Order Number 9215052 Language games: An exposition and defense of W ittgenstein's later philosophy Allen, Robert Francis, Ph.D. Wayne State University, 1991 U MI 300 N. Zeeb Rd. Ann Aitoor, MI

LANGUAGE GAMES: AN EXPOSITION AND DEFENSE OF WITTGENSTEIN'S LATER PHILOSOPHY ROBERT FRANCIS ALLEN DISSERTATION Submitted to the Graduate School of Wayne State University Detroit, Michigan in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY 1991 by MAJOR: PHILOSOPHY Approved by: Adviser v;/ date To My Parents, Mr. and Mrs. Francis C. Allen Acknowledgements I am most grateful to my adviser, Barbara Humphries. She patiently taught me the views that form the core of my thesis and never accepted anything but my best presentation of them. Thanks are also due to the other philosophers on my committee, Lawrence Powers and Lawrence Lombard. Their criticisms made me see the problems facing a defender of Wittgenstein, forcing me to strengthen my arguments. The linguist on my committee, Stephen Lapointe, also provided me with constructive criticisms for which I am grateful. Thanks are due as well to Richard Angell, William Stine, Robert Yanal, and Gerald Powers for their advice and encouragement. For their patience and care, I thank my typists, James Allen and Ruth Ann MacPherson. Finally, I will be eternally grateful to my wife, Ann. Her love, encouragement, and devotion were invaluable to me as I struggled to wrap up this project. Table of Contents Dedication Page ii Acknowledgements Page iii Introduction Page 1 Chapter One: The Going On Problem Page 2 Chapter Two: The Public Practice Theory of Guidance Page 34 Chapter Three: Giving the Standards of Mathematics Page 99 Chapter Four: Wittgenstein and Plato Page 158 Chapter Five: Wittgenstein and Kant Page 190 Bibliography Page 220 Abstract Page 223 Autobiographical Statement Page 225 i v The origin and the primitive form of the language game is a reaction; only from this can the more complicated forms develop. Language-1 want to say-is a refinement 'in the beginning was the deed'. Wittgenstein Introduction This dissertation is a discussion of Wittgenstein's later philosophy. In it, Wittgenstein's answer to the "going on problem" will be presented: I will give his reply to the skeptic who denies that rule-following is possible. Chapter One will describe this problem. Chapter Two will give Wittgenstein's answer to it. Chapter Three will show how Wittgenstein used this answer to give the standards of mathematics. Chapter Four will compare Wittgenstein's answer to the going on problem to Plato's. Chapter Five will describe Kant's influence on Wittgenstein's later philosophy. The leit motif of these chapters will be that the way human beings apply a rule is the source of justification for its application. 1 Chapter One: The Going On Problem What is the problem Wittgenstein believes he has posed? It is best seen in the following "remarks" from the Philosophical Investigations: Now we get the pupil to continue a series (say +2) beyond 1000- and he writes 1000, 1004, 1008, 1012. We say to him: "Look what you've done!"-He doesn't understand. We say: "You were meant to add two: look how you began the series!" -He answers: "Yes, isn't it right? I thought that was how I was meant to do it."- Or suppose he pointed to the series and said: "But I went on in the same way." It would now be no use to say: "But can't you see. . . ?"-and repeat the old examples and explanations.1 In the next remark Wittgenstein gives what he takes to be the question posed in the above passage: "How is it decided what is the right step to take at any particular stage ?. . . Or, again, what at any stage we are to call 'being in accord' with that sentence ('add two.') (and with the mean-ing you then put into the sentence - whatever that may have consisted in)."2 So the problem given in remarks #185 ard #186 is this: A teacher has given a pupil the standard training for use of a concept, addition. The pupil performs according to the teacher's purported expectations up to a certain point. But thereafter he gives answers to the teacher's questions that the teacher and the other members of the community consider wrong. But it has yet to be shown, 2 3 according to Wittgenstein, what makes these answers wrong. What determines, Wittgenstein asks, what the right answers are? Wittgenstein sees this problem arising in other contexts as well. Prior to #185, he discusses it in connection with "ostensive definitions" of colors, length and, numbers. Here we get closer to the crux of the problem: 28. Now one can ostensively define a proper name, the name of a colour, the name ot a material, a numeral, the name cf a point on a compass, and so on. The definition of the number two, "That is called 'two' " - pointing to two nuts- is perfectly exact.- But how can two be defined like that? The person one gives the definition to doesn't know what one calls "two"; he will suppose that "two" is the name given to this group of nuts!- He may suppose this; but perhaps he does not. He might make the opposite mistake when I want to assign a name to this group of nuts he might understand it as a numeral. And he might equally well take the name of a person, of which I give an ostensive definition, as that of a colour, of a race, or even a point of the compass. That is to say: an ostensive definition can be variously interpreted in every case. In this remark Wittgenstein describes what could be the predicament of someone trying to ostensively define a term. How much simpler and clearer can one get than to define the number two by pointing to two nuts? One would think that there is no possibility of a student misunderstanding such training. Yet even here, Wittgenstein points out, there is room for confusion. For it is true that there is more than one way to take such an explanation. It is not likely that one would take the above explanation to be anything besides a definition of 'two' because nearly everyone would understand that a definition of 'two' was being given. That is just a fact about people. But if one did take it as the telling of "the name 4 given to this group of nuts--" why would he be guilty of a misunderstanding? (Why is it not likely that one would take the above explanation to be anything besides a definition of 'two'? This is not likely because nearly everyone would understand that a definition of two was being given here. People wouldn't get any other idea from this training. That is just a fact about us.) That is the question, according to Wittgenstein, that the equivocality of training bases gives rise to: 29. Perhaps you say: two can only be ostensively defined in this way: "This number is called 'two' ". For the word "number" here shews what place in language, in grammar, we assign to the word. But this means that the word "number" must be explained before the ostensive definition can be understood.- The word "number" in the definition does indeed shew this place; does shew the post at which we station the word. And we can prevent misunderstandings by saying: "This color is soand -so", "This length is called so-and-so", and so on. That is to say: misunderstandings are sometimes averted in this way. But is there only one way of taking the word "colour" or "length"?-Well, they just need defining.- Defining, then, by means of other words! And what about the last definition in this chain? (Do not say "There isn't a 'last' definition". That is just as if you chose to say: "There isn't a last house in this road; one can always build an additional one".)3 Here Wittgenstein shows that we can't clear up this equivocality even by becoming more explicit in our instructions. To avoid the above misunderstanding we think it is enough to point out to our student that it is a number we are defining here. This move, it is thought, will focus his attention on the 'right idea' by ruling out all competitors. But suppose the student doesn't understand what 'number' means. We will have to explain this concept to him if it is to aid him in grasping the original definition. But to do so we must employ "other words," thus risking further "misunderstandings." For at any point in our "chain" of definitions our student may become "deviant." But that he would have misunderstood us at this point can be claimed only if we can make our meanings clear. (Why can we claim that he would have misunderstood us oniy if we can make our meanings clear? This is so because if we can't make our meanings clear there is nothing for him to misunderstand. If we don't make our meanings clear then a skeptic can plausibly put forth an interpretation we wouldn't want to accept and say 'this is what you really meant one to do'. After all, since our meaning is unclear perhaps that is what we intended?, perhaps that is following the rule? This doubt is the genesis of the going on problem.) But that is possible only if our "last definition" is unambiguous, is given in terms that admit of one and only one interpretation. This, however, is what Wittgenstein does not think is possible: "an ostensive definition can be variously interpreted in every case." In these remarks Wittgenstein points out why a "deviant" pupil can't be shown to be wrong. We think that our most basic ostensive definitions settle how a concept is to be used. But Wittgenstein believes the above examples show that these definitions are not univocal, as we had assumed. That is to say, Wittgenstein takes these cases to throw into doubt our belief that there is only one right way to take the most basic ostensive definition. The definitions are equivocal because we can not 'pin down' how one is to apply them. We say they are to be taken one way, the skeptic says they are to be taken another. Unfortunately, we can not give a 6 reason why our application is preferable to his. That is, we can not cite any fact about the definition that shows how it points to our application rather than his. Thus the definition is equivocal in the sense that it lends itself to more than one interpretation, none of which can be regarded as the correct interpretation. What is wanted, though, is for the definition to give one and only one application of itself. We should think the problem is with the definition, because it is supposed to produce agreement- but it doesn't. We would like to say that the skeptic is just being perverse, but that would beg the question 'why is our taking of the definition the correct one?' We have not yet shown why our taking is to be favored over his, therefore we can not call him perverse. The definition is sound if and only if it guides its takers one way rather than all other possible ways of taking it. So far it has not been shown how this would be possible, since it has not been shown how the skeptic's taking is to be ruled out. Thus we should think the problem is with the definition. It has not dene its job. All definitions admit of multiple applications. The going on problem involves showing why one of them is to be preferred over the others-deemed correct. 'Deviant' is in scare quotes here because it has not yet been shown that the pupil is guilty of anything but deviating from our way of doing things, taking the definition-which is not to say he's done anything incorrect. It has yet to be shown that he's deviated from what is right, that he's not correctly following a rule. To show this we would have to point out 'the fact about the definition' that makes our application of it correct and his incorrect. 7 We get to the crux of the problem here because the same problem underlies the teacher's dilemma in #185. He thought the "exercises and tests given . . . up to 1000" settled how the concept of addition was to be employed beyond 1000. These exercises were to function as the ostensive definitions of color, length, and number supposedly do. But given that basic explanations can be "variously interpreted in every case," the teacher can not prove that his charge has misunderstood the import of his training, the exercises and tests given. The teacher must "prove" his charge has misunderstood the impact of his training so that it can be justifiably claimed that the teacher's way of taking the training is the correct way. If this can't be proven, if it can't be shown that a misunderstanding has taken place, then there is no reason for the teacher to believe that what he does is follow a rule and what the pupil does is go against it. It then follows that the student's "deviant" answer cannot be shown to be not in accord with his training. In Remarks#28 and #29 Wittgenstein shows how the teacher himself could take his student to be right, not just doing what "comes natural" to him: nothing about the training itself rules out the deviant interpretation as incorrect. Thus Wittgenstein poses a skeptical problem regarding the possibility of rule-following. There can be rule-following only if there is one and only one right way of taking the training for following any given rule. There can be rule-following only if there is one and only one right way of taking the training for a rule because if there isn't there is no way to settle disputes over what is 'doing the right thing'. Were multiple "correct" ways of taking the training possible no one could justify that he is following the rule: for the others could present their interpretations, say they are correct, and call their competitors 'out of line'. 'What does following the rule imply one should do hereT There would be no way of answering this question if "every course of action could be made out to accord with the rule." For the question of how one should apply a ruie in given circumstances demands an unequivocal answer: its askers would not be satisfied by the reply 'well you could do this or you could do that . . . it really doesn't matter anything is correct'. Such an answer leaves one free to do whatever one pleases. But following a rule is a normative matter; it can not be a matter of 'doing what one pleases'. There should be one and only one correct application of a rule in any situation to which it is brought to bear. How it should be applied in any situation should be unambiguous, given by one and only one action. The above remarks of Wittgenstein are meant to cast doubt on the possibility of this necessary condition for rule-following being fulfilled. Without the fulfillment of the necessary condition we are left, as Wittgenstein puts it, with the "paradox (that) no course of action could be determined by a rule, because every cause of action could be made out to accord with the rule."4 Here is how other philosophers see the problems W 'tgenstein poses in the Philosophical Investigations. Professor Barbara Humphries takes Wittgenstein to be presenting a problem regarding the possibility of guidance. She writes: However, this intuition (that rule-following implies the possibility of explicit guidance) is problematic in light of other considerations adduced by Wittgenstein, which seem to show that it is impossible for anything to guide us in that way. Anything that might be presented as a rule is compatible with innumerable courses of action; it does not appear to single out any one set of steps as uniquely correct, i.e., as steps that it points out, steps which fit the rule. If various incompatible steps equally "fit" the definition or rule, then no explicit awareness of any presentation of the rule really guides us, determines what is to be done. And if explicit guidance is impossible, then (according to the intuition) so is implicit guidance and rule following generally.5 Essentially, then, Professor Humphries' interpretation agrees with the present writer's. Someone wants to teach someone else how to follow a rule. To do this he presents his charge with something he wants to be a guide for following said rule. This would-be guide can be, depending on the rule being taught, samples of an item to be termed or of a kind of problem whose algorithm is supposed to be grasped by working out the sample problems. Later applications of the rule in question are supposed to be justifiable in terms of this guide. Humphries, like the present writer, sees Wittgenstein's problem arising because no sample can fulfill the role of a guide. That is, no "training base" (Humphries' term) can be used to prove that any given application of its rule is in accord with it. The equivocality of a sample, the way it lends itself to multiple interpretations, is what makes this impossible. Since the possibility of guidance is a necessary condition for the possibility of rule following, it follows that rule following is impossible, at least for a trainee if not for his teacher. This is Wittgenstein's skeptical problem as seen by Humphries and the present writer. 10 Professor Saul Kripke gives this problem a different twist and in so doing, according to some, gets to the real heart of the Wittgensteinien paradox. Kripke takes Wittgenstein's remarks to bring into question the possibility of forming a specific intention, of meaning something definite by one's terms. Kripke writes: This, then is the skeptical paradox. When I respond in one way rather than another to such a problem as '68+57', I can have no justification for one response rather than another. Since the skeptic who supposes that I meant quus cannot be answered, there is no fact about me that distinguishes between my meaning plus and my meaning quus. Indeed there is no fact about me that distinguishes between my meaning a definite function by 'plus' (which determines my responses in new cases) and my meaning nothing at all.6 The skeptical argument, then, remains unanswered. There can be no such thing as meaning anything by any word. Each new application we make is a leap in the dark; any present intention could be interpreted so as to accord with anything we may choose to do. So there can be neither accord nor conflict. This is what Wittgenstein said in #202J Kripke arrives at this interpretation by kicking "the ladder" away from the teacher in Wittgenstein's examples. As those cases were presented above, it was assumed that the teacher knew what he meant by 'add 2' or 'blue'. The problem lay in conveying those meanings via training bases to a student. Kripke, though, posits a skeptic who asks the teacher to show what his terms mean to himself. For Kripke, the teacher becomes his own student. It turns out that the teacher can't even justify to himself the applications he makes of his terms in terms of any "instructions" he gave himself, i.e., in terms of their training bases. Anything that was before the teacher's mind when he attempted to institute a term's meaning is compatible with innumerable uses. Training bases prove to be equivocal for teacher as well as student. Thus, as Kripke writes, "the entire idea of meaning vanishes into thin air."8 But Professor Kripke has not given a different skeptical problem than the one posited by Humphries. At bottom both of them have Wittgenstein making the same request. It is the request for something that could function as a guide for how to follow a rule. Kripke's skeptic wants to know what fact about an individual shows what he means by his terms, i.e. how he intends to use them. This is a request for what was before an individual's mind when he learned how to use a term or was using it. From this object one is supposed to be able to read off one's intentions regarding said term.9 And what is offered by Kripke himself, when he tries to answer for the skeptic's opponent, is the object one has taken for a guide, the color samples or sample addition problems. When these prove to be of no use in answering the skeptic, because of equivocality, the paradox ensues. To wit: Normally when we consider a mathematical rule such as addition we think of ourselves as guided in our application of it to each new instance. . . . In addition, I may give myself directions for further computations of 't', stated in terms of other functions and rules. In turn, I may give myself directions for the further computation of these functions and rules, and so on. Eventually, however, the process must stop, with ultimate functions and rules that I have stipulated for myself only by a finite number of examples, just as in the intelligence test. If so, is not my procedure as arbitrary as that of the man who guesses the continuation of the intelligence test?10 1 2 Here Kripke gives the necessary conditions for a practice being rule-governed. A practice is rule-governed only if the explanation of how it is to be done terminates in unambiguous directions, given by "a finite number of examples" of the practice in question. But these two conditions cannot both be met: the finitude of the examples makes the directions-their import-ambiguous. Given a finite number of addition problems, e.g., there will always be a question of how they tell one to solve other problems involving the 'plus' sign. There will always be a question here because a skeptic can always challenge an interpretation of the problem's directions by putting forth a reading of his own and claiming that it is the correct way to go on. Given this, our way of going on from the standard training for addition, according to Kripke, is, contrary to what we believe, "as arbitrary as that of a man who guesses the continuation of the intelligence test." From a finite series of numbers he guessed at how the series should be extended: he cannot justify his way of going on, though it may seem even to others to be correct. Our way of going on from addition's standard training is no less unjustified: this standard training is also composed of a finite number of examples whose import is thus 'up for grabs', a situation a skeptic can exploit for the purpose of calling our procedure guessing, "arbitrary." The same problem arises in connection with the training for the use of color words: It has been supposed that all I need to do to determine my use of the word 'green is to have an image, a sample, of green that I bring to mind whenever I apply the word in the future. When I 13 use this to justify my application of 'green' to a new object, should not the skeptical problem be obvious to any reader of Goodman?11 Were I to try to convince a skeptic that I was following a rule, being guided, when I applied 'green' to an object not included in my training base by citing the examples of green that make up this training base, I would be in the same predicament as those who try to justify their practice of addition by citing a finite number of addition problems. The skeptic could say to me, as he said to the above "adders," "you have shown me only a finite number of instances of your practice. What about thêe instances determines that the practice should be continued in the manner you have proposed? You say this patch of grass is the same color as the things in your training base. But what about them makes this so? How do they "point" to this grass as something to which the term 'green' can justifiably be applied? As a matter of fact, I think your samples guide one to now apply 'green' to the sky, although yesterday when you showed me them they were the same color as the grass. Why am I wrong here? What about your sample shows I have not correctly interpreted their directions?" This is how Kripke employs Nelson Goodman's new riddle of induction to make clear Wittgenstein's skeptical paradox. (Kripke, op. cit, pp. 20 and 58.) Thus Kripke too has Wittgenstein questioning the possibility of guidance even though his Wittgenstein formulates this questioning in terms of a request for the fact of the matter of intention. Indeed, though Kripke entertains other candidates for the fact to the matter of meaning besides training bases, such as dispositions and sensations, he stipulates on Wittgenstein's behalf that "there is a 14 condition that any putative candidate for such a fact must satisfy. It must, in some sense, show I am justified in giving the answer '125' to '68+57'. The 'directions' that determine what I should do in each instance must somehow be 'contained' in any candidate for the fact as to what I meant."12 That is to say, the fact of the matter of guidance must give instruction regarding each case to be settled. This stipulation shows that Kripke, like Humphries, sees Wittgenstein as looking for what makes guidance possible. To sum up the exposition so far, we've seen Wittgenstein's posing a problem regarding the possibility of guidance. Initially the problem had to do only with the possibility of one person guiding another. But then it was shown that an individual might not even be able to show how he guides himself. The possibility of intentionality was called into question. (I say the possibility of intentionality was called into question because it was shown that one cannot prove that he intended to do, when he was being trained to follow the rule in question, what he is now claiming is an application of said rule.) Underlying both of these versions of the Wittgensteinien paradox, though, we saw the same problem: the equivocality of the training bases for rules. It is their apparent failure to determine any one course of action as in accord with them that lies at the heart of Wittgenstein's rule following skepticism. As Humphries writes, "Wittgenstein asks: How is (guidance) possible? What sort of thing could meet both the criterion of determining correct use and the criterion of 'presentability'?"13 Here is Wittgenstein posing this question: 1 5 How does in come about that this arrow > - > - - - - » points? Doesn't it seem to carry in it something besides itself? - "No not the dead line on the paper. . . "u What we've seen so far is that Wittgenstein sought the fact that would prove the above arrow does not fail to point. Before considering the candidates Wittgenstein rejected for this fact of the matter of guidance, the view that Wittgenstein didn't formulate a skeptical paradox must be addressed. Professor William Tait's position is representative of this view. He writes: But it does not seem a reasonable view, and certainly Wittgenstein does not hold it (e.g. #358), that the meaning of an expression is the meaning conferred on it by something about us when we utter it. It seemed to me that Wittgenstein is correct in holding that when we speak about the meaning of an expression, we must ultimately be speaking about the role that it plays in our language. Thus to the extent that Kripke intends either to be formulating a skeptical paradox or ascribing this intention to Wittgenstein, I think that he is mistaken. There is nothing paradoxical about the fact that nothing about me on the occasion that I utter A determines whether or not A is true or anything else about the meaning of A.15 Here Wittgenstein is taken to be repudiating a faulty way of looking at language, a view that creates "an air of paradox." Once this confusing view is rejected, once we give up the idea that "the meaning of a sentence must be the meaning conferred on it by some fact about us when we utter it," the air of paradox is dissolved according to Tait. But is it? Something must confer meaning on a sentence. Tait believes it was Wittgenstein's view that the role it played in our language served this purpose.16 But one can ask: what gives a sentence's 1 6 role? It comes on Tait's view from the role it plays for a number of speakers. But if there is no individual amongst them who can spell out this role, as the skeptic believes, then it can ha**e no significance for the group either. The skeptic is going to ask each individual to prove that he can mean what the group assumes everyone means by an expression. The term 'blue* presumably has a role in our language. And Tait is right in concluding that Wittgenstein thought that this role is what gives the term its meaning, as will be shown later. But he is wrong in assuming that Wittgenstein stopped there. For Wittgenstein still wanted to know how it was possible that there could be such a role, i. e., regular use. To put things in my terms, Wittgenstein did believe a term's training base guided us in its use, that is, gave its meaning, but he was puzzled about what made this possible: he sought the fact about a training base that allowed it to guide.17 The training base for 'blue' supposedly guides us to call only things like it 'blue'. But in virtue of what?, Wittgenstein asks. What makes it the case that there is only one type of thing one could be guided to call 'blue', given its training base, as must be the case for this training base to be a guide to a regular use? Later Tait writes that "that Jones means addition by '+' is a fact about the world and, indeed, is a fact about Jones,"18 viz., that he has the ability to add. Here he is addressing the concern that no one ever means anything specific by a term he uses, which, as we've just seen, must be taken care of before we can talk about what expressions mean in a common language. But Tait offers no insight into what this fact might be-and Kripke wants it described. It is 17 a fact about Jones, let us assume, that he was given the standard training for addition. But in light of #28 and #29 this fact alone can't warrant us in asserting that Jones means addition by Tait writes that "what he says is a criterion for the fact that he means addition by V ." 19 But this will not do either. For, as Kripke shows, what Jones says, the answers he gives to various addition problems, is consistent with his meaning other operations besides addition by Thus Tait does not succeed in showing that Wittgenstein intended no skeptical paradox. Even if we grant that no fact obtaining at the time one makes an utterance determines its meaning, we are still faced with the problem of determining what does give it significance. The existence of this problem gives rise to Wittgenstein's skeptical paradox. The solufHn to his skeptical paradox he laid the most stress on repudiating is, in Kripke's terms, "the classical empiricist" approach.20 Here is how Kripke characterizes this view: This picture suggested that association of an image with a word (paradigmatically a visual one) determined its meaning. For example (#139), a drawing of a cube comes to my mind whenever I hear or say the word 'cube'.21 Colin McGinn formulates it as follows: Wittgenstein's most characteristic formulation of the conception he is against is in terms of something which 'comes before the mind': what he is saying is that meaning something consists in some item coming before one's mind- for example to mean cube by 'cube' is to have before one's mind the image of a cube. Thus meaning is continued as a species of 1 8 picturing where the picture occurs in the medium of consciousness.22 Thus, on this account, one acquires an image or mental picture of a term's training base. This image is then supposed to guide one in the use of the term to which it corresponds. Wittgenstein's rejection of this solution is succinct and convincing. First, he says that in fact we do not always use a term by consulting an image of its training base. We often speak unreflectively: To see that the process of obeying the order can be of this kind, consider the order "imagine a red patch". You are not tempted in this case to think that before obeying you must have imagined a red patch to serve you as a pattern for the red patch which you were ordered to imagine.23 That is to say, someone who is trained to "imagine a red patch" needn't bring before his mind a red patch to serve as his model for what color of patch he is to imagine when he is told to "imagine a red patch." He will simply imagine a red patch. Thus the classical empiricist account fails to provide necessary conditions for being guided. Secondly, Wittgenstein says that an image of a training base is no more univocal than the training base itself. Well, suppose that a picture does comes before your mind when you hear the word "cube", say the drawing of a cube. In what sense can this picture fit or fail to fit a use of the word "cube"?- Perhaps you say: "It's quite simple;- if that picture occurs to me and I point to a triangular prism for instance, and say it is a cube, then this use of the word doesn't fit the picture."