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Wittgenstein's Lectures in 1930-33 G. E. Moore Mind, New Series, Vol. 63, No. 251. (Jul., 1954), pp. 289-316. Stable URL: http://links.jstor.org/sici?sici=0026-4423%28195407%292%3A63%3A251%3C289%3AWLI1%3E2.0.CO%3B2-J Mind is currently published by Oxford University Press.

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http://www.jstor.org Fri May 18 09:01:23 2007

NO. 251.1

VOL. LXIII.

[July, 1954

MIND

A QUARTERLY REVIEW OF

PSYCHOLOGY A N D PHILOSOPHY P



I.-WITTGENSTEIN'S LECTURES IN 1930-33

(p)

THE third kind of " proposition " mentioned in Part I (p. lo), of which a t the very beginning of (I)Wittgenstein gave mathematical propositions as an example, saying that they are a " very different sort of instrument " from, e.g. " There is a piece of chalk here ", and of which he sometimes said that they are not propositions a t all, were those which have been traditionally called " necessary ", as opposed to " contingent ". They are propositions of which the negation would be said to be, not merely false, but " impossible ", " unimaginable ", " unthinkable " (expressions which he himself often used in speaking of them). They include not only the propositions of pure Mathematics, but also those of Deductive Logic, certain propositions which would usually be said to be propositions about colours, and an immense number of others. Of these propositions he undoubtedly held that, unlike " experiential " propositions, they cannot be " compared with reality ", and do not " either agree or disagree " with it. But I think the most important thing he said about them, and certainly one of the most important things he said anywhere in these lectures, was an attempt to explain exactly how they differed from experiential propositions. And this attempt, so far as I can see, consisted in maintaining with regard to them two things, viz. (Pf) that the sentences, which would commonly be said to express them, do in fact, when used in this way, " say nothing " or " are without sense ", and (P") that this supposed fact that 1

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such sentences. when so used. are without sense. is due to the fact that they are related'in a certain way t b "rules of gramniar ". But what, precisely, was the relation to grammatical rules. which he held to be the reason whv thev had no sense ? This question still puzzles me extremely. For a time I thought (though I felt that this was doubtful) that he held so-called necessary propositions to be identical with certain " grammatical rules-a view which would have vielded the conclusion that sentences, which would commonly be said to express necessary propositions, are in fact always merely expressingu rules of " prammar. And I think he did in fact hold that the very same expressions, which would commonly be said to express necessary propositions, can also be properly used in such a way that, when so used, they merely express rules of grammar. But I think he must have been aware (though I think he never exu pressly pointed this out) that, if so, then, when such expressions are being used merely to express rules of grammar they are being uscd in a verv different wav from that in which. on his view., thev are being used when they would commonly be said to be expressing necessary propositions. For he certainly held, if I am not mistaken, of all expressions which would commonly be said to be expressing necessary propositions, what in the Tractatus he had asserted to be true of the particular case of " tautologies ", viz. both (1)that, when so used, they are "without sense " and " say nothing ", and (2) that, nevertheless, they are, in a certain sense " true though he made plain, in these lectures. that he thought that 'the sense in whiLh tthky are "true " was very different from that in which experiential propositions may be q) = p ; giving as an example that the logical product " It's raining and I've either got grey hair or I've not " = " It's raining ". If he did mean this, and if, as he heenled to be, he mas using " sajs nothing " to mean the same as "is without sense ", one important point would f o l l o ~ namely, ~, that he was not using " without sense " in the same way in the case of " tautologies " as in the case of " contradictions ", since he ~vouldcertainly not have said that p. (q.- q) = p. But it gives us no further explanation of how he was using " without sense " in the case of " tautologies ". For if he was using that expression in any ordinary way, then I think he was wrong in saying that " It',$ raining, and I've either got grey hair or I've not " = " It's raining ", since, in any ordinary usage, n e should say that the " sense " of " either I've got grey hair or 1'1-e not " was different from that of, e.g., " either I'm six feet high or I'm not ", and should not say, as apparently he would, that both sentences say nothing, and therefore say the same. In connexion with his use of the phrase " without sense ", one other thing which he said or implied more than once should, I think, be mentioned, because it may give a partial explanation of why he thought that both " contradictions " and " tautologies" are ~vithoutsense. He said in (I) that " the linguistic expression " of " This line can be bisected " is " ' This line is bisected ' has sense ", while a t the same time insisting that " the linguistic expression " of " This line is infinitely dirihlble " is not " ' This line is infinitely divided ' has sense " (he held that " This line i s infinitely divided " is senseless) but is " an infinite possibility in language ". He held, therefore, that in many cases the " linguistic expression " of " It is possible that p should be true " or " should have been true " is " The sentence ' p ' has sense ". And I think there is no doubt that he here meant by " possible " n h a t is commonly called. and ITas called by him on a later occasion, " logically poshible ". But to say that a sentence " p " is the " linguistic expression " of a proposition " q ", would

