formula
150 ‘“The grammar of the word ‘knows’ is evidently closely related to that of ‘can’, ‘is able to’. But also closely related to that of ‘understands’. (‘Mastery’ of a technique,)”
151-154 (understanding is not a mental process)
151 “Let us imagine the following example: A writes a series of numbers down; B watches him and tries to find a law for the sequence of numbers. If he succeeds he exclaims: “Now I can go on!”
154- “Try not to think of understanding as a ‘mental process’ at all—for that is the expression which confuses you. But ask yourself in what sort of case, in what kind of circumstances, do we say, ‘Now I know how to go on,’ when, that is, the formula has occurred to me?—
In the sense in which there are processes (including mental processes) which are characteristic of understanding, understanding is not a mental process.”
165, 170-175 (reading and being guided)
165 ‘But surely the words come to me in a /special way/ as I read!’
170 It seems like the written words guide us!
- 172 Consider the variety of cases of “being guided”—no one feature in common!
- 173 “Isn’t being guided a particular experience?” Here one is being misled by a particular instance of this experience!
175 Drawing a scribble and then copying it. Influence!
179-80 (‘now I can go on!’)
179 “It is clear that we should not say B had the right [in (151)] to say the words “Now I know how to go on”, just because he thought of the formula—unless experience shewed that there was a connexion between thinking of the formula—saying it, writing it down—and actually continuing the series.”
180 One might rather call these words a ‘signal’; and we judge whether it was rightly employed by what he goes on to do.
185-190 (Deviant rule follower)
§185: think of the person who writes 1004, 1008 instead of 1002, 1004- if we say ‘Look what you’re doing! You’ve started it wrong’, he might respond by suggesting that he thought that was what he was supposed to do. “we might perhaps say: this person finds it natural, once given our explanations, to understand our order as we would understand the order “Add 2 up to 1000 , 4 up to 2000 , 6 up to 3000 , and so on”.”
-186 “‘The right step is the one that accords with the order—as it was /meant/.’—So when you gave the order +2 you meant that he was to write 1002 after 1000—and did you mean that he should write 1868 after 1866, and 100036 after 100034, and so on—an infinite number of such propositions?”
§189: In: “But are the steps then not determined by the algebraic formula?”. But this contains the mistake. We might talk about the steps being determined by the formula in the sense of people who have been appropriately trained all reacting in the same way when presented by the formula. Or we might talk about “formulae which determine a number y for a given value of x”. “But it is not clear offhand what we are to make of the question “Is y = x2 a formula which determines y for a given x ?””
§190: In: “how the formula is meant determines which steps are to be taken”. But what is the criterion for how the formula is meant? Is it the kind of way we always use it (as we were taught to)? Ask yourself: if one used ‘x!2’ first to mean x2; then 2x, how did one mean the one thing or the other by x!2?
193-194 (Machines)
-193 “The machine as symbolizing its action: the action of a machine—I might say at first—seems to be there in it from the start. What does that mean?—If we know the machine, everything else, that is its movement, seems to be already completely determined.
194 When doing philosophy we find ourselves saying that the possible movements of the machine are already in it. “The possibility of a movement is, rather, supposed to be like a shadow of the movement itself.”
198-199 (How a rule teaches one)
§198: In: “But how can a rule teach me what I have to do at this point? After all, whatever I do can, on some interpretation, be made compatible with the rule.” This is not true- interpretations by themselves do not determine meaning. Consider the question of what the expression of a rule- say a signpost, has to do with my actions. Don’t only say, because I have been trained to react in a particular way to this sign, and now I do so react to it, because this is only to point out a causal connection- not what this following-the-sign really consists in.
“I have further indicated that a person goes by a signpost only in so far as there is an established usage, a custom.”
§199: “It is not possible that there should have been only one occasion on which only one person followed a rule. […] To follow a rule, to make a report, to give an order, to play a game of chess, are customs (routines, institutions).”
201-2 (this was our paradox)
§ 201 . “This was our paradox: no course of action could be determined by a rule, because every course of action can be brought into accord with the rule. The answer was: if every course of action can be brought into accord with the rule, then it can also be brought into conflict with it. And so there would be neither accord nor conflict here.”
This argument mistakenly suggests that “we place one interpretation behind another, as if each one contented us at least for a moment, until we thought of yet another lying behind it. For what we thereby show is that there is a way of grasping a rule which is not an interpretation, but which, from case to case of application, is manifest in what we call “following the rule” and “going against it”.”
“That’s why there is an inclination to say: every action according to a rule is an interpretation. But one should speak of interpretation only when one expression of a rule is substituted for another.”
§202: “That’s why ‘following a rule’ is a practise. And to think one is following a rule is not to follow a rule”. This is why we can’t follow a rule ‘privately’- thinking one was following a rule would be the same thing as following a rule.
205-6 (Objection: intention)
§205: In: but that’s just what is remarkable about /intention/- that the existence of a custom or technique isn’t necessary to the mental process. This is why two people would be able to play a game of chess in a world in which otherwise no games existed. “But isn’t chess defined by its rules? And how are these rules present in the mind of someone who intends to play chess?”
§206: “Following a rule is analogous to obeying an order. One is trained to do so, and one reacts to an order in a particular way. But what if one person reacts to the order and training thus , and another otherwise ? Who is right, then?” Here, as when we would try to decipher a completely unknown language, we would look to shared human behaviour for our interpretations.
208-212 (teaching)
§208: “Then am I explaining what “order” and “rule” mean in terms of “regularity”? — How do I explain the meaning of “regular”, “uniform”, “same” to anyone?” If the person had not got these concepts yet (rather than just having them in another language), I would teach them by means of examples and exercises, e.g. though showing how multiply things can be the same, by teaching them to continue an ornamental pattern ‘uniformly’, and to continue progressions in those patterns, and so on. I would influence him through expressions of agreement, rejection, expectation, encouragement, and so on.
we can distinguish teaching which is only meant to apply to the given examples and that which ‘points beyond’ them.
§209: ““But then doesn’t our understanding reach beyond all examples?” — A very curious expression, and a quite natural one!” We might here think that I have a deeper understanding, something more than I give in the explanation.
§211-2: the student doesn’t always need reasons which explain what he grasps here, just as the teacher doesn’t have comprehensive reasons that explain what he knows- the teacher’s reasons will soon give out, and then he will act, without reasons. We can see our acting in such a way (without reasons) when someone we are afraid of tells us to continue a series.
211-217 (reasons give out)
211 “…my reasons will soon give out. And then I shall act, without reasons.”
213 “A doubt is [only] possible in certain circumstances.”
217 If I have exhausted the justifications I have reached bedrock, and my spade is turned. Then I am inclined to say ‘this is simply what I do.’”
215-216 (The same)
- 215 “But isn’t /the same/ at least the same?”
- 216 “‘A thing is identical with itself.’—There is no finer example of a useless proposition, which is connected with a certain play of the imagination.”