- But doesn't it fit? I have purposely so chosen the example that it is quite easy to imagine a method of projection according to which the picture does fit after all. The picture of the cube did indeed suggest a certain use to us, but it was possible for me to use it differently.24 This criticism is tantamount to the aforementioned criticism of the citing of the training bases themselves as guides. In both cases non-standard interpretations of the objects leave one in doubt as to their import.25 If the picture of a cube, just like the actual cubes one might have 'cube1 ostensively defined by, can "direct" one to apply the term cube to any one of a number of things, then the experience of it can not be cited as evidence for the fact that one is being guided in the use of the term 'cube'. Our skeptic could say that one meant to include triangular prisms in the extension of the concept cube, so that one is guilty of misapplying the term 'cube' if one applies it to cubes but not triangular prisms, even if one had a cube before one's mind when making this application. Wittgenstein is short with the reply that "that not merely the picture of the cube but also the method of projection comes to mind." For a skeptic could just as easily posit a non-standard interpretation of any method of projection.26 That is to say, a method of projection would be a rule for interpreting a rule. Thus it, no less than the rule it was supposed to facilitate an understanding of, could have its training taken in more than one way. Thus we would be faced with the same problem as before, the problem the method of projection was supposed to clear up: out of all the possible ways to go on from the rule's training, 'what is the way that would be following the rule?'. The method of projection, because it is equivocal, cannot remove the ambiguity of the original instruction. 20 Thus the having of an image of a training base before one's mind does not show that one is being guided in the use of a term. The classical empiricist account gives neither necessary nor sufficient conditions for being guided. What we are after here is an analysis of 'guided' and a way to tell whether an application is correct. What is means to be guided would tell us how to apply a term. For one is to apply a term in the way in which one was guided to do so. Conversely, if we knew what a correct application of a term is, upon being given training in its use, we would know what it means to be guided in its use. For to be guided in a term's use is to correctly use it. The classical empiricist can help us find neither an analysis of 'guided' nor a way to tell whether an application of a term is correct. For reasons identical to those cited against the above formulation of the classical empiricist account, Wittgenstein rejects the notion that meaning consists in having a certain feeling (intuition) as one's guide. This version of the empiricist's theory must be used in cases like those of adding where images of training bases are not thought of as guides, e.g., in doing addition where one would not form an image of the problems by which one was shown how to add. As before, feelings are not always present when one, e.g., adds. Moreover, even were they always present, it is not clear what they might direct one to do: So it must have been intuition that removed this doubt?- If intuition is an inner voice- how do I know how I am to obey it? And how do I know it doesn't mislead me? For if it can guide me right it can also guide me wrong.27 Thus the suggestion that the experience of a given feeling could guide one in following a rule like that of addition fails to persuade 28 One could feel that one should, in order to accord with one's intentions, answer '125' when asked the sum of '68+57' without it being the case that that answer is the one meant to give. Perhaps having the intuition in question was supposed to tell one not to give the answer one is inclined to give? Voices also have to be interpreted. Kripke briefly discusses another theory positing a psychological fact as constitutive of meaning. This is the view that "meaning addition by 'plus' is a state even more sui generis than we have argued before . . . a primitive state not to be assimilated to sensations or headache or any 'qualitative' states, but a state of a unique kind of its own."29 What Kripke has in mind here is someone replying to Wittgenstein that being guided is not to be reduced to some other psychological state. The state of being guided, of according with one's intentions, on this view, is just the state of being guided. Like the state of being in pain, this state is irreducible to another state. Kripke calls this move "desperate," since it leaves the state of meaning "completely mysterious."30 More importantly, he cites passages where Wittgenstein finds "considerable logical difficulty" with the view that being guided is a mental state. To wit: "meaning is not a process which accompanies a word. For no process could have the consequences of meaning."31 The objection here is that 22 meaning, e.g., addition by 'plus', involves intending to give an infinite number of answers. One who grasps the rule for addition is supposed to be prepared to give the answer to each one of an infinite number of addition problems. But our minds, as Kripke points out, are "finite." Thus it does not seem possible that being in any of its states could have the consequence that one "must give a determinate answer to an arbitrarily large addition problem."32 That is to say, no finite state of mind could contain the infinite number of intentions requisite to truthfully say upon answering an extremely complicated addition problem, "I intended to give this answer". So it is not logically possi1 for being guided to involve just being in a state of mind. There must be more to meaning than that. (Having an "algorithm" before one's mind is not going to help either, as it too requires an interpretation. The question would thus be 'which algorithm has one learned?'.) We now move on to a discussion of the individual disposition theory of meaning. This theory says that the fact that one means, e.g., addition by 'plus', is that one is disposed to answer with the sum to each addition problem posed to one.33 Kripke has Wittgenstein rejecting this view. He bases his interpretation on remark #258 where Wittgenstein says if "whatever is going to seem right to me is right . . . we can't talk about right."34 In this connection he might also have mentioned the dictum "to think one is obeying a rule is not to obey a rule."35 The point is that the fact that one is disposed to give an answer to an addition problem, even if it accords with standard practice, does not justify the belief that one is being guided in the 23 use of the plus sign. In general, we do not take the fact that one is disposed to do something as evidence for the fact that one is following a rule. This should be clear from what goes on in mathematical instruction. Here there must be a distinction between what one is disposed to regard as correct and what is correct. There can't be rule-following where 'whatever one thinks is correct' is correct. For then one could never be wrong; but there must be a right and a wrong way to apply a rule. Kripke discusses several revisions of the individual disposition theory. But in the end he finds each version wanting for the same reason he rejected the original formulation: Our conclusion in the previous paragraph shows that in some sense, after giving a number of more specific criticisms of the dispositional theory, we have returned full circle to our original intuition. Precisely the fact that our answer to the question of which function I meant is justificatory of my present response is ignored in the dispositional account and leads to all its difficulties.36 The fact to the matter of meaning is supposed to show that I am justified in thinking I am being guided in my application of a rule. But that I am disposed to make one application rather than another cannot fit this bill. What I am disposed to do may be unguided. But on the "dispositional account" this couldn't be claimed: because 'what i am disposed to do' is what is correct, following the rule. That the disposition was produced in a certain way would not make things any better. For the dispositional account does not lack empirical verification; it is logically flawed: it fails to do justice to the "grammar" of rule-following, which requires a way of 24 distinguishing what an individual is disposed to do from what he should do. Colin McGinn rejects Kripke's treatment of Wittgenstein's view on the individual dispositional analysis of meaning.37 He bases his rejection on three reasons. I will examine each one in turn. First, McGinn accuses Kripke of failing to find passages where Wittgenstein explicitly rejects a dispositional analysis.38 Now it is true that in the passage Kripke cites, #258, the concept of dispositionality is not mentioned. Nevertheless, what is said there -that there must be a way of distinguishing between 'what seems right to me' and 'what is right'-does back up Kripke's point that a dispositional analysis fails to capture the justificatory aspect of meaning. So, in the absence of added support for the dispositional analysis, Kripke is at least entitled to the claim that Wittgenstein would reject this view, even if he didn't explicitly do so. McGinn next cites #149 and says of it that Wittgenstein doesn't reject a dispositional analysis there but, rather, "(suggests)" it.39 This is a spurious claim. All Wittgenstein does in this passage is draw a distinction between brain states and their behavioral manifestations. That he does not reject a dispositional analysis at this point in no way suggests a preference for it. McGinn can only conclude from this passage that Wittgenstein, as he puts it, wanted to "construe dispositions in terms of counterfactuals about behavior."40 But this can hardly be read as an endorsement of the dispositional analysis McGinn favors. McGinn's third attempt to saddle Wittgenstein with the individual dispositional analysis also fails. He cites #140 and says 25 it "hardly fits with Kripke's claim that differences of dispositions to use do not suffice to establish differences of meaning."41 Well and good. But it's essentially a negative point Wittgenstein makes in #140: what comes before the mind does not establish meaning. Thus, while Kripke may have to backtrack on the above claim regarding the negative use to which Wittgenstein would put the concept of dispositionality, it is not yet established that he needs to concede to McGinn that Wittgenstein favored the individual dispositional analysis. For that concession must be made only if Wittgenstein claimed further that the sameness of dispositions established sameness of meaning. But this is a claim Wittgenstein rejects: in #187 the deviant adder and conventional one share the same dispositions up to a point without sharing the same conception of addition. Thus McGinn should content himself here with establishing that "there is an important difference between (conscious states and application) with respect to determination of meaning."42 Sameness of dispositions may be a necessary condition of sameness of meaning, but it is on Wittgenstein's line not a sufficient one. McGinn finally tries to rely on #187 to support his interpretation. "What is notable about this passage," he says, is Wittgenstein's willingness to employ a counterfactual about what someone would have said in explication of that person having meant something."43 Now it is true that Wittgenstein employs counterfactuals here. But it would be a mistake to assume for that reason that he believed that was all there was to an analysis of meaning. For it had yet to be established what going on in 26 accordance with the training base for addition consisted in. Wittgenstein alluded to this notion when he wrote #187 but it was not until #1SC that he explicitly stated it: It may now be said: "The way the formula is meant determines which steps are to be taken." What is the criterion for the way the formula is meant? It is, for example, the kind of way we always use it, the way we are taught to use it.44 Thus McGinn is entitled to assert Wittgenstein believed certain dispositions revealed understanding only because the latter had himself decided which dispositions specifically were the products of guidance. That is to say, Wittgenstein establishes what Kripke calls "the justificatory aspect of meaning" in #190: he tells there why someone should answer '1002' when asked the sum of '1000+2', after having been trained to do addition. It is this establishment that allows him to make the claim he does in #187. McGinn has put Wittgenstein's cart before his horses. This becomes obvious when we consider McGinn's own attempt to incorporate the normative aspect of meaning into his own reading of Wittgenstein. To mean addition, McGinn says, is to have a certain "capacity:" To mean addition by '+' at + is to associate with '+' the capacity to add at +, and to mean the same by '+' at +' is to associate with '+' the same capacity at +' as at +.45 But one may properly ask: what is the capacity to add?, what does it mean to be guided by the training base for addition?. That is the question at the crux of the Wittgensteinien paradox. McGinn's failure to give Wittgenstein's answer to it makes his exegesis only 27 half the truth. We can't say which answers accord with a training base and thus reveal the acquisition of the capacity that was supposed to be taught by it until we know what it means to be guided by it. Finally we come to Kripke's version of Wittgenstein's own solution. Kripke has Wittgenstein giving a "skeptical solution" to the skeptical paradox. This is a solution that is analogous Hume's answer to the problem of causation: it concedes to the skeptic that there is no fact of the matter at hand.46 Just as there was for Hume no fact of the matter regarding talk of causal connections; according to Kripke, there was no fact of the matter for Wittgenstein. The sought after truth conditions for statements of the form "he means 'X' are abdicated in favor of "assertability conditions": From this we can discern rough assertability conditions for such a sentence as "Jones means addition by 'plus'." Jones is entitled, subject to correction by others, provisionally to say, "I mean addition by 'plus'," whenever he has the feeling of confidence- "now I can go on!"- that he can give 'correct' responses in new cases; and he is entitled, again provisionally and subject to correction by others, to judge a new response to be 'correct' simply because it is the response he is inclined to give. These inclinations (both Jones' general inclination that he has 'got it' and his particular inclination to give particular answers in particular addition problems) are to be regarded as primitive. They are not to be justified in terms of Jones's ability to interpret his own intentions or anything else. But Smith need not accept Jones's authority on these matters: Smith will judge Jones to mean plus by 'plus' only if he judges that Jones's answers to particular addition problems agree with those he is inclined to give, or, if they occasionally disagree, he can interpret Jones as at least following the proper procedure.47 28 An individual on this view, can believe he understands the concept of addition if he has confidence he is adding properly. Acting on this belief is a case of acting "without 'justification' but not 'wrongfully'."48 There is no fact one consults to tell oneself how to add. One just does it as one is confidently inclined. This is different from the dispositional theory because here one is not given justification by being disposed to do something. One's peers, on the other hand, will say one knows how to add only in the absence of bizarre uses of the plus sign. The giving of bizarre answers to addition problems is sufficient reason to proscribe another's admittance to the community of adders. The community though, on Kripke's view, like the individual has no sufficient conditions for saying of someone 'he means addition by '+' '. All we can say here is that if someone has been admitted into the community of adders his answers to addition problems agree often with those his peers are inclined to give: he's been tested and not found wanting.49 Kripke also stresses that Wittgenstein also wanted us to look at the " utility" of practices like the one just described.50 The utility of the practice of ascribing to someone the concept of addition, Kripke says, is "evident": we depend on such ascriptions to show us on whom we can rely to carry out the numerous activities involving addition.51 This then is Kripke's interpretation of Wittgenstein's solution to the skeptical paradox. Since Kripke does not provide the specific passages from which he culls his exegesis, it is not possible to base an objection to his claim on a misreading of a specific remark. 29 Nevertheless, his exposition does provide the key to understanding the error I want to insist he commits. The interpretation I will defend in the next chapter is what Kripke would call a "straight solution." I believe there is ample textual evidence to support such a reading.52 And Kripke cites it! The key to understanding Kripke's error lies in the first paragraph of page 96 of .sis exposition. There he discusses the importance of "agreement" for the language game of concept ascription. But, though he says it's "essential for our game of ascribing rules and concepts," he fails to see in this notion any possibility for offering a straight solution on Wittgenstein's behalf to the skeptical paradox.53 It is this possibility I will explore shortly. This exploration combined with an overturning of Kripke's objections to a community disposition account of meaning will show the just described skeptical solution fails to get to the heart of Wittgenstein's later philosophy. To sum up Chapter One: we have shown that Wittgenstein posed a skeptical problem regarding the possibility of guidance. His rulefollowing skepticism was based on the notion that it wasn't possible for the training base of a rule to guide one in the rule's application. This notion leads to the paradox of guidance since it contradicts the belief that rule-following is possible. It is believed that rulefollowing is possible. But if it can't be shown what fact about a training base makes it point to some applications of its term but not others, then this belief is without support: we have no fact of the matter for statements of the form 'he is following a rule'. A number of solutions to this problem were mentioned and found wanting for reasons Wittgenstein adduced. We are now faced with the task of showing how Wittgenstein resolved his rule-following skepticism. We have found that the classical empiricist, anti-reductionist,54 and individual dispositionalist accounts of meaning fail to adequately respond to Wittgenstein's challenge to provide a fact to the matter of meaning. Further, reasons were adduced to reject Kripke's skeptical solution as an interpretation of Wittgenstein's response to this challenge. 31 Notes 1. Ludwig Wittgenstein, Philosophical Investigations (New York: Macmillan Publishing Co Inc., 1968) #185. 2. Ibid., #186. 3. Ibid., #28 and #29. 4. Ibid., #201. 5. Barbara Humphries, "Wittgenstein and Public Practice," p. 3. 6. Saul Kripke, Wittgenstein on Rules and Private Language, (Cambridge, Mass: Harvard University Press, 1982), p. 55. 7. Ibid., p. 21. 8. Ibid., p. 22. 9. Ibid., p. 13. 10. Ibid., p. 18. 11. Ibid., p. 20. 12. Ibid., p. H . 13. Barbara Humphries, "What Are Meanings Like?," p. 1. 14. Wittgenstein op. cit., #454. 15. William Tait, "Wittgenstein and the 'Skeptical Paradoxes'," I M Journal of Philosophy. Vol. LXXXIII No. 9, pp. 482-483. 16. Ibid., p 482. 17. Wittgenstein, op. cit., #28 and #29. 32 18. Tait, op.cit., p. 483. 19. Ibid., p. 483. 20. Colin McGinn, Wittgenstein on Meaning (Oxford, England: Basil Blackwell, 1984) p. 3; Henry Finch, Wittaenstein-The Later Philosophy (Atlantic Highland, New Jersey: Humanities Press, 1977) p. 64; Kripke op. cit., p. 63 n. and pp. 43-44. 21. Kripke, op. cit., p. 42. 22. McGinn, op. cit., p. 3-4. 23. Wittgenstein, The Blue and Brown Books (New York: Harper and Row, 1960). 24. Wittgenstein, The Philosophical Investigations, #139. 25. Kripke, op. cit., pp. 42-43; McGinn, op. cit., pp. 6-7. 26. Wittgenstein, The Philosophical Investigations, #141. 27. Ibid., #213. 28. Kripke, op. cit., pp. 42-44. 29. Ibid., p. 51. 30. Ibid., p. 51. 31. Wittgenstein, The Philosophical Investigations, p. 218. 32. Kripke, op. cit, p. 53. 33. Ibid., pp. 22-23. 34. Ibid., pp. 23-24. 36. Kripke, op. cit., p. 37. 37. McGinn, op. cit, pp. 72-73. 38. Ibid., pp. 73. 39. Ibid., pp. 73-74. 40. Ibid., p. 74 n. 41. Ibid., p. 74. 33 42. Ibid., p. 75. 43. Ibid., p. 75. 44. Wittgenstein, The Philosophical Investigations. #190. 45. McGinn, op. cit, p. 174. 46. Kripke, op. cit., p. 86. 47. Ibid., pp. 90-91. 48. Ibid., p. 87. 49. Ibid., pp. 91-92, 93-95. An important difference between the individual's ascriptions to himself and the community's ascriptions to him is that the latter, unlike the former, are made with "justification." Cf. bottom of page 95. It is the "agreement" with others that provides this justification. 50. Ibid., p. 92. 51. Ibid., pp. 92-93. 52. Cf. #190, #87, #355, #242, and esp. #206. 53. Kripke, op. cit, p. 96. 54. Ibid., p. 41. "Why not argue that "meaning addition by 'plus'" denotes an irreducible experience . . .?" Chapter Two: The Public Practice Theory o.f._Quidagce Wittgenstein did believe guidance was possible. The Philosophical Investigations contains several formulations of the theory behind this belief. It can be called "the community disposition theory of guidance." This is the view I will formulate and defend in this chapter; I will defend it as both a good interpretation of Wittgenstein and a solution to his problem. Professor Humphries, who also holds this view, expounds it as follows: Here is where the public comes in, according to the interpretation of Wittgenstein that I advocate. The reason that an individual can be not only caused, but also told to do something by a rule is that there is a specific way that humans beings generally go on from the presentation of a rule (in context and with the concomitant training). Given these examples of blue in this context of training, people generally go on to pick out certain objects rather than others; this public practice is the right (according to the rule) way to go on. Public practice determines the unique way (among all the ways that are, in the abstract, compatible with the samples) to go on which is dictated by the samples. Public practice provides an independent, current standard of fittingness, to which an individual may or may not conform. That is why the individual's actions can be said to be guided, and not just caused, by the definitional samples (or other presentations of the rule).1 The problem was to prove that there was something about a training base that allowed it to function as a guide. What Humphries is saying is that the fact that human beings are disposed to go on as one from any given training base shows that guidance is 34 35 possible. (Presumably we share such dispositions because of our common physical nature. But this explanation needn't be correct: for it is the common dispositions, whatever their source, that make rule-following possible.) In other words, that human beings generally agree upon how to apply the rules governing their linguistic practices is the fact of the matter of guidance. Citing this fact about any given training base, e.g., the samples of the color blue or elementary addition problems, proves that it can function as a guide, i.e., justification for making an application of the rule for which it is a training base.2 That is to say, given any statement to the effect that a rule is being followed, there is a fact that would make this statement true, viz., the fact that one is going on from its training bas^ as anyone who took this training would. This fact about the training shows how it can function as a guide by providing a way to go on from it that is not random, i.e., subject to an individual's whims, which is what the skeptic claimed anyone's practice was determined by. The skeptic challenged individuals to show how seeming to follow a rule could be distinguished from following a rule. By saying that following a rule involved going on as anyone would from its training, we meet this challenge: for one can seem to follow a rule without going on from its training as anyone else would. Thus how the public takes a rule's training can provide a standard, independent of how an individual would apply said training, to which an individual must adhere to follow said rule. Why the public's way of going on should function as the standard for rule-following will be presently made clear. But for now it should be noted how this 36 standard meets the skeptic's challenge to distinguish seeming right to an individual from being right. The individual disposition theory cannot meet this challenge. Turning to Kripke's formulation of the skeptical paradox, we elaborate the above theory by giving its answer to Kripke's skeptic. The fact this skeptic sought must meet, according to Kripke, "two conditions." First, it must give an account of what fact it is (about my mental state) that constitutes my meaning plus not quus. But further, there is a condition that any putative candidate for such a fact must satisfy. It must, in some sense, show how I am justified in giving the answer '125' to '68+57'. The 'directions' mentioned in the previous paragraph, that determine what I should do in each instance, must somehow be 'contained' in any candidate for the fact as to what I meant.3 The first condition is met by our fact of the matter because one trained to do addition would have been given training that directed him to answer '125' when asked the sum of '68+57'. It is this fact "that constitutes (his) meaning plus, not quus." It does so; and thus satisfies the second condition, because the training base for addition, given the public practice it initiates, directs one to "give the answer '125' to '68+57'." Thus two facts are being given here: the fact of the matter of what I meant: that I was given training that directed me to answer '125' when asked the sum of '68+57', and the fact that makes it possible for this training to give this direction: that anyone given this training would answer '125' when asked the sum of '6 8 + 5 7 '. When I cite my training in addition as justification for believing 37 that I meant to answer '125' when asked the sum of '68+57' I can do so because my training has been given the significance of guiding one to answer '125' when asked this sum because anyone who took this training would give this answer. I can mean something because my training, which I cite to give what I meant to do, can give guidance show someone to do one thing rather than other things. My training can have significance, be a guide to some applications of it rather than others, because there is a way anyone would go on from it. My answering '125' when asked the sum of '68+57' combined with the fact that I was given the arithmetical training that directs one to give this answer in virtue of the fact that anyone would give it justifies one in saying of me 'he is doing what he intended to do when he was trained to give sums'. To put the matter another way, we can say '125' is not a random answer to '68+57', because anyone trained to do addition would eventually form the intention to give this answer, if asked the sum of '68+57'. This is just a fact about people, perhaps explainable by reference to a common physical make-up. This fact provides for, in Humphries' words, "an independent, current standard of fittingness . . ." (Humphries, quoted on page 34.) Thus when a pupil does give the answer '125' when asked the sum of '68+57', we can say to a skeptic that his answer is justified in terms of directions he was given, which come from the training base for addition. That this training gives directions, is a guide, is shown by the fact that human beings are disposed to find its import univocal. Though there are many ways we could go on from the training base for addition, we agree that there is only one way we should go on. Thus we have 38 our standard for correctness which makes '125' the guided answer to '68+57'. This interpretation of Wittgenstein's answer to the skeptical paradox is culled from passages like #190 in the Philosophical !.DYfi.sti.gajJuar)£: It may now be said: H that the way the formula is meant determines which steps are to be taken". What is the criterion for the way the formula is meant? It is, for example, the kind of way we always use it, the way we are taught to use it."4 Here Wittgenstein is saying that we shall recognize how a training base should be taken, i.e., what it guides one to do, by seeing how our fellows normally go on from it. Since there is a normal way to take a training base, it can be concluded that there is "a way the formula is meant," i.e., there is a guided way to go on from a training base. It is the fact that human beings agree in their reactions to definitional data that gives Wittgenstein the answer to his question "how does it come about that this arrow - » - > points?"5 Even with cases never before confronted, public practice will set the standard for correctness. For, though there isn't a way we have normally gone on in them, there is a way we would go on. It is this as yet unspecified practice with which an individual must agree if he is to follow the rule in question. On this account, justification is given for a way of following a rule by the directions of its training. These directions are dete-mined in turn by how people would go on from said training. So one is justified in answering '125' when asked the sum of '68+57' because that is the answer anyone would give after being trained to 39 do addition. (I will argue in Chapter 3 that the public's disposition to answer '125' is also what makes it the sum of '68+57'.) The public's way of going on from a rule's training provides a way of following said rule that is independent of how an individual thinks it should be followed. That is to say, it gives the right way of doing things, with which an individual may or may not be in agreement. It was our task to provide a way of going on from a rule's training that could be distinguished from how an individual thought he should go on. Thus language use rests on our agreement in practice. It is possible to use linguistic rules only because people generally agree on how to apply these rules, since the agreed upon way of doing things provides the requisite correct way to go on from a rule's training. That is not to say that the public can't misapply a rule. There are cases where we would say it has been oeceived regarding how it meant to follow a rule. Where the public can't be faulted, however, is in doing that which is justified in terms of a rule's training. There is a difference between justifiably and unerringly applying a rule. #201 is also illustrative of this one point: It can be seen that there is a misunderstanding here from the mere fact that in the course of our argument we give one interpretation after another; as if each one contented us at least for a moment, until we thought of yet another standing behind it. What this shews is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call "obeying the rule" and "going against it" in actual cases.6 40 What it will mean to follow a rule, i.e., be guided by a rule's training base, is given, Wittgenstein says here, by what human beings say is in accord with its training base. That is to say, to follow a rule is to do what others, who have been trained as one has, do in following said rule. "Hence," he concludes in the following remark, "also 'obeying a rule' is a practice."7 The corollary Wittgenstein draws next shows that he thought one is guided by one's training only if one follows it in accordance with the public practice said training initiates: "it is not possible to obey a rule 'privately' . . ."8 I will presently