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daturally mean that the sentence " p " and the sentence " q " have the same meaning, although for some reason or other " p " can be called a " linguistic expression ", though the sentence " q " can not. And that he did hold that, if an expression " p " is " the linguistic expression " of a proposition " q ", then the expression " p " and the expression " q " have the same meaning was also suggested by a passage late in (111), where, having explained that by " possible " he here meant " logically possible7', he asked the question " Doesn't ' I can't feel his tooth-ache ' mean that ' I feel his toothache ' has no sense '2 " obviously implying that the right answer to this question is '' Yes, it does ". And he also, in several other places, seemed t o imply that " p can't be the case ", where this means " It is logically impossible that p should be the case " means the same as " The sentence ' p ' has no sense ". I think that his view in the Tractatus that " contradictions " are " without sense " (sinnlos) may have been a deduction from this proposition. But why should he have held that " tautologies " also are " ~ i t h o u tsense " ? I think that this view of his may have been, in part, a deduction from the conjunction of the proposition that " It is logically impossible that p " means the same as " The sentence ' p ' has no sense " with his principle, which I have already had occasion to mention (p. ll), and which he said "gave us some firm ground ", that " If a proposition has meaning, its negation also has meaning ", where, as I pointed out, he seemed to be using " proposition " to mean the same as " sentence ". For it is logically impossible that the negation of a tautology should be true, and hence, if it is true that " It is logically impossible that p " means the same as " The sentence ' p ' has no sense ", then it will follow from the conjunction of this proposition with his principle, that a " tautology " (or should we say " a n y sentence which expresses a tautology " 2 ) also has none. But why he thought (if he did) that " It is logically impossible that p " means the same as '' The sentence ' p ' has no sense ", I cannot explain. And i t seems to me that if, as he certainly held, the former of these two propositions entails the latter, then the sentence " It is logically impossible that p " must also have no sense ; for can this sentence have any sense if the sentence " p " has none ? But, if " It is logically impossible that p " has no sense, then, so far as I can see, it is quite impossible that it can mean the same as " The sentence ' p ' has no sense ", for this latter eirpression certainly has sense, if " having sense " is being used in any ordinary way. (P") With regard to the expressions " rules of grammar " or " grammatical rules " he pointed ou$ near the beginning of (I),

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where he first introduced the former expression, that when he said " grammar should not allow me to say ' greenish-red ' ", he was " making things belong to grammar, which are not commonly supposed to belong to it " ; and he immediately went on to say that the arrangement of colours in the colour octahedron " is really a part of grammar, not of psychology " ; that " There is such a colour as a greenish blue " is " grammar " ; and that Euclidean Geometry is also " a part of grammar ". In the interval between (11)and (111)I wrote a short paper for him in which I said that I did not understand how he was using the expression " rule of grammar " and gave reasons for thinking that he was not using it in its ordinary sense ; but he, though he expressed approval of my paper, insisted at that time that he was using the expression in its ordinary sense. Later, however, in (111),he said that ".any explanation of the use of language " was " grammar ", but that if I explained the meaning of " flows " by pointing at a river " we shouldn't naturally call this a rule of grammar ". This seems to suggest that by that time he was doubtful whether he was using " rule of grammar " in quite its ordinary sense ; and the same seems to be suggested by his saying, earlier in (111), that we should be using his " jargon " if we said that whether a sentence made sense or not depended on " whether or not it was constructed according to the rules of grammar ". I still think that he was not using the expression "rules of grammar " in any ordinary sense, and I am still unable to form any clear idea as to how he was using it. But, apart from his main contention (whatever that may have been) as to the connexion b~tween" rules of grammar " (in his sense) and necessary propositions, there were two things upon which he seemed mainly anxious to insist about " rules of grammar ", namely (y'), that they are all " arbitrary " and (y") that they " treat only of the symbolism " ; and something ought certainly to be said about his treatment of these two points. As for (y') he often asserted without qualification that all " rules of grammar " are arbitrary. But in (11) he expressly mentioned two senses of " arbitrary " in which he held that some grammatical rules are not arbitrary, and in one place in (111)he said that the sense in which all were arbitrary was a " peculiar " one. The two senses. of which he said in (11)that some " prammatical rules were'not arbitrary in those senses, were (1) a sense in which he said that rules about the use of single words were always " in part " not arbitrary-a proposition which he thought followed from his proposition, which I have mentioned before \

