I want someone to explain to me a certain game & to make it eas[y|i]er I put the question to him: “tell me what a man does to winn the game.” Someone might say “I don't want to know what a man does to win it, this is a question about human beings; I want to want to know what the game is they play.”
  The analogy we might be mislead by is this: you ask the question “

  You ask, what does it mean that “a rod is 6 inches long”. Someone answers one finds [it|ou]t whether it is so by using a measuring rod divided into equal parts. “What does this mean?” – One divides it into equal parts in such & such a way. I have given a definition in terms of the way of verification. “But isn't this an indirect definition?” Sometimes it is, sometimes it isn't.
  Sometimes how we look for something may determine what we are looking for, sometimes it doesn't. – We are always liable to think of the fact that we can find out that there is a chair here in many different ways & we forget that this is just conditioned by the particular use we make of the word “chair”, “table” & in general the generic names of physical
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objects. ⌊⌊ [s|S]upposing we said “what does it mean to have an enlarged liver & someone answered “we ver[y|i]fy it by looking at the persons eye & seeing …” ⌋⌋
  Describe an object by describing its use.
  Describe an object by saying what hollow it fits into.
  More ore less of it's use is expressed by different forms of a prop.
Concider this! The sense of a prop is what you must know to understand it.
  What does understanding a question consist in?
  What does it mean to understand a mathematical question?
  Would you understand ‘25 × 25 = ?’ if you didn't know how to calculate it? Would you say you understood the a position of a board game if you had no idea of the way the game was played? ˇAsk How much must you know to understand it? Would you not be inclined to say that you understand it more & more the more you knew about the game? But we could also imagine a case whe in which you would say that you understood the position even though you knew nothing didn't know the exact rules of the game, even if these rules had not yet been given!
  Now concider such a question as “are there an inf. nr. of primes or not,
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& if not, how many?” I show you what we call a prime nr. & ask you if you understand this question. Prima facie you all say yes. Now I want to show you that you could also look at it from a different & perhaps more ‘exact’ point of view & say ‘no’. We have here a question but we have not yet got a method of it's solution & I want you to think of it in terms of 25 × 25 = ? when we don't know what multiplication is. Now I'll say (what I've said in a similar case before): The question for you gets it's sense by the idea picture of a small finite nr. of cardinals etc.. But what does that mean? In the case of the small nr of cardinals you have a method, you know what to do, here you don't know it, so how can what does it mean, that “the question gets it's sense from the case in which you do know it”? Our mind works on the line that there is something which hasn't yet been calculated which could but for our weakness be calculated it takes ˇno notice of the fact that we have no method & although this can't alter the facts it determines the way of expressing: We say we don't yet know so & so; & if someone shows
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us Euler's proof we say that now we know the answer to the question we have asked. But are we bound to express ourselves in this way? Can't I persuade you to adopt a different way of expressing ourselves of which too we can't say that it is inconsistent with the usual use of words? What if I say: This question i.e. the form of words was indeed suggested by the finite case, but the analogy just brakes down because there is no method of solution. Eulers “proof” needn't be conceived as answering the question “how many primes are there”.
  This question might perfectly well be said to be nonsensical. (As e.g. “what colour has visual space.”). “But is it in our power to regard as question as nonsensical or as making sense? And what about Eulers proof?” Need we ask such a question as “how many cardinal numbers are there”? This question which seems in some way to get hold of the infinite i.e. the enormous for this reason might appeal to some of us & might, on the other hand, repell some of us, – e.g. me. Funeral Concider such a prop as: “There are as many squares as there are cardinals”. If we look at it like this: 1, 2, 3, 4, 5, 6, 7, 8, 9 … we should be
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inclined to say that there were less squares than cardinals; if we think of them as 1², 2², 3², 4², …, we shou say, there are as many. ⌊⌊ Thinking in terms of an analogy doesnt mean that this analogy is constantly before our mind. The Idea of finding out something about the series of cardinals. ⌋⌋ Why shouldn't we draw the conclusion that this whole question doesn't make sense? But we actually say that it does, & part of it's charm that the answer is in a way paradoxical adds ˇfor some to it's charm. (Some + some = some). It seems to us that we have discovered a new element with utterly different properties. I should like to get rid of this analogy. – Can “the heptagon be constructed?” – A “Now surely this question makes sense!” – B “Now surely this question makes no sense!” – What argument would A use: “you know what it means ‘to construct the pentagon, etc. hexagon, so … , ˇyou know what a heptagon is, what construction means”. B: “It makes no more sense to say ‘can the 7 gon be constructed’, than to say ‘can the 5-gon be constructed’. I know what we call ‘a constructed (as opposed to measured) pentagon’, I know what we call ‘the pentagon-construction’. We use this expression because of certain obvious analogies. But I don't [k|c]all anything heptagon construction. So don't ask such a question as can it be …. Compare this with the statement “on this animal's forhead there
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was a heptagon constr.’ – answer: I don't know what you're talking about. “But what about the proof that the heptagon can't be constructed? As there is such a proof, it is the answer to that question of which you say it makes no sense. “Must I conceive of this proof as the answer to that question?” When the proof is given I can say: you have now given the expression 13 gon sense & you have decided that the expression construction of the 7 gon is not never to be used at all’. Further you have now given the question: “can the 7 gon be constructed” sense, analogous to that can 735912 be devided by 19.