explain this corollary. For a community to have a disposition, on this view, is for its members to uniformly 'go about' a given activity. That is to say, just in case there is a single way the members of a community would perform a given task, we say said community is disposed to act in the way given by their common behavior. E.g., human beings would agree in giving '12' as the sum of '7+5', having been trained to do addition. Thus, we say human beings have the disposition to answer '12' when asked the sum of '7+5'. Here we are in agreement with Professor David Lewis, who says, "a convention is a regularity in behavior." (David Lewis, Convention, p. 51.) What we are calling "public practices" Lewis terms "conventions." Both refer to ways in which the members of a community agree in 'doing things'. When there is a public practice or convention vis-a-vis a given activity, what will be observed is a uniform conducting of said activity, everyone will do it the same. We also employ, as Lewis does, these uniform conductings as standards of rule-following. That is to say, we agree with Lewis 41 that following a rule "consists in" going on from its training in a "restricted" manner-as anyone who took said training would go on. Thus, as Lewis says, one can justify one's application of a rule, if it conforms to public practice, by citing the "conformity" of others. The community disposition theory of rule-following is further developed in the next remarks. In #206 Wittgenstein says: Following a rule is analogous to obeying an order. We are trained to do so; we react to an order in a particular way. But what if one person reacts in one way and another in another to the order and the training? Which one is right? Suppose you came as an explorer into an unknown country with a language quite strange to you. In what circumstances would you say that the people there gave orders, understood them, obeyed them, rebelled against them and so on? The common behaviour of mankind is the system of reference by means of which we interpret an unknown language.9 There can be such common behavior because human beings are neurologically similar and share goals and their environment. E.g., given the standard training for addition any normal human being will answer '150' when asked the sum of '100+50'. It is agreement like this that Wittgenstein believes is the foundation of language. So Wittgenstein would have Professor Quine's linguist do his translations by bringing in understandable human beings to take the natives' training in language use. The way these human beings go on from the natives' training will determine what it means. Meaning is use. It should not be supposed that there is more to meaning than this, so that the natives and "civilized" human beings could be 42 applying the natives' rules in the same way, agreeing in their use, yet mean something different by them. Quine says: "One is ready to say of the domestic situation in all positivistic reasonableness that if two speakers match in all dispositions to verbal behavior there is no sense in imagining semantic differences between them. It is ironic that the interlinguistic case is less noticed, for it is just here that the semantic indeterminacy makes clear empirical sense." (Quine, Word and Object, p. 79) But Wittgenstein would argue that the "interlinguistic" case should be treated no differently than the "domestic" one. Quine is forced to treat them differently because of his too narrow definition of meaning: the stimulus that would prompt assent to the question 'is this an X?' is term X's meaning. Thus his translator cannot be sure how he should translate the natives' term 'gavagi', which seems to mean 'rabbit'; since 'gavagi' shares a stimulus meaning not only with 'rabbit' but also with 'stage of rabbit', or 'rabbit parts'. Wittgenstein would undo his perplex.ty by asking him to determine whether or not the natives use 'gavagi' as we use 'rabbit parts' and 'stage of rabbit'. By 'we' I mean the speakers Quine himself supposes have made their languages understandable to each other, the ones in the "domestic situation" whose agreement in "dispositions to verbal behavior" makes communication possible between them. 43 Do the natives use 'gavagi' as we use 'rabbit part'? Do they use 'gavagi' as we use 'rabbit stage'? If not, then we would have no reason to translate 'gavagi' as anything but 'rabbit'. The n. .jiing of rabbit parts' and 'rabbit stage' includes more than the stimuli associated with them. We must also consider other features of the situations in which these terms are used, where their stimuli occur. The natives' use of 'gavagi' would have to fit with these other features, not just the stimuli present, for us to say that it was appropriate to translate 'gavagi' as 'rabbit parts' or 'rabbit stage'. E.g., in using the term 'rabbit parts' we would make an effort not only to point to a rabbit, but also to distinguish its appendages. If we didn't notice the natives making a similar effort in using 'gavagi', we would have no reason to translate it as 'rabbit parts'. On the other hand, if their use of 'gavagi' conformed to our use of 'rabbit', e.g., if they spoke of gavagi as they went hunting or sat down to a meal, then we would have sufficient reason to translate 'gavagi' as 'rabbit', having ruled out the alternatives. To conclude this discussion of Quine, his views do not show that there can be no "common human behavior," actions of the kind Wittgenstein makes the foundation of language. Given, e.g., several roses and told they were red, ali persons wouid go on, unless they were color blind, to term embers 'red', if asked their color. Quine himself allows translation between kindred languages, like German and English. So we should imagine no problem in making understandable to the German our training for 'red'. Once we have, his reactions will match ours. By extension we could develop this convention in other kindred cultures. 44 The point here is that the members of the original culture- here English speakers- find that they share reactions to a training base. They then make their application of it the standard for following its rule. And it turns out that other human beings agree with them that this is as should be. Agreement like this, according to Wittgenstein, is the foundation of language: a primitive language game. Quine does not mean to unearth this foundation. His problem has to do with understanding those who have not been a party to its construction. He does not see how we could translate their meanings into ours, do "radical translation." This problem did not arise in the "intracultural" cases because therein there was no need to translate meanings: the different languages were "variants of one and the same intracultural verbalism." But there is more to it than that. What Quine calls "variants of one and the same intracultural verbalism" we call a manifestation of a common human nature, a tendency of people to agree in how they use language. That is what makes translation between kindred languages possible. Quine makes such translation unnecessary, fearing that, like with the native to domestic situation, it would be impossible, if it had to be done on the basis of "stimulus meaning," leaving one with no possibility of language. But we do not have to make translation between kindred languages superfluous, since our definition of meaning is broader than Quine's. We translate German into English based on the discernment of sameness in use, which for us is meaning. The 45 German who applies 'rot' to some roses, embers, and beets, but not the grass has shown us that he means 'red' by 'rot': he uses this term as we use 'red'. Stimulus meaning will not allow for such translation because of its ambiguous significance: one has no way of ruling out the alternatives to one's hypothesis. We can try to rule out these alternatives by seeing whether or not the term in question is being used as we would use it were said alternatives our meanings. Thus our system leaves us with the hope of understanding not only those using kindred languages, but Quine's nat:ves as well. #206 is a direct answer to Kripke's skeptic. This skeptic posits that a training base could rightly be taken in a non-standard way. It is this position that allows him to cast doubt on the assertion that one couldn't have gone on from the training base for addition to mean 'quus'.10 The skeptic's opponent in Kripke's dialogue insists that one could not be justified in answering '5' when asked the sum of '68+57', having taken the training for addition. He claims that someone giving this answer could not have been guided by addition's training base. Kripke's skeptic denies this. In #206 Wittgenstein gives his grist for the anti-skeptic's mill: human beings would not be guided to give this answer. There is a common answer human beings would give to this problem; all of them are disposed to answer '125'. It is this fact that makes addition's training base a guide, i.e., shows how it 'points'. It does not point to '5' as the answer, given this fact; therefore, giving this answer is not following the rule of addition. Thus we have referred to the "common behavior of mankind" to understand how to add. 46 Wittgenstein's idea in the above passage is that one must always make such a reference in order to understand a language. There are, of course, other instances of uniform human conduct. All of us are disposed to call certain roses 'red', certain creatures 'fish', certain boxes 'square', etc. The community disposition theory says that we must look to our agreement in practice for the purpose of determining how to follow a rule. It is the specter of multiple "correct" interpretations of training bases that casts doubt on the possibility of intent'onality. For if one could be guided to give, e.g., the answer '5' when asked the sum of '68 + 45' then one cannot cite the training base for addition as proof that one intended not to give this answer, but '125'. Wittgenstein entertains this possibility in the first paragraph of #206, in its last he rejects it: the concept of intentionality is wedded to the concept of a public practice. Wittgenstein reaffirms this marriage in #207: Let us imagine that the people in that country carried on the usual human activities and in the course of them employed, apparently, an articulate language. If we watch their behavior we find it intelligible, it seems 'logical'. But when we try to learn their language we find it impossible to do so. For there is no regular connexion between what they say, the sounds they make, and their actions; but still these sounds are not superfluous, for if we gag one of the people, it has the same consequences as with us; without the sounds of their actions fall into confusion- as I feel like putting it. Are we to say that these people have a language: orders, reports, and the rest? There is not enough regularity to call it "language".11 47 Here Wittgenstein is saying that were someone to go on from, e.g. the training base for addition, in a bizarre fashion, we could not maintain that he is following a rule, that is, according with an intention. If there is no "regularity" in a practice, that is, if it doesn't conforms to our standards of what it means to be guided by its training bases, then we cannot say its practitioners are intending to do anything, i.e., "have a language." In the face of the skeptic's challenge we can save the concept of intentionality only by uniting it to the idea of a public practice. If we don't form this unity, then we are left without a reply to the skeptic who claims one could have intended to go on from a training base in a way we consider bizarre. That is why Wittgenstein later says that "if a lion could talk, we could not understand him."12 The requisite regularity in his practices would presumably be lacking. Thus we could not ascribe intentions to him. His talk is essentially meaningless, given that it cannot fit into our framework for understanding, viz.; 'the way we do things'. (However, if we could learn what a lion was 'up to' then his talk would be understandable.) Given behavior that seems haphazard from our standpoint intentionality- rule-following- cannot be ascribed. A framework for understanding actions is required. Only our public practices can provide this framework. "The common behavior of mankind is the system of reference by means of which we interpret an unknown language." That is to say, unless there is agreement between our dispositions and the way one is conducting himself, it can't be said that a rule is being followed by said one. There has to be some way of determining what one is 'up to' in claiming one follows a rule. Without such a means of understanding, it would not be possible to follow said rule. Its training taken in isolation from our application of it does not point one way rather than another; it is ambiguous. There is nothing besides our taking of a piece of training that would show its import. An individual's way of going on won't give what it means to follow its rule; for were this what we had to refer to, following the rule would be what he thought was following the rule. Thus the community's dispositions vis-a-vis one's training must be brought in to decide its import, i.e., what its rule is. Wittgenstein returns to these themes in #241. "So you are saying that human agreement determines what is true and what is false?" - It is what human beings say that is true and false; and they agree in the language they use. That is not agreement in opinions but in forms of life.13 We can differ, it is said here, in some opinions. Disputes are possible when it comes to post training applications of a rule. (These can be attributable to unfavorable perceiving conditions or differences in abilities, e.g. . . .) But when it comes to paradigm cases, that is, how we should handle the training bases themselves, there must be agreement for there to be language: "The word 'agreement* and the word 'rule' are related to one another, they are cousins. If I teach anyone the use of one word, he learns the use of the other with it."14 What this means is that we must concur about what it's justified to do upon being given training in a rule's application. For a rule to be instituted, there must be a number of cases about which all parties agree vis-a-vis how said rule applies to them. The institutions given by such agreements Wittgenstein calls "forms of life." E.g., our practice of addition is a form of life, a fundamental way of organizing experience and thus guiding conduct. We use addition to regulate our lives. This is possible only because there is general agreement regarding how to go on from the training for addition. Such agreement vis-a-vis other practices does not imply unerring application of a rule. We could go wrong about what we wanted to do due to perceptual confusion. What we can't be wrong about, however, is in being justified in how we apply a rule. That things greatly seem to us to be in favor of applying a rule is all that is needed for justification in applying it. And we must be capable of agreeing, regarding our training for a rule, that its cases at least greatly seem to merit handling one way rather than another. In the following remark Wittgenstein explains why such agreement is necessary for the working of our language: If language is to be a means of communication there must be agreement not only in definitions but also (queer as this may sound) in judgments. This seems to abolish logic, but does not do so. It is one thing to describe methods of measurements, and another to obtain and state results of measurement. But what we call "measuring" is partly determined by a certain constancy in results of measurement.15 That is to say, we could understand each other only if our dispositions to go on from terms' training bases were uniform. It is not enough that we agree upon how to formulate a lexicon: we must also be able to concur with each other when it comes to 'earning a dictionary's definitions. Were there not such agreement the resulting disputes would make linguistic communication between us 50 impossible. How could there be communication if each time ws needed to add, e.g., disputes arose over the correct sum. How could we employ a color vocabulary if we couldn't agree about the color of many things? (In these cases what is needed is a standard for resolving the disputes.) Were agreement regarding what would be given as the most basic examples of a concept impossible, our talk would achieve nothing. Thus agreement regarding paradigm cases is necessary for communication. Wittgenstein therefore explains how language use presupposes agreement between its users by consideiing what is required for its purpose, viz., communication. Something must show how a training base guides, so tha.i disputes about its use can be resolved. Why does it point one way rather than another? We've seen that a training base can't point in social isolation. Considered apart from how someone would take it, it gives no guidance: since how someone takes it must be definitive of its import, i.e., what it tells one to do. We've also seen, however, that how an individual takes a training base, i.e., is disposed to go on from it, cannot be definitive of its import: for if that were the case 'what one thought one was being told to do1 would be 'what one was being told to do'. Thus, so that there can be a distinction between following a rule and thinking one is following a rule-which distinction is necessary for rule-following- how one's community goes on from a rule's training must set the standard for following its rule, i.e., what one must be in accordance with in order to foilow said rule. "That this doesn't abolish logic," i.e., that statements' truthvalue do not necessarily depend upon what human beings say they 51 are, is shown by the fact that disagreement is possible in nonparadigmatic cases: e.g., what we state regarding "the results of measurement" can be wrong. (Perhaps due to unfavorable viewing conditions.) What we can't be unjustified about are the basic judgements 'hat give rise to, e.g., "a certain constancy in results of measurements." Agreement in basic judgements is required to institute a system of measurement- and in general all forms of communication. Professor Humphries, who also defends Wittgenstein against charges of abolishing logic, puts these points as follows: He does not try to define correct application in terms of public practice, nor does his fundamental problem require him to do so. Consider, for example, #241 "So you are saying that human agreement decides what is true and what is false?" -It is what human beings say that is true and false: and they agree in the language they use. That is not agreement in opinion but in form of life." That is, the agreement called for, the kind of correctness being explicated is not that of application: public practice does not decide what is true (correct application) but correct use (understanding, meaning language). And #242 "If language is to be a means of communication there must be agreement not only in definitions but also (queer as it may sound) in judgements." That is when your reasons have run out, you must apply "grellow" to what the others do if you are to count as understanding the term, using it correctly. If we did not intend to agree in such cases, there could be no rules, no meaning, no language.16 That is to say, art application of a term can be justified, in accordance with a guide's dictates, but "incorrect," i.e., make for a false judgement. One has used a term with justification, on Wittgenstein's account, just in case one's use is in accordance with the public's practice with said term. Having used it this way, 52 however, does not guarantee that one has judged correctly. For one may be following a group that has been deceived regarding what it thinks it is doing. Nevertheless, one must follow this group in order to be justified in one's application, if not correct. But Wittgenstein was not trying to figure out when a judgement was correct. His project was to determine when a judgement was guided. The only way to make this determination, it has been shown, is to apply the standard of how the public would go on from their training bases to apply the terms used in a given judgement. That this theory should not by itself yield a theory of truth should not be surprising, considering that one can expect to have justification for saying things that turn out to be false. I will return to this subject in the following chapters. Again, one who goes against his community and turns out to be right has not necessarily demonstrated "superior understanding" of the rule in question. Unless he can explain his divergence to his fellows, his applications are unguided, even if they turn out to be true. The problem we are trying to solve concerns rule-following, not truthfulness. And one must determine what it means to follow a rule before one can begin to understand truth. It has been proven that following a rule essentially involves going on from its training as human beings would. There can be no predetermined way to go ori from a rule's training. Someone has to figure out how to apply it, whether the training is a Platonic form or an empirical example. Thus someone who called a whale a 'mammal', before his fellows arrived at this judgement, could not appeal to a standard that existed independently of his fellow's judgement. There can be no such standard. The only way that he could show his 53 judgement was guided, and not just one that turns out to be correct, is by persuading his fellows that they were being deceived about a property of whales. For, though they can't be wrong about what it is justified to do, they could be misled regarding the truth. The same thing applies to mathematical judgements. One who says the sum of '100+2' is '104' has not failed to adhere to a mathematical fact that obtains independently of anyone's judgement. There could be no way of doing addition given solely by facts obtaining independently of anyone's judgement: for all facts require interpretation vis-a-vis how they are to be applied to other facts. Any way of doing addition must come from someone's practical understanding of some type of arithmetical training. One who violates a rule of addition is misguided because they have failed to go on in accordance with the public practice of addition. The community disposition theory of guidance is last stated in the Investigations on p. 230. Here Wittgenstein is reflecting on the results of his work, reiterating the intimate connection between guidance and human nature: I am not saying: if such-and-such facts of nature were different people would have different concepts (in the sense of a hypothesis). But: if anyone believes that certain concepts are absolutely the correct ones, and that having different ones would mean not realizing something that we realize-then let him imagine certain very general facts of nature to be different from what we are used to, and the formation of concepts different from the usual one© will become intelligible to him.17 Our conception of the world, Wittgenstein posits here, is a function of "certain very general facts of nature." One can speculate 54 that included anongst these facts would be the way our perceptual organs function, that we have such organs in common, and the laws governing the changes in physical objects. We can deny the skeptic's charge that our worldview is incoherent, that no rules govern the way we speak about things only because there are such facts. They are the preconditions of meaning. Were these things not to be case, it is possible that our world view would be radically different- though not incorrect or incoherent. But of such things we can only speculate. That is to say, since rule-following depends upon agreement in practice, whatever secures agreement in practice is the basis for rule-following. Wittgenstein speculates that the laws of nature are responsible here. They are what allow for our agreement in practice, and thus make conceptual "law and order," to use Professor Pear's phrase, possible. Were these laws different we might have a different system of law and order. Were there no laws of nature, we could not organize our experience. The agreeing that is necessary for rule-following could not be secured. A skeptic could point to the different applications of a rule's training and say "the standard for following a rule- according with public practice- cannot be met-there is no public practice." As noted above, a corollary of Wittgenstein's views on meaning is that "one cannot follow a rule privately." This is the famous private language argument. Rejections of this claim lead directly to an overturning of the community disposition theory. For if it is possible to obey a rule privately, our theory becomes otiose. Thus we need to begin our defense of it by formulating and handling criticism of Wittgenstein's private language argument. 55 What is a private language according to Wittgenstein? and why does he think it is impossible? #243 provides the answer to the first question: But could we also imagine a language  which a person could write down or give vocal expression . his inner experiences-his feelings, moods and the rest- for his private use?- Well can't we do so in our ordinary language?- But that is not what I mean. The individual words of his language are to refer to what can only be known to the person speaking; to his immediate private sensations. So another person cannot understand the language.18 That is to say, a private language would be such that its user could not teach it to another person. Given their private nature, its training bases- private sensations-could not be a guide for anyone but the person whose private experiences they are. That is to say, since a person's sensations, qua his private experiences, cannot be experienced by anyone else, they could not be used to teach anyone else how to engage in a practice. Thus terming them would be a practice no one could engage in besides that person. It would be his private language. Wittgenstein gives his reasons for thinking a private language is impossible in several places. #202 is the first: And hence also 'obeying a rule' is a practice. And to think one is obeying a rule is not to obey a rule. Hence it is not possible to obey a rule 'privately': otherwise thinking one was obeying a rule would be the same thing as obeying it.19 That is to say, 'to obey a rule' is not to form interpretations of its training base, whether they be verbal explanations given to others or heuristics devised for oneself. Rather, it is to use this training as a guide for engaging in a practice that serves one's needs. 56 To be considered a guide a piece of training must be capable of making one do something besides interpret in words its dictates; it must show one how to work with it, to do something with practical results. Explanations of a practice must eventually end, otherwise 'how to do it' could not issue forth- and practices are meant to be done, not just explained forever. Moreover, obeying a rule must be more than believing one is doing so. Merely believing that one is being guided must be distinguished from having reason to believe one is being guided, doing something with practical results. It follows from this that one cannot obey a rule that could not be taught to others. For the only standard for obeying such a "rule" would be 'what one thought was obeying it'. But this makes it possible for rule following to be a wholly subjective enterprise; it takes the necessary objectivity out of determinations of being guided. Thus Wittgenstein rejects the possibility of a private language. It will not do to say here 'the standard for rule-following is going on in the way I intended; and I can be wrong in thinking that * did that'. For if this were the standard for rule-following, then what I would be wrong about would be 'what I thought I should do'. But there is nothing to yield the contents of this intention besides my judgement regarding it. Thus what it means to follow the rule can be decided only by me. So following the rule and what I think is following the rule are necessarily conflated. What would make my application of the rule wrong could only be my thinking that I've not followed it. But there is more to being wrong that thinking one is wrong. 57 My intention is supposed to institute a rule. Something must determine when it has been correctly applied. If this can only be my understanding of my intention, then following the rule is wholly subject to my discretion. I am then, Wittgenstein would say, like a person who can verify a paper's report only by checking another copy of the same paper. This is not, as can be seen, a problem about how others would verify that I'm following a rule, although it seems counterintuitive to say that I could be following a rule while acting in a way others consider bizarre, i.e., that I could justify to others my idiosyncratic application of a rule by saying 'this is how I intended to apply it'. No, this is a logical point, one about the "grammar" of rulefollowing . The problem lies in the necessary conflation of following the rule and thinking one is following the rule. Never mind others, in my private "language" I could determine I was following the rules only by seeing whether I thought I was following the rules. In #258 he fleshes out this idea: Let us imagine the following case. I want to keep a diary about the recurrence of a certain sensation. To this end I associate it with the sign "S" and write this sign in a calender for every day on which I have the sensation.- I will remark first of all that a definition of the sign cannot be formulated.- But still I can give myself a kind of ostensive definition. - How? Can I point to the sensation? Not in the ordinary sense. But I speak or write the sign down, and at the same time I concentrate my attention on the sensation-and so, as it were, point to it inwardly.- But what is this ceremony for? for that is all it seems to be! A definition surely serves to establish the meaning of a sign.- Well, that is done precisely by the concentrating of my attention; for in this way I impress on myself the connexion between the sign and the sensation.- But, "I impress it on myself" can only mean: this process brings 58 it about that I remember the connexion right in the future. But in the present case I have no criterion of correctness. One would like to say: whatever is going to seem right to me is right. And that only means that here we can't talk about 'right'.20 Here Wittgenstein describes what it would be like to try to use a private language. His case is of someone who wants to keep track of the times he has a sensation by "associating" the sign "S" with it. Each time he has this sensation he will "write this sign in a calendar." What is associated with this sign, the experience that occasions the writing of it, however, will be known only to him. It will be privately defined in the sense that no publicly visible criterion will be given for its occurrence. His "(concentration of his attention) on the sensation" will be the only way to get in touch with it, know what its like. But this action, according to Wittgenstein, is superfluous: it is not a case of learning a standard. For, with only what he thinks is this sensation to give him when this sensation occurs, there is no sense in talking about right or wrong applications of "S". One cannot learn how to use a sign where "whatever is going to seem right. . .is right." Thus Wittgenstein concludes that a private sensation language is impossible. Again, where the only arbiter of success can be 'what one thinks is successful', we have a situation in which rule-following is not possible, senseless. A necessary condition for rule-following is a standard of success (in following rules) that is independent of 'what one thinks is successful', i.e., a standard that one can fail to be in accord with. One cannot fail to follow a rule 59 where what it means to follow it can be given only by 'what one thinks is following if. Finally, he ties the discussion together in #256 by specifying what essential component of language is lacking in a private "one." Let us imagine a table (something like a dictionary) that exists only in our imagination. A dictionary can be used to justify the translation of a word X by a word Y. But are we also to call it a justification if such a table is to looked up only in the imagination?