,

(p. 7), that all single words are significant only if " we commit ourselves " by using them, and (2) a sense in which to say that a rule is an established rule in the language we are using is to say that it is not arbitrary : he gave, as an example, that if we followed a rule according to which "hate " was an intransitive verb, this rule would be arbitrary, whereas " if we use it in the sense in which we do use it ", then the rule we are following is not arbitrary. But what, then, was the sense in which he held that all grammatical rules are arbitrary ? This was a question to which he returned again and again in (11), trying to explain what the sense was, and to give reasons for thinking that in that sense they really are arbitrary. He first tried to express his view by saying that it is impossible to " justify " any grammatical rule-a way of expressing it to which he also recurred later ; but he also expressed it by saying that we can't " give reasons " for grammatical rules, soon making clear that what he meant by this was that we can't give reasons for following any particular rule rather than a different one. And in trying to explain why we can't give reasons for following any particular rule, he laid very great stress on an argument, which he put differently in different places, and which I must confess I do not clearly understand. Two of the premisses of this argument are, I think, clear enough. One was (1) that any reason " would have to be a description of reality " : this he asserted in precisely those words. And the second was (2) that " any description of reality must be capable of truth and falsehood " (these again were his own words), and it turned out, I think, that part of what he meant, by this was that any false description must be significant. But to complete the argument he had to say something like (what again he actually said in one place) " and, if it were false, it would have to be said in a language not using this grammar " ; and this is what I do not clearly understand. He gave as an illustration of his meaning that it cannot be because of a " quality in reality " that " I use sweet " in such a way that " sweeter " has meaning, but "identical " in such a way that "more identical " has none ; giving as a reason " If it were because of a ' quality ' in reality, it must be possible to say that reality hasn't got this quality, which grammar forbids ". And he had said previously " I can't say what reality would have to be like, in order that what makes nonsense should make sense, because in order to do so I should have to use this new grammar ". But, though I cannot put clearly the whole of his argument, I think one important point results from what I have quoted-a point which he himself never expressly pointed out. It results,

'

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namely, that he was using the phrases " description of reality " and " quality in reality " in a restricted sense-a sense, such that no statement to the effect that a certain expression is actually used in a certain way is a " description of reality " or describes " a quality in reality ". He was evidently so using these terms that statements about the actual use of an expression, although such statements are obviously experiential propositions, are not to be called " descriptions of reality ". He was confining the term " descriptions of reality " to expressions in which no term is used as a name for itself. For if he were not, it is obviously perfectly easy to say what reality would have to be, like in order that " more identical ", which is nonsense, should make sense : we can say that if " more identical " were used to mean what we now mean bv " sweeter ". then it would make sense : and the proposition that " more identical " is used in that way, even if it is a false one (and I do not know for certain that the very words " more identical " are not used in that way in e.g. some African language) it is certainly not one which English grammar "forbids " us to make-it is certainly untrue that the sentence which expresses it has no significance in English. It seems, therefore, that though in (11) he had said thzt what he meant by saying that all " grammatical rules " are " arbitrary " was that we cannot " give reasons " for following any particular rule rather than a different one, what he meant was only that we cannot give reasons for so doing which are both (a) " descriptions of reality " and (b) " descriptions of reality " of a particular sort, viz. descriptions of reality which do not mention, or say anything about, any particular word or other expression, though of course they must use words or other expressions. And that this was his meaning is made, I think, plainer from a passage late in (111) in which he compared rules of deduction with " the fixing of a unit of length " (or, as he said later, a " standard " of length). He there said " The reasons (if any) for fixing a unit of length do not make it ' not arbitrary ', in the sense in which a statement that so and so is the length of this object is not arbitrary ", adding " Rules of deduction are analogous to the fixing of a unit of length ", and (taking " 3 3 = 6 " as a n instance of a rule of deduction) " ' 3 3 = 6 ' is a rule as to the way we are going to talk . . . it is a preparation for a description, just as fixing a unit of length is a preparation for measuring ". He seemed, therefore, here to be admitting that reasons of a sort can sometimes be given for following a particular " grammatical rule "., only not reasons of the special sort which a well-conducted operation of measurement may give (once the meaning of " foot "

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has been fixed), for, e.g., the statement that a particular rod is less than four feet long. He did in fact mention in this connexion that some " grammatical rules " follow from others ; in which case, of course, that they do so follow may be given as a reason for speaking in accordance with them. In this case, however, he would no doubt have said that the reason given is not a " description of reality ". But it is obvious that reasons which are, in any ordinary sense, " descriptions of reality " can also be given for following a particular rule ; e.g. a particular person may give, as a reason for calling a particular length a " foot ", the " description of reality " which consists in saying that that is how the word " foot ", when used for a unit of length, is generally used in English. And, in this case, of course, it may also be said that the reason whv the word "foot " was orininallv used, in English, as a name for the particular length which we do in fact so call, was that the length in question is not far from the length of those parts of a grown man's body which, in English, are called his " feet ". In these cases. however. I think he might have urged with truth both (a) t h a t the *eason given, though a " description of reality ", is a description which