- "Well, yes; then it is a subjective justification."- But justification consists in appealing to something independent.-"But surely I can appeal from one memory to another. For example, I don't know if I have remembered the time of departure of a train right and to check it I call to mind how a page of the time-table looked. Isn't it the same here?"- No; for this process has got to produce a memory which is actually correct. If the mental image of the time-table could not itself be tested for correctness, how could it confirm the correctness of the first memory? (As if someone were to buy several copies of the morning paper to assure himself that what is said was true.)21 To begin with, it will not do to reply to Wittgenstein that "we can be right or wrong, though, perhaps, we can't tell which we are. So what?" For if there is no conceivable way to test whether or not one is right or wrong, then it is senseless to talk of correctness. If all one has to go on in determining whether or not one is following a rule is 'whether or not one thinks one is following a rule', then it is not possible to follow rules. Rule-following requires objective standards: standards with which an individual can fail to be in compliance. One cannot fail to comply with the "standard" 'what one thinks is correct'. But, again, rule-following implies meeting standards that are not wholly discretionary. 60 The test, which, if passed, would legitimate a claim of rulefollowing has to be done according to objective standards. If the time table in the above example were not something written down in a public place, it would not make sense to speak of verifying one's recollection of a train's departure time. If all I had to go on here were my memories, there would be nothing for me to be correct about. My memories can't make themselves correct, they can be correct only if there is something of which they can be true. Thus correctness requires objective standards, whether it involves following rules or being truthful. Where we can't test our judgements by objective standards, there is nothing about which we can be correct. In a private "language" one would not have the resources to speak about correctness. A private language has no "independent" standard of correct use. That is why "whatever is going to seem right . . . is right," when it comes to applications of its terms. That is to say, to the individual attempting to use a private language his thinking he is obeying a rule is the same as his obeying it. But this is to Wittgenstein's mind a wholly unsatisfactory state of affairs: we do not ordinarily equate thinking that something is right with its being right. The purported user of a private language would have to make this eq"ation because it would be wholly 'up to him' what correctness is. Given the unteachability of his "language," he can be the only arbiter of success in applying it. One, who believes that there can be a question of whether 'his thinking he is following a rule' really is 'following a rule', is thinking that there is another 61 arbiter of success here. But if this were the case, the language would no longer be private, i.e., unteachable; for others could meet this standard. Thus the defender of the possibility of a private language is faced with a dilemma: either he makes his standard of rulefollowing unteachable to others, in which case 'following the rule' must be conflated with 'thinking one is following the rule', or he can deny this conflation has to be made, in which case he commits himself to there being a determiner of following the rule besides the individual's judgement which means the language is no longer unteachable, private. Given the many cases where one thinks one is right but subsequently is proven to have been wrong, we believe we must allow for a distinction between the concepts of being right and thinking one is right. In contexts where this distinction could not be made, such as in a private language, Wittgenstein rightly believes "that . . . we can't taik about 'right'. " It is not just that a private linguist could not prove that his application of a term is right; but also that there is no way he could wind up wrong, since 'what he says is correct' is the only thing that can be correct. Every application of the term, which he says is correct, has to be regarded as correct, since no one else's understanding of its training base can be brought to bear. Given the equivocality of his training bases, he can only refer to what he thinks is right when making his judgements: how to go on from the training base is left solely up to him. But an independent, objective standard is needed here, according to Wittgenstein, so that there is at least the possibility 62 of him being wrong. There cannot be rule-following where what it means to follow a "rule" would be to do what one thinks is following the rule. But such a possibility is lacking in a private language. A private linguist's word is the sole criterion of success so that he cannot be wrong. But this situation is analogous to one where a fighter could win a boxing match simply by raising his hand. And just as we would say there is no sport of boxing where this is so, we can rule out the possibility of language where there is no criterion of correct use besides a single person's word. The skeptical paradox showed us that there is no non- relational property of a training base that makes it a guide. That is, there is no property a training base has independently of its relationship to other things that makes it a guide. To make a training base a guide we needed to refer to one of its relational properties, viz., how human beings would take it. This property could not be had by a training base of a private language. The only pertinent relational property it could have is how its one and only student takes it. But as we've just seen having this property is not enough to make it a guide. Thus a training base of a private language could not institute a language. Ultimately the Wittgensteinien criticism of a private language boils down to the Wittgensteinien criticism of the individual disposition theory of meaning: it lacks the normative element essential to language use. One should not ask here 'in virtue of what is it true to say that the community knows how to go on?' For the community's practices are not justified by what facts obtain. That they are the standards 63 for correctness is not made true by anything. They are to be judged solely on the basis of their utility. So it is in virtue of the utility of its practices that the community can be said to know how to go on, i.e., set the standard for correctness. This is not to say, however, that 'it is true the community knows how to go on'. For this could be said only if it was the obtaining of a fact that justified the community's practices, besides being useful. Moreover, there could be no fact/standard, obtaining independently of the community's understanding, by which to assess the community's practices for truthfulness. For any standard of correctness has to have its significance determined by the community: we have to decide how to apply it in particular cases. Thus one can not get away from human understanding playing a roie in determining how to follow a rule by positing standards obtaining independently of human judgement, i.e., over and above 'how we do things'. Again, our practices should be used because they are useful, not because they correspond to the truth. The community's practices are neither truthful nor untruthful. What they can provide, however, is a rule-following standard to which individuals must adhere to be rule-followers. And it was the problem of determining how an individual could follow a rule--what his guide could be-with which we were wrestling. This theory, however, should not be taken to imply that the last living speaker of a language has no language. For he couM, on this theory, have a language if his practices were such that we could understand them, if only we'd survived to try to engage in them. 64 Here is how other writers view the private language argument, first Kripke: Let me, then, summarize the 'private language argument' as it is presented in this essay. (I) We all suppose that our language expresses concepts-'pain', 'plus', 'red'--in such a way that, once I 'grasp' the concept, all future applications of it are determined (in the sense of being uniquely justified by the concept grasped). In fact, it seems that no matter what is in my mind at a given time, I am free in the future to interpret it in different ways-for example, I could follow the skeptic and interpret 'plus' as 'quus'. In particular this point applies if I direct my attention to a sensation and name it; nothing I have done determines future applications (in the justificatory sense above). (Kripke, p. 107) Here the private language argument is seen as an extension of the skeptical paradox to sensation language: at the time someone "directs (his) attention" to a sensation, there is nothing in his mind that would justify the later applications he could make of the term with which he designated said sensation. Nothing about his direction warrants thinking about any future sensation that it is the same as the one upon which his attention was directed. To find what would warrant judgements of sensations being the same we must, according to Kripke, consider something beside an individual's private acts: Instead we must consider how we actually use: (i) the categorical assertion that an individual is following a given rule (that he means addition by 'plus'); (ii) the conditional assertion that "if an individual follows such-and such a rule, he must do so-and-so on a given occasion" (e.g., "if he means addition by '+', his answer to '68+57' should be '125'"). That is to say we must look at the circumstances under which these assertions are introduced into discourse, and their role and utility in our lives. (3) As long as we consider a single 65 individual in isolation, all we can say is this: An individual often does have the experience of being confident that he has 'got' a certain rule (sometimes that he has grasped it 'in a flash'). It is an empirical fact that, after that experience, individuals often are disposed to give responses in concrete cases with complete confidence that proceeding this way is 'what was intended'. We cannot, however, get any further in explaining on this basis the use of conditionals in (ii) above. (Kripke, p. 108) We get nowhere, on this view, "as long as we consider a single individual in isolation." For everything he says and does in using terms is compatible with his actions being haphazard. He may be "disposed" to use his terms in a certain way, he may have "confidence" that he is following rules in doing so, yet his behavior for all that could be capricious. This applies in particular to his naming of sensations. Kripke doesn't stress it but what this boils down to is Wittgenstein's point that in a private language whatever seems right is necessarily conflated with what is right. With nothing in his mind at the time he initiates his "practice" to justify the later applications of its term, all an individual has to go on is 'what he's inclined to do'. But this leaves his practice, as Kripke says, without a "justificatory element." That one is disposed to do something doesn't not justify him in doing it. To put a justificatory element in his practices he must be able to include them in the context of a community's doings. In other words, his dispositions must accord with those of other human beings: (4) If we take into account the fact that the individual is in a community, the picture changes and the role of (i) and (ii) above becomes apparent. When the community accepts a particular conditional (ii), it accepts its contraposed form: the failure of an individual to come up with the particular responses the community regards as right leads the community 66 to suppose that he is not following the rule. On the other hand, if an individual passes enough tests, the community (endorsing assertions of the form (i)) accepts him as rule follower, thus enabling him to engage in certain types of interactions with them that depend on their reliance on his responses.22 A community can give a justificatory element to linguistic practices by being the judge of what is rule-governed behavior, by providing with its judgement a way for an individual to distinguish what seems right to him from what is right. We can then have rulegoverned practices because there is agreement in our community regarding what is following a rule, because individuals do not differ in their judgements of what is guided and what is capricious. Were there not such agreement, the individual could gain nothing by consulting his fellows. Terming of sensations can be done, on this view, because a community can judge whether or not such a practice is rule-governed by observing "the individual's behavior and surrounding circumstances," the publicly visible criteria associated with sensations, that go along with having them. Kripke calls this a "skeptical solution" to the "going on" problem because he does not think that it provides a fact of the matter of guidance. I disagree with him here because I believe 'that an individual is going on from training as his fellows would' is the fact of the matter to guidance. That is to say, to the skeptic, who wants to know what justifies one in applying a rule as one does, one can cite the fact that one is going on from said rule's training as anyone who took it would, adhering to the way one should go on from said training- the standard of correctness. Training guides in virtue of the fact that there is a way anyone would go on from it. The conventional way of going on 67 from one's training becomes, then, the guided way of going on from it; of all the ways one could go on from it, it is the way of following the rule in whose application the training is supposed to be a guide. The public practice initiated by a rule's training is how said training points to guided applications in that this practice gives how one follows said rule, the way one should go on from said training. Next we have Pears' version: If we go into the matter more deeply we shall see that Wittgenstein's second private language argument is derived from the fundamental premise that there must be tension between language and the world. We shall also see that his first private language argument is derived from the same source.23 What Pears means here by "there must be tension between language and the world" is what I've been referring to as the necessity of distinguishing between seeming right and being right. There would be no tension between language and the world, according to Pears, if whatever seemed right had to be taken as right, i.e., if there was no way what seemed right could be wrong. That a private "language" does not offer a way that 'what seems right' could be 'wrong' makes it lack the essential justificatory element of a language. It does not offer such a way because there is nothing in a solipsistic world besides 'what its inhabitor judges to be the case vis-a-vis the realization of his intentions' to determine whether or not his intentions have been accorded with. It needs a way to distinguish seeming right to a person from what is right because according with an intention- following a rule- is a practice where success matters and what seems right, we know, can 68 be wrong. One could conduct an activity in random manner. But in a private language one would have to take this as following a rule, since what seems right can't be taken as randomness if "whatever seems right is right." One, who would reply to this that "at best a private language does not offer a way to test" whether or not one is following a rule, has missed Pears' point. It is not just that an individual can't verify whether or not he is according to a standard of rule-following. The problem is that in a private language there is nothing by which anyone could make this judgement-there is no standard of rulefollowing . For how to apply a rule could be settled in a private language only by 'what its "user" thinks is following the rule', since no one else could understand him. But 'what one thinks is following the rule' can not be a standard for rule-following: such a "standard" lacks a justificatory element. One cannot justify a claim of rulefollowing by saying 'I think I'm following the rule'. Thus in a private "language" there could not be the materials out of which to construct a proper standard of rule-following. An opponent of Pears must show that this claim is false, not suggest that there is a standard of rule-following for a private language against which, unfortunately, the individual "using" said language can't measure his performances. Finally we have Professor Wright's view: The leading suggestion about the PLA in (my book, Wittgenstein as part of the considerations about rule following: an argument, essentially, that the sort of objectivity of meaning necessary if we are to think of the truth values of unconsidered, uninvestigated statements as determinate independently of any investigation we may carry out, can find 69 no refuge in the situal'on of a single speaker and his idiolect.24 We cannot make our judgements of following a rule "objective," Wright is saying, if we leave ourselves with only the resource we would possess were each one of us unable to communicate with others. We think of judgements of rule following being true or false independently of what one may think is the case regarding one's practices, that something makes them true besides what one thinks is the case. But in a private language 'what would make something the case' besides 'what one thinks is ihe case' is lacking. As shown above, there is no way in a private language to construct a proper standard of rule-following, no criterior whose meeting one could cite as justification for following a "rule" as one did: 'I think I'm applying it right' won't suffice. Thus, there would be no way we could think of the truth-values o* other judgements as "determinate independently of any investigation we may carry out." If what one means by 'red' cannot be objectively determined then 'that something is red', i.e., 'that something is what one means by 'red" cannot be objectively determined either- it will be a factual judgement that is subjectively determineo, based solely on what one thinks. 'What is red' becomes here 'whatever one thinks is red'. For this reason Wright rejects on Wittgenstein's behalf the idea of a private language. The idea these interpretations have in common is also shared by my reading: since he is unable to distinguish between seeming right and being right, a private linguist cannot have in his idiolect the normative element essential to language use. 70 Of course, the private language argument has been met with skepticism in some philosophical circles. Why does an individual need to be able to teach his language to others before he can communicate to himself with it?, certain philosophers have asked. I will discuss two views that are representative of this position. Each asserts a different trait as that which enables an individual to use a private language. Alan Donagan argues that an individual's "memory" is sufficient for allowing that individual to correctly term sensations without reference to a community's practice. Referring to #258 he says: But Wittgenstein did not deny that some of the recollections of players of the E-game can be independently tested. Cartesians might therefore argue that nothing prevents a player of the Egame from forming the general concept of recollection as true or false, and from applying that concept to his recollection of what sensation he was recording when he wrote down a particular sign. Wittgenstein would presumably disagree. But on what ground? Unverifiability of given recollection does not entail that it is pointless to think of it as true or false.25 What is asserted here is that despite the fact in a private language others can't verify the veracity of its user's recall of how he meant to term a sensation, the individual can use his own memory to keep his practice coherent, rule-governed. He can use his memory in keeping this practice coherent, even though he cannot independently test whether or not he's correctly applying his sensation terms, by applying a concept of correct remembrance he's gained in another context. He will succeed in this endeavor just in 71 case the sensations he terms 'S' are the same as the sensation he originally termed 'S'. Donagan rejects the "grounds" Wittgenstein would offer against this assertion, saying "the unverifiability of a given recollection does not entail that it is pointless to think of it as true or false." But, Wittgenstein would stick to his guns. He would ask: what does it mean to have the same sensation as before?. To Donagan's reply that it means to have a sensation that is the same as the one previously had, Wittgenstein wouid counter: what will determine what counts as the same sensation? The previous discussion of the equivocality of training bases makes it clear that nothing about the sensation itself makes it point to another sensation as the same as it. It's not as if a future sensation could announce itself as the same one previously had. To suggest here that there are "natural kinds" of sensations would be to beg the question 'what is a natural kind?'. We've already shown that this question can be answered only be reference to how someone would go on from a training base: there is nothing about a training base considered in social isolation that dictates how it is to be used. Thus it will not do to assume that nature dictates by itself how sensations are to be grouped. Thus, whatever the individual, who is instituting a private sensation language, thinks is the same sensation as one previously had must be considered the same sensation. But then this does entail "that it is pointless to think of (this individual's assertions regarding what is the same sensation) as true or false." Where no distinctions can be drawn between what one thinks is true and what is true we cannot talk of 72 right and wrong judgements. That is to say, where it must be left up to a single individual to decide what it means to follow a rule, we cannot conceive of rule-following. Rule-following essentially involves reference to a public practice. An individual who could not teach his language to others, given the possibility of randomness, cannot be thought of as a rule-follower. This does not rule out a factually private language, however, because all it requires is that it is possible for one to teach his language to others, not that one actually be able to do so. If Robinson Crusoe's rescuers would understand his language, then he is using one, even though in his current situation he can't teach his language to anyone. Donagan thinks that the factuality of the original sensation, the would be private linguist's training base, is enough to lend objective currency to a public language. It is simply a matter of remembering how it was. But this is not enough. For the only criterion here for remembering what it was like is what the would be private linguist thinks is remembering what it was like. If he says a particular sensation is like the one he had before, then all that could be said is 'he has remembered what it was like'. But, again, to have to conflate remembering aright and thinking one has remembered aright is to have to dispense with the concept of correct recollection. That is why Donagan's model of a private sensation language fails to hold water. One can still ask: is the concept of correct remembrance one has taken from another context being correctly applied in the one at hand?. If it is only the individual who can decide, we cannot even make sense of the question. 73 Much the same can be said of a recent criticism of the private language argument by Simon Blackburn. It is Blackburn's contention that through a responsible attitude towards a practice one could privately conduct it in a coherent manner. He writes: How can this attitude be appropriate? A technique is something that can be followed well or badly; a practice is something in which success matters . Now in the usual scenario, the correctness or incorrectness of the private linguist's classification is given no consequence at all. It has no use. He writes in his diary, and so far as we are told, forgets it. So when LW imagines a use made of the report (e.g., to indicate the rise of the manometer) he immediately hypothesizes a public use. He thereby skips the intermediate case where the classification is given a putative private use. It fits into a project--a practice or technique-of ordering the expectation of recurrence of sensation, with an aim at prediction, explanation, systematization, or simple maximizing of desirable sensation. To someone engaged in this project, the attitude that whatever seems right is right is ludicrous. System soon enforces recognition of fallibility.26 That is to say, Blackburn does not see why a careful person could not successfully engage in the terming of sensations without reference to a practice besides his own. After all, such a person has a stake in maintaining the integrity of his practice. But Blackburn, like Donagan, fails to see the focus of Wittgenstein's criticism. Just as his criticism of Donagan's position did not depend on the fallibility of memory, so his charge against Blackburn needn't involve discrediting an individual's claims of conscientiousness. The private language argument presents a logical problem, not simply a problem regarding human shortcomings. The idea of rule-following is at odds with the idea of a subjective 74 standard, i.e. whatever seems right is right. And in a private language they must become synonymous. This is the logically unacceptable state of affairs that leads Wittgenstein to reject the idea of private language. To say that an individual can be careful or has a good memory does not take make this state of affairs any more tenable from a logical point of view. Be he as careful and as sound in memory as a person can be, a solitary individual cannot lend any currency to the notion of foilowing a rule besides seeming to follow a rule. Thus Blackburn has not proven that a private language is possible. One should not think I've begged the question here. I am not assuming that in a private language there could be no distinction between randomness and rule-following I've given a proof of it. What is the only standard to which the user of a private 'language" could appeal in trying to decide how to follow a rule? What standard would my opponent think said user is following? Training bases are equivocal considered in social isolation: by themselves they can't tell one what to do in a particular situation. Thus it must be in virtue of one of their relational properties that they guide. In a private language the only relational property a training base has is how its user would apply it. Thus, in a private language how to follow a rule is necessarily settled by how its user would apply it. That is to say, the only standard to which the user of a private language could appeal in trying to decide how to follow a rule is 'what he thinks he should do'. But it is absurd that one's only standard for following a rule should be 'what one thinks one should do to follow it'. Thus a private language is impossible. In saying this, I've not failed to address Blackburn's point. I realize that he thinks the user of a private language can come to recognize cases of error. But I still ask: 'what is his standard for deciding when an error has been made?'. Granted that the user of a private language would transcend the "attitude that whatever seems correct is correct": how could he get beyond having only his judgement to rely upon when it came time to decide how to follow a rule? (Italics mine) He couldn't overcome this limitation. Thus, though he could doubt himself several times over in trying to decide how to follow a rule, in the final analysis what he thinks is following said rule is following said rule. There is nothing else by which this decision can be made. So his applications are correct because they are made according to the only standard of correctness: 'what he thinks is correct'--by being his applications. But his leaves the defender of private languages in no better shape than he was in before "the individual (struck) back." This Blackburn has not aided the cause of those who believe in private languages. The most serious objection to the community disposition theory comes from Kripke. He cites several passages to support "(taking) Wittgenstein to deny that he holds such a view."27 I will discuss each in turn. Kripke first cites a passage from Remarks on the Foundations 76 "Does this mean, e.g., that the definition of the same would be this: same is what all human or most human beings . . . take for the same?"28 But the next sentence in this remark belies Kripke's claim that this remark is a denial of the community disposition theory. For of course I don't make use of the agreement of human beings to affirm identity. What criterion do you use, then? None at all.29 That is to say, in defining 'the same' I make use of certain examples that function as its ostensive definition. But, though I do not point to human agreement that these things are the same, it is this fact that allows my examples to be a guide, an ostensive definition. What Wittgenstein would want to distinguish here is an ostensive definition from what allows it to function as a guide. That what allows something to function as a guide, viz., human agreement, is not shown as a part of that guide does not tell against the community disposition theory. For it is not a theory about what guides should be; it is a theory about makes guidance possible. Same is what makes all or most human beings take for the same. But the phrase 'what all or most human beings take for the same' can't not function as an ostensive definition for 'the same'. For this purpose one needs examples of sameness. The above mentioned phrase happens to refer to these examples, but this is only because there is agreement amongst human beings regarding what is the same, viz., said examples. It is only by identifying these examples with what allows them to function as a guide that Kripke can take Wittgenstein to be denying the community disposition theory. 77 That is to say, Wittgenstein cites the fact that human beings agree regarding the training for and application of 'sameness' as what makes it possible for this term to be defined and applied according to a rule. This is the community disposition theory: so, to correctly apply this term one needs to apply it to what all human beings would call 'the same'. This theory, however, does not entail that one defines 'sameness' as 'what all or most human beings take for the same'. Wittgenstein has said elsewhere that definitions must ultimately involve more than rephrasings. One ostensively defines 'sameness'. Nevertheless, one needs something else here: something to determine how one's definition is to be used, something to make it applicable. This, as stated above, is the way in which all human beings would use it. Kripke, I maintain, is confusing the definition, examples, with what makes it usable: the fact that there is a way in which all human beings would go on from the training for 'sameness', i.e., that there are things that are what all human beings take for the same. To someone who would ask here 'can't we be wrong about what is the same?', I would reply 'no'. For this question presupposes that there is a fact of the matter of sameness over and above our usage of 'sameness', a predetermined way of applying this term-a practice whose correctness is given by facts we do not establish. I deny that there could be any such practice, since all facts need their applicability determined by how someone would apply them. Even if such facts were waiting to guide us, which is empirically false, we 78 would still need to figure out what to do with them-what they were telling us to do. Thus no practice could have its correctness given by facts requiring no interpretation: how to go on from an instance of training is determined by said training in virtue of someone's understanding of what it tells one to do with it in particular cases. What counts as the same could not be determined independently of how we would go on from the training for sameness. Thus we should dispense with the notion that there is a fact of the matter of sameness over and above our usage of sameness; since the necessary condition for the obtaining of such a fact, viz., that something be able to guide one in its use without being interpreted, could net hold. Nothing could relieve one from having to decide how a rule applies to a particular situation. No training could make such a decision for one. What rule says to do is determined by how it is to be applied in particular situations. Thus, what decides how a rule is to be applied in particular situations determines said rule's meaning. Thus no training by itself, whether it be facts established independently of how we use language or our own more modest methods, could determine the meaning of one's training, i.e., how a rule is to be applied in particular situations. We must look, then, to the relational properties of one's training to find its import: how someone decides it should be applied will yield its meaning. Given the private language argument, our theory maintains that this someone is the community. But someone who would ask 'can't the community be wrong in deciding how a rule should be applied?' believes that the community could be wrong 79 because it has not adhered to facts that decide by themselves how a rule should be applied. Thus, since we have shown that there could be no facts of this sort, the answer to this question is 'no': what could make the community could not obtain. However, on our view, the community's practices aren't right either: as Wittgenstein says, they are just the way we do things. This should not be taken to mean, though, that ti.„ community can't be deceived about whai it shouid do: the community can be unclear about the facts. Nevertheless, it would not lack justification for its application of a given rule to them as they appear. Its error should not be described as a failure to comply w!!h a standard that determines, independently of human judgement, what correctness is. There could be no such standard. Rather, it should be regarded as a nrsperception of the facts. They have complied with the only standard there could be for applying a rule: according to whether or not things appear to them to bs such t.,ac said rule applies. The problem is that things have turned out to be other than they originally appeared, not that they've misunderstood the standard for said rule's application. Much the same can be said of Kripke's reading of the i,< d passage. He cites: Certainly the propositions, "Human beings believe that twice two is four" and 'twice two is four" do not mean the same.30 Though the two propositions are defined differently, this does not mean that the truth of the former is not what makes 'dance possible. What humans agree upon on vis-a-vis the answers to 80 addition problems and what addition is do not have to be defined in the same fashion for human agreement to be the fact of the matter of guidance. In fact, Wittgenstein later states in the same passage the community disposition theory. But what would this mean: "Even though everybody believed that twice two was five it would still be four"?- For what would it be like for everybody to believe that?-Well, I could imagine for instance, that people had a different calculus, or a technique which we should not call "calculating". But would it be wrong? (Is a coronation wrong? To beings different from ourselves it might look extremely odd.)31 Thus, this remark can't be cited as evidence against reading Wittgenstein as a proponent of the community disposition theory either. For in it, he gives voice to the view that the question of how a technique is to be practiced is to be settled by referring to how the community, in which it is a technique, would practice it. Wittgenstein is reacting here against the view that a community, whose practices are odd according to our standards, is necessarily "confused" or doing something wrong. He believes this view is based on the mistaken assumption that there is a standard besides utility by which a community could justify its practices. There could be no such standard, Wittgenstein maintained, because any standard of rule-following requires someone to be the authority in determining how it is to be applied in particular cases. No training considered by itself is unequivocal vis-a-vis how it is to be applied to a particular case. Thus someone, who posits a standard of rule following that transcends how the community would go on, must explain what 81 decides how the standard is to be applied in particular cases, what singles out from all the ways one could go on from said "standard" the way in which it should be applied. The private language argument proves that the individual can't single out how one should go on from a standard. The community is the only source left. Thus Wittgenstein concluded that it was pointless to speak of standards of rule-following that transcended how a community would go on from the training for its practices. The people who calculated differently than we do, therefore, would not necessarily be wrong, though their practice would remain unjustified in our eyes until such time as they could demonstrate to us said practice's utility: how we could use it. Finally Kripke cites #240 and #241 as evidence against my interpretation of Wittgenstein. #240, far from being evidence against the community disposition interpretation, actually favors such a reading, it says human agreement-"(that) people don't come to blows over (rule-following)," is constitutive of guidance, "is part of the framework on which the working of our language is based . . ." Thus it refers to the fact that there is uniformity in how people apply rules as something upon which language use depends. That is, what the community is disposed to do, go on as one from the training for its rules, is cited by Wittgenstein as the basis from which language develops, and, thus, what makes it possible for one to justify using language as one does. One can justify how one applies a term, e.g., by referring to the fact that one is applying it as one's community is disposed to apply it. Clearly, then, this remark is intended by Wittgenstein to support the view that the 82 communitf's disposition plays a fundamental role in making language possible. #241 is the remark in which Wittgenstein distinguishes between the framework for making judgements and the veracity of individual judgements. Agreement is needed in "forms of life," but not all "opinions," for there to be judgement at all. That human agreement does not determine truth, does not mean it doesn't play an essential role in the framework of our language. It is only when "explanation has come to an end" that human agreement is the sole criterion for rightness of judgement. Wittgenstein did assert this and #241 is only his way of distinguishing between this view and what is constitutive of truth in cases where explanation has not come to an end. Thus #241 also fails to support Kripke's position. That is, for there to be truthful judgements there must be meaningful statements. For there to be meaningful statements, there must be agreement in a number of cases vis-a-vis whether or not terms have been applied according to a rule. This agreement constitutes our "forms of life": the "opinions" shared by all people, e.g., that 7+5=12', that 'stab wounds are painful, that 'the sky on a sunny day is blue' etc. These forms are basic to our understanding of how concepts should be applied. We use them to 'get at the truth'. But the truth is not necessarily what most people regard as the truth: for an individual may have at his disposal knowledge with which he could persuade the majority to change its mind, though its former view was not unjustified. 83 What cannot happen, however, is that one could be justified in opposing the public's view when one in principle could not persuade others to see the 'error of their ways'. When one's explanations have come to an end, one either adopts the community's view or is unjustified---even if someone else should come along and change the public's mind by showing wherein it had been deceived. Thus, necessarily one is following a rule if and only if one is applying it as anyone who took its training would. This is not a theory of truth, but justification for following a rule. But its establishment is a precondition for developing a theory of truth. That is what those, who bring up cases where the public has been deceived as counterexamples against Wittgenstein's view, fail to realize. For unless we can find a way to answer the skeptic, who denies one could be justified in claiming one is following a rule, we can not give a theory of truth. E.g., unless it has been determined what a justified application of 'red' is, there is no point in debating whether or not the truth conditions for applying this term have been met. If we don't know what a red thing would appear like, we can't determine whether or not a thing is really red. Failure to realize this results in counterexamples being produced that beg the question: 'what justifies one in thinking that a rule has been followed by those who 'show up' the community?'. The rule-following skeptic does not believe this question can be answered, let alone 'what is the truth?'. We have an answer to the former question: the deviant in the "counterexample" is doing what the community would do, if only it had access to his information. 84 Thus this case wold not refute our theory since it is obviously not a case where explanation has come to an end. Again, it is only in cases where explanations have come to an end where public practice determines how one should go on from the training for a rule. Out of all the ways one could go on, something must determine which way one should go on. If one can give no reason why his deviant practice should be regarded as correct, rather than the public's; if one can cite no evidence that would show the community that it has been untruthful, if not unjustified, one is not following a rule. To sum up our discussion of #241, if something appears to the community as being such that a certain concept is applicable to it, then said concept can be applied to it with justification This makes it a further question whether said concept truly applies to the thing in question. For something may appear to a community to have the features that make a concept applicable to it when in fact it lacks them. But in order to get at the truth about something, it is first required that we understand what, given its appearance, we are justified in calling it. If, as the rule-following skeptic would have it, we are "justified" by the training for a rule in calling it anything, then there is no sense worrying about what it truly is, whether what it really is makes the concept we've applied to it applicable, i.e., what we would apply to it. I will now defend the community disposition theory as a theory of guidance against the criticisms Kripke would raise against it. Kripke says the community disposition theory "would be open to at least some of the same criticisms as the (individual disposition theory),"32 He doesn't elaborate, but since he believes that there is one objection that is the most basic, we must above all attend to it. This is the objection that denies that a dispositional account can provide the necessary normative element for a theory of guidance: Our conclusion in the previous paragraph shows that in some sense, after giving a number of more specific criticisms of the dispositional theory, we have returned full circle to our original intuition. Precisely the fact that our answer to the question of which function I mean is justificatory of my present response is ignored in the dispositional account and leads to all its difficulties,33 As stated above, Kripke bases this objection on Wittgenstein's dictum that if "whatever is going to seem right to me is right . . . we can't talk about 'right ." But this objection is inapplicable to the community disposition theory. This theory does not say that whatever seems right to an individual is right. Rather, recognizing that an individual may be capricious or merely compelled to go on from a training base as he does, it posits the public's practice as the siandard for be, ng guided. Thus the community disposition theory provides, in Professor Humphries' words, "an independent current standard of fittingness." It thereby has the normative element lacking in the individual disposition theory. The individual disposition theory was faulty because it had to equate being guided with thinking one was guided. Kripke could retort that shifting the standard for guidance from the individual's dispositions to the public's practice really doesn't relieve a theory from this fault. Because then, using Wittgenstein's words, one can say whatever seems right to the public is right and hence we can't talk about right. Your standard is independent of what an individual thinks is right, the objection would continue, but is nonetheless not normative. It still depends on the inclinations of someone, albeit a large group. Wittgenstein, however, would reply that this objection does not make sense when raised against a community's inclinations.34 It makes sense to say, as Kripke dc."c, that an individual may merely be compelled to go on as he dees from a training base, so that he has no justification for his actions. Furthermore, there is the intuition that what an individual thinks he should do, cannot be equated with what he should do. But it does not make sense to say of a community that its practices are simply compulsions, when everyone in it thinks that these practices are what should be done. Also, the way a community takes its most basic definitions cannot be wrong---it is, in Wittgenstein's words, "just the way they do things." What someone who would argue against this theory must show is how it could be possible that a community could be unjustified in its most basic judgements, e.g., that '7+5=12' that 'the sky appears blue on a sunny day'. It makes sense to deny that what an individual thinks is justified is necessarily what is justified because there is another standard besides 'what op individual thinks is justified', viz., what the community thinks is justifies. What standard is someone who criticizes our theory appealing to in suggesting that a community's moves within its practices don't justify themselves? 87 If one has such a standard in mind, then he must hold that it is possible that we could be wrong in such basic judgements as those mentioned above. The skeptical problem shows that there is no nonrelational property of a training base that determines how one should go on from it. Thus, how someone takes a training base must determine how it is to be applied. The critic of Wittgenstein is, therefore, committed to the view that someone could give a reading of e.g., the training for addition, that would make unjustified the one used by all human beings. But we would have no reason for accepting such an interpretation were it proposed, rather than treating it as we would treat the practice of errant firstgrader. Thus, there could be no standard for going on from the training for addition-or, by extension, any other rule- besides public practice, which means it makes no sense to ask 'couldn't the public be unjustified?', since asking this question makes sense only if there could be such a standard. Wittgenstein's skeptic asks of each one of us 'why do you go on from your training as you do?'. Given the private language argument, no one can answer this question by himself: everyone must appeal to a standard besides 'what one is disposed to do'. Such an appeal can be made, and, thus, it makes sense to require one to make it, because there could be a standard besides 'what one is disposed to do', viz., 'what the community is disposed to do'. The community, however, has no other standard besides 'what it thinks is justified' to which it could appeal for guidance. Thus it 88 makes no sense to require it to seek justification for its practices, over and above being usable. The community could appeal to no other standard besides 'how it does things' because being able to do so would mean that what it is disposed to do is not necessarily what one is justified in doing. This implies that the community could be unjustified even in its most basic judgements, e.g., that '7+5=12', that 'the sky appears blue on a sunny day', which is absurd. Anyone who took the training for addition or the application of 'blue' in such a way that he denied the justness of the above judgements could not be understood. Thus the community's practices cannot have their justification- that they are usable-called into question, which implies that there is no standard besides 'how it does things' to which the community could appeal in justifying how one should go on from the training for a rule. Thus the community's dispositions are beyond reproach in a way that the individual's are not. It does not make sense to raise the objection raised against the individual disposition theory against the community disposition theory. Kripke's basic objection cannot be used against the community disposition theory. Kripke has another objection to the effect that the community disposition theory fails to provide a normative element in its theory of guidance. That a community's dispositions are finite and thus cannot prescribe what should be done in cases involving, e.g., extremely complex addition problems, is supposed to tell against it being constitutive of guidance.38 But we can answer this charge as well. Our project was not to give the answer to each addition problem. Rather, we wanted to know what made the answers that would be given guided ones, i.e. how one should go on. Our theory says that an answer is guided just in case it agrees with the public's practice. All we need to say about the answers to extremely complex problems is that they would be guided ones, were they given, just in case they agree with the public's practice of addition. It is true that we cannot specify what answer the community would give, since it has not given and actually never will give an answer. This does not mean, however, that what the community would do can't function as the standard of rule-following here. For there is an answer the community would give, viz., the one it would give were it given more time. What the community actually will do is finite, what it would do isn't. I shall have more to cay about Wittgenstein's philosophy of mathematics in the next chapter. But for now it can be said that the actual finiteness of a community's dispositions does not tell against the community disposition theory. Kripke's second objection, thus, also fails to show that our theory is lacking in a normative element. We have answered both of his charges. The final objection to the community disposition theory is that it leads to the "absurd" consequence that one can deduce that others exist from the fact that one means something by a given term (since to mean something by a given term one must be able to teach its meaning to others).36 Now it is of course open to the defender of the community disposition theory to bite this bullet; and on closer inspection it doesn't appear that it would be too hard to bite. Is it is 90 really absurd that one could deduce that others exist from the fact that one means something by a given term? Someone could object that since one cannot know apriori that others exist and that one must know the meanings of one's terms before one can do philosophy, one can't do philosophy a priori. But the rebuttal here can simply be: so much the worse for philosophy's status as an a priori science. But I do not wish to embrace this tactic. Instead I will argue that the absurd consequence doesn't really follow. We do not wish to deny that Robinson Crusoe could speak a language. All we maintain is that his language must be in principle teachable. But from this principle it doesn't follow that there exists others to whom he could teach his language. All he can deduce from the fact that he means something by a term is that if there were someone who requested training in its use he could give it. Actually Crusoe's situation is more precarious than that. The attacker of the community disposition theory has assumed, since he cannot believe that an individual needs to be able to teach his meanings, that Crusoe does mean something by his terms. But we remain skeptical about this. After all we haven't been taught the meaning of his terms so that we can say they are meaningful. No, all we can say about Crusoe is that if he means something by a term then he can teach its meaning to us. Unfortunately for him, that is all he can say about himself. That is to say, Crusoe could use language meaningfully but he couldn't know himself to be doing so. Ail Crusoe can do given his isolation is think he is following rules. But, as Wittgenstein stresses, to think one is following a rule is not necessarily to follow a rule. Thus Crusoe could not be certain that 91 he is a rule-follower. For certainty here requires confirmation from one's fellows. So what follows from our theory is not that if one means something by a term one can deduce others exist. Rather, what follows is that if one knows that one means something by a term then one can deduce others exist. We are willing to countenance the result that Crusoe could mean something by his terms, and thus do a priori philosophy, yet be unable to prove to himself, if he were to turn skeptical, that he does. For he could direct all the arguments against a private language towards his "practices"---without a reply being available to him. "I apply the term 'coconut' to things of this kind, " he might say, holding up what we'd call a coconut. "But what proof have I that each time I do it I am applying it to things of one kind only?, or that I'm not under a compulsion here?" An answer as we have shown is contingent upon the arrival of a copractitioner of the "practice" at hand. And of course a favorable one implies the actual arrival of someone else on the scene, who can follow his practice. Thus the above mentioned resuit follows from our theory. We do not, however, regard this result as an absurd consequence,though it will seem as bad as the original one to an objector. It merely makes the philosophy of someone in Crusoe's position uncertifiable as meaningful. But that we or Crusoe could doubt the meaningfulness of his philosophy hardly seems absurd given the unusual nature of his circumstances. Certifiably meaningful discourse comes only through interpersonal communication. 92 Thus at the end of Chapter 2 it has been established that the fact to the matter of guidance is that there is human agreement about how to go on from any given training base. A training base can function as a guide because human beings are disposed to go on from it in a uniform fashion. It has also been shown that this is Wittgenstein's solution to his skeptical paradox. Finally, all objections to this theory were successfully handled, except the following. Wittgenstein argues that the way one should apply a rule is determined by how human beings would apply it. That is, how human beings are disposed to go on from one's training settles how one should go on from it. The human community's disposition, thus, sets the standard for correctness in rule-following. This view gives rise to the following questions, however. What grounds the belief that there is something specific this community will do in applying a given rule, that is, how can one be justified in thinking that human beings are disposed to agree upon how to extend a practice, so that there is something determinate with which an individual can accord before this community has decided how to apply the rule in question? What is being requested here is a fact that would play the role that salt's being composed of NaCI plays in the prediction 'all salt will dissolve'. In short, determinism must somehow be introduced into Wittgenstein's account: something must be constraining the community to extend a practice the way it does, otherwise there is nothing it was J.ôosed to do and thus nothing with which an individual could accord or fail to accord before the community acted, f"hich leads to the absurdity 93 that no one can correctly extend a practice until the community has actually settled the new case in question. Without an element of determinism in his account, Wittgenstein would be unable to answer other questions as well. First, he would not be able to account for an instructor's confidence that his pupil can go on correctly from the training he's been given. Secondly, he would not be able to provide the grounds for a pupil's belief that he's mastered his lessons to the point where he can correctly extend the practice in question without his instructor's coaching. What is missing in both cases is a basis for an ability. That is, in both cases one wants to say that someone can do something. But if there is nothing about the person in question that would enable him to perform the operation in question, then one cannot justifiably say he is able to do it. Wittgenstein, of course, would have introduced this element of determinism by reference to the findings of neuroscience. He suggests as much on page 230 of the Investigations: If the formation of concepts can be explained by facts of nature, should we not be interested, not in grammar, but rather in that in nature which is the basis of grammar?- Our interest certainly includes the correspondence between concepts and very general facts of nature. (Such facts as mostly do not strike us because of their generality.) That human beings are in general neuroanatomically identical is the basis for their being disposed to agree on how to extend a practice. In other words, there is something specific human beings are determined to do, vis-a-vis extending a practice, given that they share a brain type. We can speak of there being a disposition of 94 human beings in general because of the fact that the vast majority of them are neuroanatomically identical. This fact, one would suppose, is one of the "very general facts of nature" to which Wittgenstein attributed the development of our conceptual scheme. Thus, to answer the first question posed above, our being neuroanatomically identical makes for there being a rule-following standard- what human beings are disposed to dõwith which an individual can accord or not before his peers have actually settled the case he's handled. That there is such a disposition, one might suppose, is the result of our "form of life," to use Wittgenstein's term, becoming genetically coded. We have the brain we have because our form of life, selected for its utility, has determined our genotype. One can also refer to the findings of neuroscience to solve the other problems posed above. On the basis of his neuroanatomical identity with them, one's teachers can conclude that one will go on correctly from one's training, which has previously served to initiate others into the practice at hand. The idea is that a mechanical relationship has been discovered to exist between a physical structure, our brain, and the training involved in learning to follow rules: one's brain can be "programmed" by the training for a rule to agree with others in its application, that is, follow it. Understanding this relationship, one's teachers are justified in their belief that one will be competent in the practice for which they've provided the instruction. The pupil, for his part, can use the same reasoning to justify being confident that he will be a rule-follower. Having been given 95 the same training as others who are neuroanatomically like him and went on to become rule-followers, the pupil can proceed with confidence in extending on his own the practice at hand: he knows he is of sound mind and has had reliable training. Having relied on the empirical findings of neuroscience to provide the justification for beliefs regarding abilities, however, one is faced with what has been called "the multiple realization" problem. To wit, one would not want to deny that someone, who had mastered a certain technique, was following the associated rule simply because he was neuroanatomically different than human beings. Wittgenstein himself seems to have had this problem in mind when he said later in the passage quoted above: But our interest does not fall back upon these possible causes of the formation of concepts; we are not doing natural science; nor yet natural history-since we can also invent fictitious natural history for our purposes. The point is that what physically enables one to master a technique, develop an ability, is inessential to being master of said technique, having said ability. What one wants to say here is that one can follow a rule as long as there is something about him that would enable him to master the technique of its application. What is essential to following a rule is functioning in accord with human beings vis-&-vis its application. What is doing the functioning is unimportant. We made recourse to our knowledge of what enables us to function as rule-followers in order to explain the community's agreement and the confidence of its members regarding having the ability to follow rules. But we needn't have. What would have also 96 worked there is past agreement and success. That we have always agreed in following a rule gives one a defeasible reason to hold that we are disposed to agree; that one has so far been successful in following a rule gives him and his teachers defeasible justification for believing he has tne requisite ability. In the latter case, past agreement is being 'banked on' to justify believing there will be the agreement between the individual and the community that justifies the individual's application of the rule in question. The justification here is defeasible because of the possibility of there not being future agreement. But sustained success would make for a very strong inductive argument in favor of believing one will remain accredited. The same could be said of an alien creature: the more successful he is at employing the technique in question the more confident we and he can become in his having the requisite ability and the less sense it makes to fear he will begin to go astray. 97 Notes 1. Barbara Humphries, "Wittgenstein and Public Practice," p. 4. 2. Barbara Humphries, "What Are Meanings Like?," Il:2. 3. Saul Kripke, Wittgenstein or, Rules and Public Practice, p. 11. 4. Wittgenstein, The Philosophical Investigations. #190. Cf. also #198 and #692. 5. Ibid., #454. Cf. also #197 and 198. 6. Ibid., #201. 7. Ibid., #202. 8. Ibid., #202. 9. Ibid., #206. 10. Kripke, op oil, pp. 17-18. 11. Wittgenstein, op. cit., #207. 12. Ibid., #223. 13. Ibid., #241. 14. Ibid., #224. 15. Ibid., #242. 16. Humphries, "What Are Meanings Like?," 111:14. 17. Wittgenstein, op. cit., p.230. 18. Ibid., #243. 19. Ibid., #202. 98 20. Ibid., #258. 21. Ibid., #265. 22. Kripke, op. cit., pp. 107-109. 23. David Pears, Ludwig Wittgenstein (New Vork: Viking Press, 1986), p. xvi. 24. Otepin Wright, "Kripka on Private Language." The Journal of PhilosoDhv. 1984. p. 759. 25. Alan Donagan, "Wittgenstein on Sensation." in Wittgenstein: The Philosophical Investiaations (Notre Dame: University of Notre Dame Press, 1966) p. 340. 26. Simon Blackburn, "The Individual Strikes Back," Synthese 58 . pp. 299-300. 27. Kripke, op. cit, p. 111. 28. Ibid., p. 111. 29. Wittgenstein. Remarks on the ..Foundations of .Mathematics, (Cambridge Mass: 1967) p. 184. 30. Kripke, op. cit., p. 111. 31. Wittgenstein. Pnilosophical Investiaations. d . 226. 32. Kripke, op. cit., p. 111. 33. Ibid., p. 37. 34. Cf. Wittgenstein. Philosophical Investiaations. dd . 226-227. p. 230: Remarks on the Foundations of .Mathematics I #155. I #162, II #73. 35. Kripke, op. cit., pp. 26-27. 36. Given by Professor T. Michael McKinsey. Chapter Three: Giving the Standards of Mathematics "The two most fundamental philosophical questions to which pure mathematics gives rise", according to Crispin Wright, "(are) the apparent necessity of mathematical truths, and the nature of our apparent knowledge of them."1 In the following chapter, I will explore Wittgenstein's answers to these questions. The leading idea here will be that Wittgenstein's philosophy of mathematics is an application of his views on rule-following.2 Accordingly, mathematical sentences, like '7+5-12', are to be treated as "norms of representation," not seen as expressive of necessary truths.3 I will be defending the view that such sentences are expressions of necessary rules, not necessary truths. The correctness of these sentences stems from the fact that human beings agree that they give the way to do mathematics, that is, extend the practice of mathematics4. Their necessity is derived from the same source: human beings can not play the language game of mathematics, without becoming confused, except by the way given in the sentences they call 'mathematically correct', e.g., '7+5-12'.5 That is, the sentences human beings deem 'mathematically correct' are, according to the view I will defend, necessary rules whose necessity stems from the fact that their formulators would find it useless to calculate in any way besides the one said sentences specify for them. Having developed a "form of life" whose maintenance requires one to 99 1 0 0 calculate in the way these sentences specify for them, they are compelled upon pain of decadence to calculate in this manner. Thence arises said sentences' necessity. Instead of considering them true, Wittgenstein treats mathematical sentences as "antecedent to truth," that is, as norms of representation for making true judgements. He considered mathematical sentences to be expressions of rules for determining what is true. What can be true are empirical claims, i.e., statements about how things are. Mathematical sentences are, thus, expressions of rules for making sense of one's experience of things; they a n , to borrow P. F. Strawson's phrase, part of "the bounds of sense." Thus, mathematical sentences can not express facts, that is, what holds independently of what anyone thinks: they are the basis of factual discourse. To deny this is to allow for an infinite search for the truth, which is absurd. (What is the basis for holding mathematical sentences to be true? What is the basis for holding as true the basis tor mathematical sentences? etc.) We institute factual discourse, then, by stipulating the bounds of sense, that is, what will enable one to make sense of his experience. We must decide what is useful in determining the facts. Mathematical sentences, amongst others, give the rules that serve this purpose. E.g., the sentence '7+5-12' enables one to determine the fact that there are twelve people in a room when one knows that there are seven boys and five girls in said room, which fact one would come to know by using the rules for counting. That there are twelve people in a room is a state of affairs that might not have obtained. That is why it makes sense to 101 consider a claim describing it as a factual one: this claim could have been false without undermining the possibility of making true claims. But mathematical sentences, since they express part of the bounds of sense, could not be made true by anything-again, they give what makes truth possible. One cannot entertain the "possibility" that these sentences are false, as one would have to do if one were to determine whether or not it was realized, since to entertain possibilities is to be guided by the rules they express, as well as the other norms of representation. This is why Wittgenstein did not see mathematicians as discoverers of facts: mathematics is antecedent to truth.6 Again, to regard mathematical sentences as true is to regard mathematical sentences as descriptive of something that holds independently of what one thinks, that was realized to be true in contrast to what was realized to be false. But if this view of mathematics is correct, then it's possible that our mathematical sentences misdescribe something: we may have failed to realize the truth. But these sentences could not be conceived as possibly misdescribing something, since they allow for the possibility of description there is no possibility of them being misdescriptions. Their being misdescriptions is what can't be described, the impossibility of description: it is nonsense. Thus, there is nothing with which to contrast the "truth" of mathematical sentences; one could not realize that these sentences describe something that holds independently of what one thinks, in contrast to what doesn't holdthere is nothing to not hold here. Thus one should not regard mathematical sentences as true. 1 0 2 The salient point here is that one cannot fathom the possibility that our mathematical sentences are rot in accord with a standard that is independent of how we do mathematics. But recognizing this possibility is what one would have to do in order to regard our mathematical sentences as descriptive of something that holds independently of what we think. If the standard for doing mathematics is independent of how we do mathematics then, though we may have brought our system into accord with it, it is possible that we didn't. One would have to recognize this possibility because, if we've discovered the correct way to do mathematics, it is because we've seen that it is the correct way in contrast to other incorrect ways, which we could have erroneously selected. The problem is that such a contrast is impossible. One cannot think of their being other ways to do mathematics, which we could have erroneously selected, since thinking is, in part, not conceiving that our mathematics could be wrong- that being inconceivable. Thus, one should not think of a mathematician as someone who examines various mathematical possibilities to see which ones are realized. In particular, one should not think of her as having determined that our mathematical sentences, like '7+5*12', correspond to a standard that transcends how human beings do mathematics. For determining is, in part, given by the rules these sentences express, which she, per impossible, would be testing for veracity. I say 'per impossible' because determining, testing can't be done without that which makes them possible: that is, in part, taking, as human beings would, '7+5' to equal '12', e.g.. So taking 103 '7+5' is a rule for determining; one cannot abdicate it, which is what one would have to do to test it, and still determine things. Wittgenstein rejected the deeply entrenched Platonistic approach to the philosophy of mathematics. Numbers being abstract entities par excellence, the philosophy of mathematics seems tailor made for a Platonistic analysis. But Wittgenstein argued against this view.7 Simply put, Platonism holds that mathematical sentences are "descriptive of an external, independent reality." This realm is "abstract, changeless and what holds there holds necessarily."8 The Platonist views the mathematician as describing the abstract realm of mathematical facts in much the same way as a scientist chronicles the world of natural, contingent facts. To state that '12+5-17' is to hold that there is a fact that makes this statement true, according to the Platonist. To know this is to have apprehended the Form that gives this fact, eternal truths being given, according to Plato, by the Forms of things. Wittgenstein saw confusions arising from the adoption of this view: The dangerous, deceptive thing about the idea: "The real numbers cannot be arranged in a series", or again "The set is not denumerabie" resides in its making what is a determination, formation, of a concept, look like a fact of nature.9 Mathematicians, on this view, are not like scientists, who discover laws of nature that were in effect before being discovered. For the mathematician, there is nothing analogous to these laws. 104 What she is doing is not discovering facts that obtain independently of the -esults of her work. Rather, her work contributes to "the formation of a concept," the development of the ideas by which mathematics is done. This development is not achieved by discovering heretofore unknown facts; it comes solely from deciding upon further correct applications of the concepts with which she has been working. That 'the real numbers cannot be arranged in a series' is not a fact that was discovered. Rather, it is the result of a decision to extend the concept of real numbers to include the concept of nondenumerability. The truth of the matter is that we create mathematical reality by doing mathematics: What harm is done e.g. by saying that God knows all irrational numbers? Or: that they are already all there, even though we only know certain of them? Why are these pictures not harmless? For one thing, they hide certain problems.- The picture of God knowing all irrational numbers is harmful because it fosters the idea that there is a series of irrational numbers that exists independently of our developing it. This series is there for God to see, even though we'll never get the chance to calculate it. Two related problems arise from this idea. The first is that our calculation of the series of irrational numbers might be in error. But this would mean that, despite our best calculations, we could fail to comprehend the series of irrational series, which is absurd. We would have no reason to accept as the series of all irrational numbers a series that failed to correspond to our best calculation of 105 the series of all irrational numbers. The series of all irrational numbers could be nothing but our best calculation of the series of all irrational numbers. The second problem that arises from this picture is a mistaken view of infinity. That God can know all irrational numbers implies that infinity is something tremendously large, which is why only God can comprehend it. But that there is an infinite number of irrational numbers does not mean this; rather it means that we have a technique for calculating irrational numbers that could be endlessly applied, i.e., will never cease to be useful as long as there is someone to apply it.10 The infinite, according to Wittgenstein, refers to a possibility, not an actuality so large as to be incomprehensible to anyone but God. No being could comprehend the infinite if that means knowing the totality of that which has no end: Suppose that people go or, and on calculating the expansion of jc. So God who knows everything, knows whether they have reached '717' by the end of the world. But can his omniscience decide whether they would have reached it after the end of the world? It cannot. I want to say: Even God can determine something mathematical only by mathematics. Even for him the mere rule of expansion cannot decide anything that it does not decide for us. We might put it like this: if the rule for expansion has been given us, a calculation can tell us that there is a '2' at the fifth place. Could God have known this, without the calculation, purely from the rule of expansion? I want to say: No.11 That is to say, it is not possible even for God to survey's pi's extension as it is established independently of our calculations, 106 which would realize said extension if and only if they were reliable and we had unlimited time to carry them out, to determine whether or not the sequence '777' appears in it. There could be no independently established extension here unless pi's extension could be unintelligible to us, which is absurd. One would have no reason to accept a sequence of numbers as the extension of pi if said sequence could not be shown to have been produced by our method of calculating pi's extension. That we could calculate an extension to be the extension of pi is the only way for an extension to be the extension of pi. Thus, God could determine whether or not '777' appears in pi only by extending pi as we would. Thus, the training base for addition, e.g., must be treated like any other training base. Its directions, what it guides people to do, is given by the way people normally take it. Thus the foundation for addition, is what provides for the agreement amongst human beings regarding the way one should go on from its training base, viz., our sharing of a brain-type and form of life. A similar thesis is to be given for other mathematical practices. In general, the standards of mathematics are given by the way people go on from the various mathematical training bases. That there is an agreement amongst people regarding the way one should take mathematical training bases is what makes mathematical rules possible. What we agre1 in doing, upon being given training for a mathematical practice, is what it is correct to do when engaging in said mathematical practice. That we are neurologically identical and share a form of 107 life is what makes for this agreement and is, thus, what provides the foundation of mathematics. What we agree in doing when we do mathematics is what must provide the standard for doing mathematics because mathematics couldn't be unintelligible to us. That is, we would have no reason to call a practice 'mathematics' unless it could be made understandable to us. And if we couldn't call a practice mathematics, then it couldn't be mathematics, if it was mathematics it could be justified as such. But making the standard for doing mathematics transcend how we would do mathematics, as in Platonism, requires accepting that mathematics could be unintelligible to us, which is impossible. After all, if the standard for doing mathematics transcends our practice of mathematics, it is possible that the two fail to correspond, so that, e.g., it would be incorrect to say "7+5' equals '12". But this is unintelligible: a standard of mathematics could not be such that it would require us to abdicate practices we could not give up, e.g., having '12' as the sum of '7+5'. Since such a standard requires the doing of what for us is impossible, we would have no reason to regard it as providing for correctness. And what we could have no reason to regard as correct would have no reason for being correct. Thus we would have no reason think what such a standard would entail-that our practices are incorrect. To disallow the possibility of being faced with such a thought, the standard for doing mathematics must therefore be 'how we would do mathematics'. 108 Here is Wittgenstein formulating this theory, which has been called "conventionalism": £!• 190. It may now be said: "The way the formula is meant determines which steps are to be taken". What is the criterion for the way the formula is meant? It is, for example, the kind of way we always use it, the way we always use it, the way we are taught to use it. We say, for instance, to someone who uses a sign unknown to us: "If by "x!2" you mean x2, then you get this value for y, if you mean 2x, that one."-Now ask yourself: how does one mean the one thing or the other by "x!2"? That will be how meaning it can determine the steps in advance. In this remark we are given what makes for the standard of mathematics. It is the behavior most human beings have in common. Our regular, habitual employment of a concept, "the way we always use it," determines its significance, and thus its proper applications. If someone presents us with a sign, like '+', and gives us training for its use in calculations, then the way we go on to employ this sign in our calculations with it gives its meaning, how it should be used. That is to say, the answers we give to problems involving this sign are the only justified ones. One can mean "one thing or the other" by a mathematical term because there is a uniform way we would go on from one's training for its use. That there is a uniform way we would go on shows how it is possible for this term to have a standard, "how meaning (something by) it can determine the steps (one should take with it) in advance." One does mean to take certain steps rather than others 109 just in case one means that which we would mean were we to take said steps. And one's meaning is given by one's practice. Wittgenstein calls the uniformity of our practice of addition a "deep fact," that, though philosophically important, goes unnoticed because it is familiar; it can be taken for granted: HEMI #162 But our interest does not attach to the fact that such-andsuch (or all) human beings have been led this way by these rules (or have gone this way); we take it as a matter of course that people- 'if they can think correctly'- go this way. We have now been given a road, as it were by means of the footsteps of those who have gone this way. And the traffic now proceeds on this road-to various purposes. Here Wittgenstein identifies correct thinking with the uniform way people have thought. People who think correctly are people who follow the established public practice of thought. Modus Ponens, e.g., is to be taken as an example of correct thinking because it is a way people have come to regard as correct, indeed can't help but regard as correct, given its inextricable connection with other practices, like decision making, whose maintenance requires its acceptance. We take these 'patterns of thought' and employ them to fashion an orderly picture of the empirical world. They suit our "purposes" in making intelligible our experience. Moreover, it is "essential" to this suitability that we be able to form, arrive at such patterns: RFM . I #266 The prophecy does not run, that a man will get this result when he follows this rule in making a transformation-but that he will get this result, when we say that he is following the rule. What if we said that mathematical propositions were prophecies in this sense: they predict what result members of 11 a society who have learnt this technique will get in agreement with other members of the society? '25x25=625' would thus mean that men, if we judge them to obey the rules of multiplication, will reach the result 625 when they multiply 25x25.- that this is a correct prediction is beyond doubt; and also that calculating is in essence founded on such predictions. That is to say, we should not call something 'calculating' if we could not make such a prophecy with certainty. This really means: calculating is a technique and what we have said pertains to the essence of a technique. Wittgenstein begins here, as he does in the preceding remark, by giving following the public's practice as a necessary condition for being guided. He deduces this from the fact that we can predict that we will say someone is following a rule only if he is going on from its training as anyone who took it would. He thus makes our judgements the arbiter of success in following a rule: it is what we will say vis-a-vis whether someone has met our standards that will decide whether or not his actions are rule-governed. 'Where reasons have come to an end' human beings taken as a group could not be wrong about how to apply a rule, since it is not possible that what is unreasonable-a transcendent standard they couldn't understand-could give them reason to think they are wrong. And if they could have no reason to think they were wrong in their application, then they couldn't be wrong. An adequate theory of rule-following must entail that it is impossible that what is unreasonable could mean we are wrong. To say that 'we could be wrong where reasons have come to an end', however, entails that it's possible a transcendent standard we couldn't understand implies we are wrong in how we apply rules. 111 Wittgenstein moves from this claim to giving the significance of mathematical propositions: their meaning is to be found in the "predictions" that can be based upon them, viz., that people will get the results we've arrived at, the results given by said propositions, if we say they've calculated correctly. The certainty with which we can make these predictions is what makes them the meaning of mathematical propositions, for Wittgenstein. This leads him to say that it is of the essence of calculating-what these propositions fr^ilitate-that such predictions can be made. Unfortunately for him, he's only shown half of this claim; he's only argued for the claim that necessarily, following public practice is a necessary condition for following a rule. Indeed, that is how he parses "calculating is in essence founded on such predictions": "we should not call something 'calculating' if we could not make such a prophecy with certainty." He can support this claim by saying that in all possible worlds we would have no justification for calling something calculating if it went against our way of d:Jng it. But how can he support the converse here? I think the next remark suggests Wittgenstein would adopt a behavioristic stance: It is essential to calculating that everyone who calculates right produces the same pattern of calculation. And 'calculating right' does not mean calculating with a clear understanding or smoothly; it means calculating like this.'2 Here Wittgenstein entertains the objection that runs 'someone might be acting with all the outward signs of calculating-saying 1 1 2 the right answers to calculating questions- without really calculating'. He rejects it out of hand, however. What reasons does he have for doing so? There isn't much to go on here; but I believe Wittgenstein would have fleshed out what he does say in the following manner. What he does say is "'calculating right' does not mean calculating with a clear understanding or smoothly; it means calculating like this." I take this to mean that we should not suppose that there is a component to calculating that is not publicly visible, like "a clear understanding." That is to say, we should not think that there could be anything missing from a consistent 'giving of the right answers' that would make such a performance flawed. On this view, it is impossible that someone should consistently produce correct answers to, e.g., addition problems and not be adding. For what could the missing component be? A 'clear understanding' entertaining the right interpretation of addition's training base? But then we would have some reasons to believe that someone could be adding while not following our technique of addition. After all, we could say 'perhaps there is something we're missing here, maybe in his mind he is adding'. Wittgenstein will have none of this. For him "what is hidden is of no interest." He adopts this view because it prevents a skeptic from undermining our belief that we do go on correctly from arithmetical training bases by putting forth alternative readings of them and challenging us to prove that they are not correct. 1 1 3 That is why Wittgenstein says ir the I nvestiqations. "that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call 'obeying the rule' and 'going against it' in actual cases."13 The Platonist's theory can give no adequate answer to the skeptic because it substitutes one expression of the rule for another.14 And since the skeptic can always interpret an expression, so that it does not guide one in the manner his interlocutor sees fit, a purported rule's training base could not be cited as guidance. Thus, on the Platonist's theory, mathematics remains without a standard. What is the correct way to carry on mathematical practices is not given by anything, since a training base cannot serve as a presentation of 'how one should engage in the practice for which it is supposed to training' unless there is something about it that determines its significance. Wittgenstein prevents the skeptic from unearthing mathematic's foundation by making it a "practice," our "technique" instead of an interpretation of a training base. EJ.. 217 "How am I to obey a rule?"-if this is not a question about causes, then it is about the justification for my following the rule in the way I do. If I have exhausted the justification I have reached bedrock, and my spade is turned. Then I am inclined to say: "This is simply what I do." (Remember that we sometimes demand definitions for the sake not o4 their content, but of their form. Our requirement is an architectural one: the definition a kind of ornamental coping that supports nothing.)15 114 This remark states that the standards of our linguistic practices come from our customary ways of engaging in them. Mathematical practices are just another case of this.16 We can have a rule-governed practice like addition because there is an agreement amongst the human beings regarding how to go on from addition's training base. (Just as there can be a rule-governed practice of predicating 'red' because there is a common way of going on from the training base for 'red'.) And what we agree to do in answering addition problems is, gives us, what is correct to do when doing addition. Thus the standard for addition is what we agree to do when doing addition, i.e., the public practice of addition. Our other mathematical practices are governed by the public practices corresponding to them. Thus knowledge of mathematics involves, for Wittgenstein, doing something, viz., what is in accord with the training for the practice in question, accordance here being given by doing what anyone would do after being given said training. It does not involve "seeing" anything, in particular a mathematical fact. Knowledge in mathematics is a matter of know-how, not knowing that. Having made the standard of our practice of arithmetic our agreement in how to go on from arithmetical training bases, we say that one has only to consistently agree with us in the way he calculates to be considered calculating. But this theory is quickly attacked by many philosophers for failing to provide an adequate account of the necessity of mathematic statements.17 On the Platonist's account, the mathematician was involved in the project of discovering facts that 115 held necessarily. Thus the Platonist has no problem when it comes to accommodating the deep-seated intuition that mathematical discoveries give us necessary truths. Wittgenstein, on the other hand, states that "the mathematician creates essence."18 This seems to fly in the face of the above intuition, since what is created does not hold necessarily. We want to say that '2+5' could not possibly fail to be 7 .' But if this answer is correct only in virtue of the fact that human beings agree that this answer is in accordance with addition's training base, it does not seem to hold necessarily. Human beings could have been such that this answer would not have been deemed the correct one by them. Thus, Wittgenstein philosophy of mathematics seems to entail that mathematical sentences express contingent truths: they give how human beings as a matter of fact do mathematics. The account of wt mathematical statements are necessary truths, that can be deduced from Wittgenstein's position on rulefollowing , is that 'necessary', like any other predicate, is to be predicated of something just in case it is the community's practice to do so.19 That is to say, if human beings are agreed in believing that a given mathematical statement could not possibly be false, then it is to be regarded as necessarily true. But this makes the necessity of mathematical truths contingent upon a fact of human nature, viz. that we can't help but see these statements as necessarily true. But, again, the intuition that mathematical truths can not possibly be false has been questioned: human beings could have been such that they didn't regard them as necessary truths. 116 Wittgenstein, though, is opposed in any event to regarding mathematical rules and logical laws as genuine assertions, i.e., as having truth-value. After all, if mathematical facts are not the foundation of mathematics, as Wittgenstein contended, there is no reason to treat mathematical sentences as being used to express statements. Having lost their claim to being true assertions, Wittgenstein suggests treating them "as antecedent to truth:" REM.. I #155. Isn't it like this: so long as one thinks it can't be otherwise, one draws logical conclusions. This presumably means: so long as such-and-such is not brought in question at all. The steps which are not brought in question are logical inferences. But the reason why they are not brought in question is not that they 'certainly correspond to the truth'- or something of the sort,---no, if is just this that is called 'thinking', 'speaking', 'inferring', 'arguing'. There is not any question at all here of some correspondence between what is said and reality: rather is logic antecedent to any such correspondence: in the same sense, that is, as that in which the establishment of a method of measurement is antecedent to the correctness or incorrectness of a statement of length.20 Two points are being made here. The first concerns why certain laws are deemed unquestionable (an idea with which he replaces "necessarily true"). The laws of logic and mathematical rules are not true in virtue of the fact that they "certainly correspond to the truth." Rather "(they are) what is called thinking." They are made the laws of thought and calculating because we cannot think of thinking or calculating in a way that would run contrary to them. That is to say, we could not violate these laws and still justifiably say we are thinking or calculating. Instead of 117 being necessarily true, Wittgenstein treats them as necessarily accepted rules. It. is not lack of imagination that limits us here. We can imagine beings with a different form of life than ours doing something akin to what we call calculating, so that we could say of them that 'they have a practice that serves roughly the same purpose as calculating serves for us'. For example, we can imagine beings who would make '13' the sum of '7+5'. We could see how they do this if they also did the counting and distributing involving this rule according to a 'baker's dozen principle'. A practice like this we could call 'calculating, though it would probably prove unwieldy for us. But if we encountered behavior so bizarre that it didn't even give a usable technique, we could not call it 'calculating'. We would have no reason to do sc. E.g., were we to encounter a tribe who posited a different sum every day for '7+5', without making discernible adjustments in either their counting or distributing, without there being a pattern to their alterations, we could not say its members calculate with those signs. Such a tribe would not be calculating differently than us, it would not be calculating at all. Earlier he says: RFM . #133. The propositions of logic are 'laws of thought', 'because they bring out the essence of human thinking'- to put it more correctly: because they bring out, or shew, the essence, the technique, of thinking. They shew what thinking is and also shew kinds of thinking. 21 This corresponds to the remark made in #155 that "it is just this (logical inferences) that is called 'thinking', 'speaking', 118 'inferring', 'arguing'." We can sum all of this up by saying that Wittgenstein believed that statements that had been called necessary truths should have been termed the indispensable forms of thought. This is not to say logic is a descriptive science; Wittgenstein does believe it is a normative one. He thinks, however, that one shows how one should think by describing the technique of human thinking, i.e., by giving the propositions of logic. The second point made in #155 is that the laws of logic and mathematics are required as a basis for making judgements that are rightly termed true or false. This is what is meant by saying they are "antecedent to truth." Thus the standards of mathematics are indispensable in two senses: they are impossible to violate without ceasing to calculate and they are required as a framework for the making of empirical judgements, which are what we properly ascribe truth and falsity to. Regarding the first sense of 'indispensable', someone who would consistently maintain that '243+371' equals '615' is not just calculating incorrectly- he isn't calculating at all, unless he can produce a rationale for this procedure as the tribesmen who made '13' the sum of '7+5' did. One can calculate incorrectly only if one knows how to calculate. But, sans a rationale, someone who believed in the above "equation" would demonstrate inability to calculate. It is violations of this sort that betoken a cessation of calculating. Wittgenstein uses an analogy with systems of measurement and measuring to make this second point. The laws of logic are 119 antecedent to truth- i.e., are required for making empirical judgement- in the same way as "the establishment of a method of measurement is antecedent to the correctness or incorrectness of a statement of length." We must decide how we are going to measure objects before we can talk about how long an object is. If we decide to adopt the metric system, then we stipulate that an object is a meter long just in case it is as long as our standard meter. But that an object's length is the same as the standard meter's is not determined by the standard meter itself. Rather, it is determined by our deciding that an application of our technique of measuring with the standard meter has shown that an object is the same length as the standard meter. It is only after making this stipulation that we can talk about whether or not an object is, say, three meters long (which it will be just in case it is three times as long as our standard meter, this rule being a further stipulation of our method). That an object is three meters is something that is true or false, since it is something that could be false, i.e., could be conceived to be otherwise without abdicating the possibility of conceiving things. It can be verified by measuring the object in question. But neither this verification nor the subsequent prediction of truth or falsity would make sense without prior establishment of the method of measurement, which is itself neither true nor false. It must be stipulated how long a meter is before it can be determined what an object's length in meters is. Thus one cannot metrically measure the standard meter without changing what a meter is, since what would metrically measure the standard meter would then become what a meter is. In other words, such a 1 2 0 measuring would countermand the original stipulation of what a meter is. And since to have the practice of metric measurement we must stipulate what a meter is, such countermanding could not be continuous. Thus it is "ungrammatical" to say the standard meter has a length in meters, since to do so is to remove it from the role of being the standard meter, that by which things are metrically measured. That is to say, claims regarding the metric measurement of the standard meter are neither true nor false; rather they are nonsensical. The salient point here is that something-what a meter is- must be accepted if there is to be the practice of metric measurement. The analogy, between this situation and the one having to do with mathematical rules, Wittgenstein would draw as follows. '1+1=2', '2+1=3', '3+ 4', (and so on) are rules of mathematics; they are established as such because we could not calculate without going along with these principles. They determine how one should calculate. Further, a mathematical system that did not enjoin us to adhere to these rules could not serve our purposes: disputes would constantly arise over, e.g., how many things there were in a room, we could not take inventories (given that standardization is needed here). Thus we make these rules our inviolab e standards for counting, (just as the standard meter is our final measure for determining an object's length in meters). Now the number of people in a room is something about which one could make a true or false judgement. We will form our judgement here by counting according 121 to the aforementioned rules. If we adhere to these rules, then our resulting judgement should be termed 'true'; we will have determined the exact number of people in the room (provided that perceptual errors have not left us with skewed data upon which to perform our calculations). But this judgement, according to Wittgenstein, is not to be confused with the methods that make it possible. It can be termed true or false because there is something about which it can be true, viz., the people in the room. The rules that make it possible to form such a judgement, on the other hand, are neither true nor false, since one is not referring to facts when one uses them. They only facilitate the making of true judgements. For there to be such a judgement something-mathematical rules-must be incontrovertible by the facts. That is why in calculating one is not concerned with what is the case, but only in 'doing things right'. The justification for one's action here must come from one's agreement with how human beings calculate, not what obtains independently of their judgement. There are things that obtain independently of what we think; but we must accept a technique of ascertaining them if we are to make them out. Mathematics, especially arithmetic, is an essential aspect of that technique, which we call 'thinking'-discovering what is true. Thus we have Wittgenstein's philosophy of mathematics. Its distinguishing feature is the way it accounts for the correctness and necessity of mathematical rules in terms of the way human beings agree they should go on upon being given mathematical training. Mathematical rules are founded upon, justified by, the agreement 122 that there is amongst human beings regarding how to take what they call 'mathematical training'. These rules are necessary because we in our present circumstances can see no other way according to which we could calculate. Wittgenstein avoids the criticism that his doctrine commits us to believing mathematical rules are contingent truths by saying that it is a category mistake to predicate truth or falsity of them. Mathematical rules, he says, are antecedent to truth. To say that one has gone on correctly from a mathematical training base is not to say one's move corresponds to what is mathematically true, i.e., a standard for doing mathematics that obtains independently of our mathematical practices. Rather, it means that one is using a mathematical technique as we would use it. The key point here is that the standards of mathematics are given by the way human beings would go on from the various mathematical training bases. This is a straightforward application of Wittgenstein's theory regarding the application conditions for terms like 'red'. Wittgenstein himself believes the cases are analogous. (Philosophical Investigations, p. 226.) The necessity of what Wittgenstein terms mathematical rules, as opposed to mathematical statements, comes from the same source. For, it is not only a fact that human beings agree in the way they go on from arithmetical training bases; it is a fact that they now can't help but agreeing. We as human beings now can see no other correct way to go on from arithmetical training bases besides the ways we actually go on. Our neuroanatomical uniformity 123 guarantees this conceptual 'tunnel vision'. Therein lies the necessity of our rules. We now can use only the ones we have. That mathematical sentences, like '7+5=12', give rules and are not used to make factual claims follows from the idea that the standards of mathematics are given by human agreement in mathematical practice. If the recognition of facts plays no role in what justifies our mathematical practices, there is no reason to regard mathematical sentences as being used to state facts. Thus one should apply Ockham's razor to these "facts." Indeed, mathematical sentences couldn't be regarded as expressing facts since they are what we use to discover facts. What could be true, i.e., state a fact, could have its veracity questioned without thereby abdicating the language game of doubting. But mathematical sentences couldn't have their "veracity" questioned because they are what is needed to question the veracity of things. As Wittgenstein would put it, to question the "veracity" of mathematical sentences is to cease to play the language game of doubting by dispensing with the rules whereby this game is played: there are no other techniques for doing such questioning. Thus it is ungrammatical- a transgression of the 'bounds of sense'- to call mathematical sentences 'true'. I will now discuss other commentaries on this position. Michael Dummett has written the most influential criticism of Wittgenstein's philosophy of mathematics. He calls Wittgenstein's view "full-blooded conventionalism" and describes it as follows: Wittgenstein goes in for a full-blooded conventionalism: for him the logical necessity of any statement is always the 1 direct expression of a linguistic convention. That a given statement is necessary consists always in our having expressly decided to treat that very statement as unassailable; it cannot rest on our having adopted certain other conventions which are found to involve our treating it so. This account is applied alike to deep theorems and to elementary computations. To give an example of the latter, the criterion which we adopt in the first place for saying that there are n things of a certain kind is to be explained by describing the procedure of counting. But when we find that there are five boys and seven girls in a room, we say that there are twelve children altogether, without counting them all together. The fact that we are justified in doing this is not, as it were, implicit in the procedure of counting itself; rather, we have chosen to adopt a new criterion for saying that there are twelve children, different from the criterion of counting up all the children together. It would seem that, if we have genuinely distinct criteria for the same statement, they may clash. But the necessity of "5+7=12" consists just in this, that we do not count anything as a clash; if we count the children all together and get eleven, we say, "We must have miscounted."22 That is to say, a rule is a necessary truth just in case our community makes it so by a public fiat. Nothing we've previously done determines that said rule must be accepted on pain of being unfaithful to these established practices. That '7+5=12' is not implied by how we count things; nothing about the latter practice forces our hand in instituting the former convention. It is a new counting technique, one we could have abjured without becoming involved in a conflict of practices. Having freely adopted it, its necessity consists wholly in our deciding that nothing could justify disobeying it. Professor Dummett can not reconcile this view with his intuitions regarding necessity.23 Unfortunately, he does not give us the remarks of Wittgenstein horn which he derives his interpretation. Thus, that this 125 interpretation is unfaithful to Wittgenstein's thought is not something that can be proven by pointing out misreading of specific passages. Nevertheless, I will prove that it is a false exegesis by showing how it is at variance with several things Wittgenstein does say. It should first be pointed out that Dummett's criticism of Wittgenstein is a straw man. He makes it look, as if, e.g., '5*7' equals '12' on Wittgenstein's view, simply because we decide that this should be so, as if it were a whim on our part. But, according to Wittgenstein, there is more to it than that. '5+7' equals '12' not simply because we decide that this should be, but because we could not help but decide that this should be so: R FM . I #155. Isn't it like this: so long as one thinks it can't be otherwise, one draws logical conclusions. This presumably means: so long as such-and-such is not brought in question at all. The steps which are not brought in question are logical inferences. But the reason why they are not brought in question is not that they 'certainly correspond to the truth'- or something of the sort,- no, it is just this that is called 'thinking', 'speaking', 'inferring', 'arguing'. There is not any question at all here of some correspondence between what is said and reality; rather is logic antecedent to any such correspondence; in the same sense, that is, as that in which the establishment of a method of measurement is antecedent to the correctness or incorrectness of a statement of length.24 Dummett has left the element of practical compulsion out of Wittgenstein's account. Given that we've established practices, whose perpetuation has moulded our nature, we are compelled to continue these practices in the way we do. For what we've done and 126 thus what we are limit what is usable for us. And usability by us is the operative factor in conceptual development. This is why he thinks human beings have "freedom of choice" in following the order "add one," and thus could make 7+1" equal '9' (thus making in this situation, on Wittgenstein's account '9' the sum of '7+T).25 Here Dummett has confused fidelity to interpretations of a rule, which Wittgenstein doesn't believe in, with following our practical inclinations, which Wittgenstein regards as being unconditionally justified.26 When this regard for our purposes is included in Wittgenstein's theory it is made invulnerable to the kind of objections Dummett raises against it. '7+5' could not equal '13' because we could not help but deciding that this shouldn't be so- we could not calculate in this manner. Human beings can decide to do something only when doing so does not violate their inclinations about how to go on from a training base, which are formed by their needs and purposes. Dummett offers two cases that he believes tell against Wittgenstein's account. The first involves someone who knows how to count but doesn't, know the rules of addition. Dummett believes that Wittgenstein is committed to saying of this person that before he is persuaded to adopt the convention '7+5=12' there was nothing in virtue of which adding 7 girls and 5 boys to get 13 people was wrong, since one needn't be faithful to the convention of counting in formulating the rules of addition.27 This is what he takes a radical conventionalist to mean. But this is to confuse mathematical "facts" with the primitive practices with which adding is inextricably associated. Again, 127 Wittgenstein did not believe that the discovery of mathematical facts-standards for doing mathematics that transcend our practice of mathematics-compelled us to practice mathematics in accordance with them, if we wanted our mathematical practices to be correct. Mathematics is "autonomous," that is, "antecedent to the truth." It is not factual, rather it enables us to discover that which is factual. Factual discourse would not be possible unless there were techniques like that of mathematics. But that we needn't consider our practices like counting, which calculating is supposed to help facilitate, when establishing the practice of addition doesn't follow from this. In fact, Wittgenstein believed just the opposite: HEM I# 4. But then what does the peculiar inexorability of mathematics consist in?"-Would not the inexorability with which two follows one and three follows two be a good example?- But presumably this means: follows in the series of cardinal numbers; for in a different series something different follows. And isn't this series just defined by this sequence?-"Is that supposed to mean that it is equally correct whichever way a person counts, and that anyone can count as he pleases?" That is to say, is the "necessity" of our mathematical practices, like counting, just a matter of them being defined a certain way, so that one who refused to follow them could be accused only of being unconventional? It being merely a convention that two follows one in the series of cardinal numbers, would it also be permissible to extend this series by 'one, three, four. . .'? We should presumably not call it "counting" if everyone said the numbers one after the other anyhow; but of course it is not simply a question of a name. For what we call "counting' is an 1 important part of our life's activities. Counting and calculating are not- e.g.- simply a pastime. Counting (and that means: counting like this) is a technique that is employed daily in the most various operations of our lives. And that is why we learn to count as we do: with endless practice, with merciless exactitude; that is why it is inexorably insisted that we shall say "two" after "one", "three" after "two" and so on. It is true that the series of cardinal numbers is partially defined by the sequence 'one, two, three' and that it is human beings who have so defined it. But that does not mean there isn't inexorability associated with counting this way. For we have so defined this series because it is the only usable definition: we could put no other definition to the tasks to which we put our definition of the cardinals. Someone who differently defined this series would not have failed to accord with the facts, any more than we are in line with them. What they would be doing, though, would be something- possibly a practice that would be akin to counting depending on whether or not we could envision circumstances in which it would be usable by us-that is unusable by us and thus could not be called 'counting'. The "peculiar inexorability of mathematics" consists in our seeing that different mathematical practices than the ones we use would lead us in our present circumstances only into confusion and failure. Thus arises the insistence that mathematics must be done our way: But is this counting only a use, then; isn't there also some truth corresponding to this sequence?" The truth is that counting has proved to pay.-"Then do you want to say that 'being true' means: being usable (or useful)?"- No, not that; but that it can't be said of the series of natural numbers- any more than of our language-that it is true, but: that it is usable, and, above all, it is used.28 129 That is to say, counting and calculating are essentially related parts of our "form of life"; they are necessarily used in conjunction with each other. As such, how we do one will determine how we do the other: they must complement each other. It is mathematical "facts" that do not provide for Wittgenstein the standard of a given mathematical rule. But he has no qualms about saying such a rule must be in concordance with the practices it is bound up with in a form of life. It must be usable. So there is a constraint upon someone formulating the rules of addition: they must be usable, which they would not be if the results calculating with them yielded conflicted with the results yielded by counting. The former system is designed to facilitate the latter. So they must work in harmony. Insuring this harmony so that counting is facilitated by calculating, so that calculating is usable, provides the constraint upon formulators of arithmetical rules that Dummett thinks Wittgenstein account lacks. There could be no conflict between counting and adding because we have not allowed for it by neglecting the former in establishing the latter, not because the latter's results are always to supersede those of the former. Dummett makes it appear as if one could count correctly and add correctly and come up with disparate results, in which case one is to declare a miscount! But we have not allowed for such an occu.rence by dovetailing the practices, for practical, not practiceindependent , reasons. If there was a miscount in the situation Dummett describes, then there hasn't been an application of one of the relevant criteria, viz., counting correctly. If the criteria were distinct, on the other hand, then there couldn't be a conflict between 1 3 0 them: those employing them would 'talk past each other', as if I said a rod was a foot long because it was the length of a meter stick and someone disagreed with me because he'd measured it with a foot ruler. There can be a conflict in our arithmetical system only when one of two or more related criteria has been misapplied while the others have been correctly employed, as in Dummett's own example. Moreover, in asking Wittgenstein to make true the claim that '7+5=11' is false in virtue of something, Dummett is missing Wittgenstein's fundamental point that mathematical rules are antecedent to truth. The reason, on Wittgenstein's account, that someone is to be persuaded that it is an error to say '7+5=11' is not because there is a fact that makes it false. Rather, it is because one cannot calculate in this manner: to calculate one must accept that '7+5' equals '12'. But this is not to say that this rule is necessarily true. It is to say that is necessarily accepted, given that one wants to maintain the practice of counting, which calculating is designed to disencumber. By the time Dummett gets to his second case against Wittgenstein, he has abandoned Wittgenstein's primary thesis, viz., that the communities disposition to go in a uniform fashion from mathematical training bases provides the foundation for mathematics. Instead, Dummett posits that an individual can lay down any rule he wants as necessary. Wittgenstein's quite different idea, that one has the right simply to lay down that the assertion of a statement of a given form is to be regarded as always justified, without regard to the use that has already been given to the words contained in the statement, seems to me mistaken. 29 131 We know that nothing could be further from Wittgenstein's thought than the idea that an individual could justifiably maintain that a rule was acceptable in the face of the objections of all his peers. The "law" in Dummett's example, Wittgenstein would reject as necessary, given that the "lawgiver's" community rejects it. Thus this case can not be used to show that Wittgenstein's account allows us to treat undecidable statements as necessarily true. The intended upshot of Dummett's cases is that Wittgenstein's view allows us to treat unnecessary statements as necessary and necessary statements as unnecessary. The former can occur because we could decide to treat any law as necessary. Pick any statement, if human beings decide it is necessarily the case, then, intuitions notwithstanding, it is necessarily the case. The latter happens because it does not seem to follow from Wittgenstein's view that the contradictions of necessary statements could not have been the case. After all, human beings could have decided to treat them as what should be held. Necessity, which is supposed to be unshakeable, is seemingly made, on this view, to stand on what could be shifting ground. Barry Stroud agrees with this interpretation of Dummett's criticism- that Wittgenstein seems to make what should be impossible possible- and sets out to show how Wittgenstein could explain what makes the denial of necessary rules "impossible" or "unintelligible."30 I will now compare his defense of Wittgenstein with my own. 132 Professor Stroud defends Wittgenstein by showing how, on Wittgenstein's theory, it is possible for human beings to posit unconventional ways of inferring, calculating, and counting without being able to understand them.31 Stroud must show how such positing is possible in order to preserve Wittgenstein's antiPlatonism . He must show that its results are unintelligible in order to explain wherein the necessity lies in Wittgenstein's account. His paper is an attempt "to say what, according to Wittgenstein, is responsible for the unintelligibility in (unconventional ways of inferring, calculating arid counting)."32 In showing that Wittgenstein can be successful in giving examples of how calculating, counting, and inferring could be otherwise while still maintaining that there is logical necessity in our rules, Stroud will refute Dummett's claim that Wittgenstein, in giving such examples, is committed to a radical conventionalism: the doctrine that "we could (infer, calculate, and count) any way at all,"33 i.e., the doctrine that, as Dummett puts it, "a statement is necessary (because we have) expressly decided to treat that very statement as unassailable."34 Thus Stroud agrees with me that Dummett's criticism of Wittgenstein is a straw man. Stroud believes, as I do, that there is more to Wittgenstein's account of necessity than the fact that human beings decide to treat certain statements as unassailable. The element that needs to be added is what will allow Wittgenstein to say the above mentioned examples are unintelligible, so that our rules can be seen, on his account, as necessary. This element, according to Stroud, is our "shared judgements," or "natural reactions" to the training given for the 1 3 3 understanding of rules.35 Once this element is added to Wittgenstein's account of necessity, it loses the unwanted leeway it afforded our decisions regarding what is necessary, since, as Stroud puts it, "our 'shared judgements'. . .are not properly seen . . . as the results of free decisions."36 This idea corresponds to what I've called the fact that "we can't help but going on in the way we do from a rule's training base," which happens to be in a uniform fashion. I also cite this element of Wittgenstein's theory to vitiate the intended force of Dummett's criticism.37 The leeway that precluded Dummett's Wittgenstein from saying our rules are necessary, given the alternatives to them, is not afforded in the interpretations just mentioned. On them it is the fact that we can't help but deciding to see certain statements as necessary that is the foundation of necessity. Wittgenstein, however, is not seen here as a Platonist given that his examples do show, in Stroud's words, "that calculating, counting, and inferring... might have been done differently."38 But this possibility does not entail that we don't necessarily calculate as we do, since we now have no choice in the matter. "The formation of concepts different from the usual ones is intelligible to us; but does not follow from this that those concepts themselves are intelligible to us."39 It is contingently true that we calculate as we do. But given that we calculate in the way we do because we can't do it any other way, the intelligibility in alternative ways decreases so that we can't help but seeing our ways as necessary: Those described as not "playing our game" are the people who are not in accord with us in the "judgements" on which the 134 possibility of language and communication rests. Wittgenstein's examples of the possibility of people like this serve to bring out the contingency of the fact that as things are, we are in accord in these "judgements." Anyone who did not go on as we do need not be simply continuing a different series (far example, "Add 2 up to 1000, 4 up to "2000," and so forth), and in that way be "playing a game" different from the one we happened to be playing; nor need he have understood the instruction in a way that can be pointed out to him by more careful explanations. But someone like this would not be fully intelligible to us. Our relation to him would be like our relation to people who naturally reacted to the gesture of pointing by looking in the direction of the line from fingertip to wrist, O' who sold wood in the way described earlier.40 Were we, e.g., to try to calculate according to the rule '7+5*13' we would have to also abdicate our usual way of counting. This we could not do. We can not count something that isn't there to be counted. It goes against our practice of counting. Thus Stroud agrees with me that Wittgenstein is not averse to the principle that calculating rules must be faithful to our way of counting. The latter is the more basic practice and to violate it is to make things unmanageable, which is what we can't do in extending practices. Thus Stroud shows how Wittgenstein can posit his antiPlaton ist examples while maintaining a coherent account of necessity. The examples can be posited because given that it is a contingent truth that we calculate as we do, we can imagine other ways of calculating. The coherent account of necessity comes from the position that though we can imagine other ways of calculating, we can't conceive of how we could now calculate in any way but the way we do. In fact, its not very clear that we can call alternative 135 ways of calculating "calculating." We can't rule out the possibility, but neither can we embrace it. Hence our rules become necessary. But this position doesn't leave our practices without a foundation, Stroud concludes. For the only foundation we could appeal to is our "shared judgements," i.e., the fact that "this is the way we do things."41 We can not justify our rules by appeal to Platonic facts, but they do not need such justification. And "to use a word without (such) justification is not to use it wrongfully."42 Our practices are not developed whimsically. We can not help but extend them as we do. Their foundation is our nature and the fact that they work.43 Crispin Wright, in his book Wittgenstein On the Foundations _of Mathematics, discusses these issues in a chapter entitled "Radical Conventionalism."44 Like Dummett, Wright states that Wittgenstein needs to avoid being committed to radical conventionalism. On the other hand, Wittgenstein's account of necessity cannot, Wright says, posit that necessary statements describe necessary facts, whose recognition by us leads to the statements describing them being called necessary.45 Thus Wright agrees with the present writer that Wittgenstein repudiated Platonism but did not want ascriptions of necessity to be the results of arbitrary decisions. Radical conventionalism, according to Wright, entails that "there is no security of conduct in certain areas," viz., when it comes to ascribing necessity.46 Like Dummett he believes that such a lack of security "entails a risk to the possibility of communication."47 136 Wright, however, takes exception to Stroud's claim that Wittgenstein succeeded in giving examples of alternative ways of calculating, inferring, and counting. Wittgenstein's anti-Platonistic view that truth should not be predicated of necessary statements is generated, according to Wright, by the rule-following considerations alone.48 That is to say, it is not the possibility that beings could calculate or infer differently than we do that gives rise to Wittgenstein's anti-Platonism. Rather, it is the view that there are no practice-independent truths determining the correct way to go on from the training bases for these practices that makes Wittgenstein deny that truth can properly be ascribed of necessary rules. Here is Wright's argument against Stroud's claim: Just because the essential role of inferential principles, on Wittgenstein's view, is to further determine the assertabilityconditions of contingent statements, even where these have received an antecedent explanation, there is no possibility of identifying as such a community who infer statements of which we have a correct interpretation by means of alternative, and doubtless- as it seems to us- invalid rules; unless they are suitably often disconcerted by the results and feel compelled to look for errors in their assessments, direct or theoretically inspired, of the truth-values of premises and conclusions. If they do, we can retain some confidence that we understand the statements which their principles of inference take them from and to; but the effects of this confidence is that we shall describe them as inferring invaiidly. In other words, once we think we have learned to communicate with a group of beings, if they begin to infer bizarrely, then we must either be ablt* to convince them of the error of their ways or give up the idea that we have been understanding them and that they are 137 inferring. We cannot countenance bizarre inferring and still think they use a language: All the examples by which Wittgenstein attempts to give the fourth strand concentration- the soft-ruler men, the wood sellers by zero, the men who count zero, the men who 'count' taking objects twice over, those who 'fancy' that (a+b)2 - a2+b2, those who infer via contradictions- turn out, if we press for detail, to de-stabilise in one of these two directions depending on how the fuller story goes. It will not do blandly to suggest, like Stroud, that we can understand the possibility of an alternative methods of inference non-constructively; that is, without it being in principle possible to construct intelligible examples. If Wittgenstein thought we could understand the suggestion in that way, it is hard to see what his objection would be to the claim, for example, that it is a possibility both that '550' does not occur in rc and that no demonstration can be given; or that our perceptions of colour could differ in radical but behaviourally inconsequential ways.49 Wittgenstein's cases, Wright says, can be interpreted in this way. And an interpreter cannot simply say here that they may be inferring or calculating, as the case may be, even though we don't understand them, given that Wittgenstein thought use gave meaning. Their doings cannot be seen as practices; we must view these people as 'going about things the wrong way'. Whether or not Wright is correct here, however, will turn on what is meant by "intelligible examples." If they must involve practices we could assimilate into our form of life, then Wright will have refuted Stroud. If, however, they could involve practices we couldn't assimilate into our form of life, although we could see how they could fit into another, then Stroud's position will have been defended. I will argue for the latter alternative. 138 It is hard to see why Wright would hold this view given that the rule-following considerations lend themselves nicely to the positing of alternative ways of going on from the training bases for inferring and calculating. The reason there could be more than one direction being issued from a training base is that there could be no practice-transcendent, Platonic standard that would make one and only one way of going on from it the correct way. Strictly speaking, 'correct' and 'incorrect' are predicable only to moves within a practice, not to practices themselves. A practice is either intelligible or not, depending only on whether or not human beings could follow it. That we would find a practice usable, even if in our present form of life we would have no use for it, suffices to make it intelligible, rational. Wittgenstein's anti-Platonism and his positing of alternative ways of going on from a training base go hand in hand. Wright's argument for this view is that a field anthropologist has two ways he can think about a strange way of "inferrinr he can reject it as a way of inferring if its practitioners are going from known truths to known falsehoods and can be persuaded to change their ways or he can reject it as a way of inferring if its practitioners are going from known truths to falsehoods and will not change their ways. The field anthropologist must have an understanding of a large part of his subjects' language, according to Wright, before he can determine whether or not they are inferring.50 One can question, though, whether a field anthropologist can simply dismiss his subjects' practice as not a case of inferring, if he cannot make them change their ways. Wright thinks that not 139 doing so precludes the anthropologist from thinking that he has understood their language at all. That is, he would have to give up too many of his interpretations of their statements' truthconditions to say he has grasped the meaning of their utterances. But it may be the case here that he has not understood their practice, but they infer "validly" with it. Why, if the subjects are not disconcerted by the anthropologist's assessment of their inferential practice as unworkable, must it be the case that there is no inferring going on here? What is needed here is a context in which to situate the practice in question. When such background information is provided what seemed nonsense may become intelligible, if not useful to us. For example, the above subjects may refuse to draw the conclusions of arguments cast in Modus Ponens. This refusal may appear nonsensical until the anthropologist discovers that they do it on the authority of a revered ancestor who was financially ruined by the loss of a large wager he'd made on the basis of the conclusion of an unsound instance of Modus Ponens. They have come to mistrust this form of reasoning, though they employ others with which we are fam iliar. Now the anthropologist here may attempt to explain, on the basis of the practices he shares with his subjects, the difference between validity and soundness. But his explanation may prove to be of no avail in convincing them to conditionally accept the conclusions of arguments cast in Modus Ponens. Are the subjects inferring here? Certainly we would have a problem in describing it as such; but this reluctance should be seen 140 as a function of our understanding of our purposes in reasoning, not a standard of reasoning transcending ali purposiveness. Given this view of the matter, however, our reluctance becomes indefensible: the subjects are more concerned with avoiding the fate of their unlucky ancestor than in reasoning "correctly." Wittgenstein does say that "the common behavior of mankind is the standard by which to asses whether or not someone is inferring."51 It does not, however, mean that those who do not conform to our standards aren't inferring at all. It just means that we can't hold them to our standards for inferring. Instead, we must take their training for "inferring'' to see how one should go on from that. If there is regularity in their practice, that is, if it's done as we would given their training, then we might want to call their practice 'inferring', albeit of a different order than ours. This determination will be made according to the degree of similarity between our practice and theirs, that is, to use Wittgenstein's term, according to whether or not there is a "family resemblance" between these practices. Those who would engage in an alternative form of reasoning, like the one described above, should be held to the standards that have been made out for it, not our practice. Correctness and incorrectness are applicable only to moves within a practice, not "across" practices or to practices as a whole. Thus, we could not necessarily dismiss the above anthropologist's subjects as irrational, since their practice as described above meets the only standard for being rule-governed: it is done according to how we would go on from its training base. We can thus avoid Wright's 141 dilemma that either we give up our belief that they are inferring or our confidence that we've understood the meaning of their utterances. There is a third alternative: they are drawing inferences from their statements according to an alternative form of reasoning. We may not be able to fit this form of reasoning into our form of life, but, as Stroud points out, that is neither here nor there when it comes to assessing its usefulness for creatures having a form of life that is different than ours. Going on to criticize Wittgenstein's positive account of necessity, Wright next states that "what is amiss with radical conventionalism is the suggestions that the decision involved in our ratification of new necessary statements are wholly arbitrary."52 This, as I've already argued, is as it should be: our decisions regarding what is necessary can't be arbitrary if they are necessitated by something. Moreover, when they are made they do not seem to be avoidable. Thus an acceptable conventionalism must show how our decision regarding what is necessary are necessitated, but not posit recognition of necessary facts as the compelling factor. Wright believes Stroud's interpretation of Wittgenstein tries to follow this line: Logical necessity is not like rails that stretch to infinity which we must follow in only one way, but neither is it the case that we are not compelled at all. There are the rails we have already traveled, and we can extend them beyond the present point only by depending on those that already exist; for the sake of navigability they must be extended in smooth natural ways-how they are to be continued is to that extent determined by the route of the rails already there.53 142 This is the iine of interpretation I've been advocating: what we've done in our practices will constrain us in how we extend them by making certain extensions more useful than others. We must extend a practice in the way that is usable by us. Necessity enters the picture when there is only one extension that is usable by us, when what we've done affords us only one way of continuing a practice- when not going said way would involve beginning a new practice. But Wright does not think this view meets the requirements for an account of necessity, as it affords those deciding what is necessary a measure of freedom they don't in fact have: A critic will ask: what is this idea of guidance being contrasted with on the other side-do we ever not have the freedom which is supposed to originate in the gap between guide and verdict here? We could give an affirmative answer to this question, indeed the situation would fit Stroud's picture quite well, if the concept of valid inference had a measure of flexibility; the kind of situation the picture brings to mind is that of a judge aiming at a fair sentence. Our judgement of the validity of an inference would be a judgement in the same sense-a guided choice with the force of further precedent for future occasions. We should thus have a responsibility to ensure that it cohered with previous judgements, that it combined with them to form a manageable set of precedents. That is to say, drawing the conclusion of a valid argument, on Stroud's view, is akin to adjudicating a legal matter according to precedent. In each case, the judgement is made so that the practice remains coherent, i.e., usable. It is necessary to make each judgement in order to maintain the workability of the practice of which it is an extension. 143 Such a picture, however, founders on the simple fact, acknowledgment of which is a precondition of talking sense about necessity, that when we make such a 'judgement', we cannot in general point to respects in which our verdict seems discretionary. If we could, the inference would seem to us to fall short of full cogency at just the places where discretion operated. There seems to be no vagueness in the idea of valid inference-at least for inferences mediated by specific rules. Nor, therefore, is the freedom, which the conventionalist needs to indicate, to be understood in terms of the model of guidance by inexact criteria. It cannot be plausibly claimed that the concept of a valid inference has the same sort of flexibility as that of a fair verdict.54 What Wright has in mind here is that once a group accepts, e.g. Modus Ponens, as a valid argument form it cannot, on pain of violating its own rules, refrain from ascribing validity to any argument that is an instance of this form. That Wright believes such a group has no discretion when it comes to making such an ascription undoubtedly stems from his rejection of the possibility of alternative ways of going on from the training bases for inferring. But, as we've seen, alternatives can be made out, albeit ones we wouldn't follow, given that they wouldn't serve our purposes in inferring. That is to say, Wright believes that the analogy between drawing the conclusion of a valid argument and adjudicating a legal matter according to a precedent does not hold, given that in drawing the conclusion of a valid argument one does not feel that one has any leeway of the sort a fair-minded jurist possesses. The problem here is that Wright has mislocated the source of a jurist's discretion. Once a judge decides to adjudicate a case according to a specific precedent, he really doesn't have any leeway 144 in giving his verdict. When he can use his discretion, of course, is in deciding by which precedent he will adjudicate a case: in determining which precedent fits the case at hand. In the same way, one who decides to argue according to, say, Modus Ponens, has, as Wright asserts, no discretion in drawing the conclusion that follows according to that rule. That is to say, it is not unconditionally necessary that that conclusion be drawn; it is necessary if and only if one decides to argue according to the rule of Modus Ponens. What conclusion should be drawn according to this rule is settled by 'what human beings would infer' by it. The justification for drawing the conclusion one should draw using Modus Ponens is 'that is how we use this rule'. One could, however, choose to go on differently than we would from the training for applying Modus Ponens. Then one would institute a different practice just in case we could follow what one was doing, even if it was a technique we could not employ within our form of life, like the one discussed above in connection with Wright's "anthropologist." Thus, just as a jurist has some discretion in deciding by which precedent he will adjudicate a case, one has a measure of leeway in choosing by which rule he will reason. If one chooses not to draw the conclusion dictated by the rule of Modus Ponens, that could only be because one has opted to employ another method of reasoning or not to reason at all. What one cannot reasonably do, however, is opt to use Modus Ponens and not draw the conclusion we would draw from using it, just as a jurist cannot decide to adjudicate a case 145 according to given precedent and deviate from the verdict it provides. Thus, the analogy between drawing the conclusion of a valid argument and reaching a legal verdict based on precedent does hold after all. Contrary to what Wright asserts, a jurist has as much leeway in reaching a verdict as one drawing the conclusion of a valid argument. In each case, one can either 'play a game' according to its rules, in which case there is something one must do in order to be reasonable, or abandon said game in favor of playing another, in which case it is not necessary that one does what the rules of the relinquished game dictates. Thus, Wright has not succeeded in showing that Stroud's exegesis of Wittgenstein's views on necessity is indefensible. These views should be seen as conventionalist in the following sense. Wittgenstein believed that human beings selected their "norms of representation," influenced by practical concerns, making them how things must be. (Things must be such that '7+5=12', e.g., we won't count '7+5=13' as a description of how things could be in our system of describing.) Here is the origin of necessity. Secondly, 'which norms of representation are rejected and which ones will take their place' is conventionally decided, though here too our hand is forced by practical considerations, especially those related to the maintenance of our 'form of life', which developed via the use of the original norms and upon which we've come to depend. Necessity is again a part of our thought. Finally, how one should apply a norm of representation is conventionally determined. That is to say, what situations are to be 145 according to given precedent and deviate from the verdict it provides. Thus, the analogy between drawing the conclusion of a valid argument and reaching a legal verdict based on precedent does hold after all. Contrary to what Wright asserts, a jurist has as much leeway in reaching a verdict as one drawing the conclusion of a valid argument. In each case, one can either 'play a game' according to its rules, in which case there is something one must do in order to be reasonable, or abandon said game in favor of playing another, in which case it is not necessary that one does what the rules of the relinquished game dictates. Thus, Wright has not succeeded in showing that Stroud's exegesis of Wittgenstein's views on necessity is indefensible. These views should be seen as conventionalist in the following sense. Wittgenstein believed that human beings selected their "norms of representation," influenced by practical concerns, making them how things must be. (Things must be such that '7+5=12', e.g., we won't count '7+5=13' as a description of how things could be in our system of describing.) Here is the origin of necessity. Secondly, 'which norms of representation are rejected and which ones will take their place' is conventionally decided, though here too our hand is forced by practical considerations, especially those related to the maintenance of our 'form of life', which developed via the use of the original norms and upon which we've come to depend. Necessity is again a part of our thought. Finally, how one should apply a norm of representation is conventionally determined. That is to say, what situations are to be 146 understood in terms of a given norm is deciaed by how we would go on from the training for said norm's use. In all of these decisions we are nowhere constrained, in order to make the correct ones, by standards that obtain independently of our thought. Nevertheless, our decisions are not arbitrary given that we were originally constrained by the necessity of forming a usable system of thought whose employmert has formed our nature and fostered thereby a form of life to which we are practically committed. In this sense our choices are necessitated. Thinking that he has refuted Stroud and, thus, that Wittgenstein is left "calling into question the very idea of logical cogency," Wright next states that Wittgenstein does not reject the notion that we must make certain moves when inferring.55 It is just the "standard picture," of this constraint originating from recognition of practice- independent facts, according to Wright's, that Wittgenstein rejects.56 But Wittgenstein, then, according to Wright, owes us another account of our warrant for accepting conditionals like "if you are to infer correctly, then you must go along with this step" To be a conventionalistic account it must have room for an element of decision in our acceptance; it can't be forced upon us by necessary facts whose recognition makes us see that there is only one correct decision to be made. On the other hand, as Wright states, this decision must be such that "concurrence in (it) is no less secure th?n our general disposition to agree in linguistic practice."57 That is to say, the decision to agree that something is necessary must be as unanimous and predictable as our agreement in the making of 147 everyday empirical judgements, although the latter but not the former will involve the "recognition" of something being the case. Wright, however, believes that Wittgenstein never did pay this debt. He does not believe there is any more to Wittgenstein's account of necessity than the negative point that rule-following is not a matter of according with practice-independent facts. Now, why precisely will this account of the inter- independence of necessary statements not serve conventionalist's purposes? Well, what the conventionalist needed to make out was a notion of guided decision. The whole point of invoking the concept of decision is lost if there is nothing to contrast it with. It has to be the case that acceptance of the conditional articulating Black's options is something which we choose, although the choice is guided and informed. That is to say, Wright questions whether the doctrine that in positing necessary statements we do not have to take into account practice-independent facts can be used as a premise for conventionalism. For there seems to be no compelling decisions involving following a rule with which one could contrast a "guided" decision like that of accepting a necessary conditional of the form 'once the rules of chess have been stipulated as X, then a player must make move Y in this situation': But this conception is not made good just by pointing out that our 'choice' is answerable to no ratification-independent facts concerning correct application of the rules of Chess. For the same point, if we accept the rule following considerations in general, holds for absolutely every judgement which we make, every contingent judgement is in this way a new judgement: there are no objective truths as yet unrecognized by us dealing in the judgements which we ought ideally to make if we correctly apprehend the world and apply our concepts properly. 1 The mutual independence of grammatical propositions, so interpreted, is just a special case of the mutual independence of all judgement. But now we have no significant contrast between our acceptance of the conditional about Black and our agreement about any new contingent judgement if either is a guided decision, it seems, then both are. The notion of decision is id lrg .58 In other words, judgements regarding what is empirically true are no different than judgements of necessity, in that neither involve recognition of facts laid down independently of our use of language, i.e., in neither case are we constrained, in order to be correct, by realized possibilities that could have been the case no matter how our linguistic practices developed (as if said practices in no way determined what could be the case). Wright believes that the impossibility of drawing such a contrast makes for a vacuous conventionalism: there should be some distinction between making a judgement of necessity and determining what is contingently true but, with regard to being constrained by practice-independent facts, they are the same. Thus, the "autonomy of grammar" doctrine does not cash out in conventionalism. Wright, as discussed above, rejects the idea that drawing the conclusion of a valid argument is like reaching a fair legal verdict by reasoning according to precedent. I have argued that there is an analogy between them given that in each case one is being constrained by a rule to do one thing rather than another if one wants to follow it. In this way, I removed the element of "discretion" from judgements of necessity that Wright believed made for insecurity vis-a-vis agreement concerning what is necessary: we can be as confident of agreement in this area as wo 149 Gan when it comes to deciding what is contingently true, thus meeting one of Wright's conditions for an adequate account of necessity. Wright also believes that the idea of grammar being autonomous- i.e., not being answerable either in its selection or application to practice-independent facts- must issue forth in a distinction between judgements of necessity and determinations of contingency. Wittgenstein, however, did not see this idea as having such a consequence. Quite the contrary, he asserted that neither judgements of necessity nor determinations of contingency are required to be in line with practice-independent facts: they are answerable only to the rules according to which they were made. One is necessitated in drawing the conclusion that follows by Modus Ponens, if one wants to use this rule, only by 'how one should use Modus Ponens', that is, by how human beings would reason according to Modus Ponens. In the same way, one is necessitated in describing an apple as 'red', if one wants to report its color, only by the rules for the use of our color vocabulary. The contrast Wright is looking for between what is conventionally determined, i.e., settled as the result of a guided decision we've made, and what is forced upon us doesn't exist, according to the conventionalist. For the conventionalist argues that there could be no practice-independent facts the recognition of which would force us, if we wanted to be correct, to develop any of our linguistic practices one way rather than another. Thus it is question begging on Wright's part to require the conventionalist in stating conventionalism to provide for this contrast. That we must 150 decide upon not only what is necessarily true, according to our rules, but also what is contingently so, given said rules, does not make vacuous a conventionalist account of necessity. The distinction one wants to draw here is between the selection of norms of representation and the application of said norms in particular circumstances, that is, between the determination of the rules for playing our language games and the decisions made in the course of attempting to play said games regarding which moves are in accord with said rules. The "autonomy of grammar" thesis emphasizes, contrary to what Platonists have thought, that the former decisions could not be made under the obligation of 'being in accord with the (necessary) facts'. Wittgenstein was attempting to point out here that it could only be practical requirements that informed such decisions. 'Given our purposes, is this practice usable?'--this question could be the only one to which we must find an answer in determining the worth of said practice. The decisions regarding how to extend a practice, on the other hand, are also to be made only so as to meet practical demands. But here the demands are of a different order than those influencing the choice of having such a practice to extend, use: they involve the maintenance of said practice, that is, keeping it usable. Finding practices that are usable versus maintaining them: with this distinction in mind one can explain the association of necessity with practices like that of Modus Ponens or our color vocabulary. For in deciding how to maintain a practice we can see how we could have been brought to make different decisions: it is 151 easy here to determine <vhat things would have had to have been different so that drv ssions different than those we are making would be warranted. But things are not so clear when it comes to seeing just how we could have selected practices different than those with which we chose to work. It is not obvious at all how we could dispense with Modus Ponens, Modus Tollens or even our color vocabulary in favor of alternative practices. That is why the selection of these practices seems grounded by what is necessarily true, whereas a particular application of, say, our color vocabulary seems justified only by what is contingently the case. That hockey pucks are lighter in color than baseballs- that seems eminently conceivable. That black should be lighter than white-that seems impossible. Yet, according to Wittgenstein, the selection of our color vocabulary is no less conventionally determined than our decision to, as things stands, call hockey pucks 'darker than baseballs'. For only those who would use something can determine if it's usable at all and by them and how it's to be kept usable by them once they've chosen to use it. A technique must suit their purposes and limitations, actual or possible. And that it be usable is the only qualification for being a language. To sum up my critique of Wright, there is more to W.agenstein's view of necessity than the negative point that practice-independent facts could not dictate how we should follow a rule. Wittgenstein provided an extensive defense of the positive view that our acceptance of conditionals of the form 'if you are to 1 5 2 follow the rule, then you must do this' is necessitated by our need to maintain our form of life. Here I agree with Stroud. Wright states that "there must be every practical reason to expect agreement about whether a particular such c" 'itional is acceptable." Wittgenstein's account of necessity draws cn the fact that there is general agreement about the acceptability of such conditionals and that, given our common nature that is a function of our sharing of a form of life, there is every practical reason to expect it to continue, providing the foundation for talk of necessity: Disputes do not break out (among mathematicians, say) over the question whether a rule has been obeyed or not. People don't come to blows over it, for example. That is part of the framework on which the working of our language is based (for example, in giving descriptions).59 Thus Wright should not conclude that Wittgenstein has failed to provide an adequate account of necessity. According to Wittgenstein, certain moves in our language games are forced upon one given that our form of life does not provide us with a way we could play said games without making them. And we can no more give up playing said games than we can abdicate being human. This completes my exposition and defense of Wittgenstein's philosophy of mathematics. To reiterate my view, I see Wittgenstein treating what had been traditionally called the necessary truths of mathematics as necessary rules. These rules, according to Wittgenstein, are antecedent to truth in that they provide for a technique for making what are properly called true judgements, viz., true empirical claims. The necessity of these rules is explained by Wittgenstein via a reference to the fact that 1 5 3 there is one and only one usable way for us to go on from said rules' training bases. Critics like Dummett, who claim that Wittgenstein makes what seems necessary the result of an arbitrary decision, are to be referred to the fact that given our nature and the past practices responsible for its development, we can see only one correct way to count, infer, or calculate. Though it is contingently true that we have the nature we do, the practices that stem from our nature are not capricious: our nature and history compel us to decide to calculate and infer as we do. I call this philosophy of mathematics "naturalism."60 154 Notes 1. Crispin Wright, Wittgenstein on the Foundations _of_ Mathematics (Cambridge, Mass.: Harvard Univ. Press, 1980) p. vii. 2. This interpretation is advanced by Wright, op. cit, as well as Backer and Hacker in Wittgenstein Rules. Grammar and Necessity, pp. 3-24 and passim. 3. Wittgenstein, Remarks on the Foundations of Mathematics. Part I #133 and #155. Backer and Hacker, op. cit, p. 205. 4. Wittgenstein, Philosophical Investigations. #190; Remarks on the Foundations of Mathematics. Part I #266. 5. Wittgenstein, Remarks on the Foundations__of Mathematics, Part I #134 and #135, Part II #29 and #30, Part III #29, #30, and #31. 6. Arguments like than can also be found in Wittgenstein: On Certainty, by Thomas Morawetz. 7. Ibid., pp. 3-20. 8. Ibid., p. 3. 9. Ludwig Wittgenstein, Remarks on the Foundations of Mathematics. (Cambridge, Mass.: The M.I.T. Press, 1956) p. 56. 10. Backer and Hacker, op. cit, pp. 197-198. 11. Wittgenstein, Remarks on the Foundation of Mathematics, p. 185. 12. Wittgenstein, Remarks on the Foundationsof Mathematics, p. 46; p. 94; p. 180; Philosophical Investigations, p. 77. 155 13. Wittgenstein, Philosophical Investigations, p. 81. 14. Ibid., p. 81. 15. Ibid., p. 85. 16. Wittgenstein. Remarks on the FoundationS-flLMathfiHialiga, P3 (#4). 17. Cf. Michael Dummett, "Wittgenstein's Philosophy of Mathematics," in Wittgenstein:ThePhilosopMcal, Investigations, ed. by George Pitcher (Notre Dame: Univ. of Notre Dame Press,1968); Wright op. cit, p.205. 18. Wittgenstein, Remarks on theJFoundations of Mathematics, p. 13. 19. Ibid., p. 45 #155; p. 77 #27 + #28; p. 3 #4. 20. Ibid., p. 45. 21. Ibid., p. 41. 22. Dummett, op. cit., pp.425-426. 23. Ibid., pp. 426, 429, 435. 24. Wittgenstein, Remarks on the Foundations of Mathematics. p. 45. 25. Dummett, op. cit., p. 428. 26. Wittgenstein, Philosophical Investigations, #190, p. 77; Remarks on the Foundations of Mathematics. I #4, pp. 3-4. 27. Dummett, op. cit, pp. 430-431. 28. Wittgenstein, Remarks on the Foundations of. Mathematics, pp. 3-4 cf. also Remarks on Jhe FQundations of Mathematics, I #9, p. 6. 29. Dummett, op. cit., pp. 434-435. 156 30. Barry Stroud, "Wittgenstein and Logical Necessity" in Pitcher, op. cit, p. 478. 31. Examples of such unconventional ways are given in RemarKS-OU, the Foundations oLMathematLcs. I, 136, 139,152, 168; II, 76, 78, 81, 84; III, 15, 17; IV, 5; V, 6,12, 27, 29, 36, 42, 43, 44. 32. Stroud, op. cit., p. 478. 33. Ibid., p. 490. 34. Dummett, op. cit., p. 426. 35. Stroud, op. cit., pp. 491-493. 36. Ibid., p. 493. 37. Page 117 above. 38. Stroud, op. cit., p. 493. 39. Ibid., p. 493. 40. Ibid., p. 492. 41. Ibid., p. 493. 42. Wittgenstein, Remarks on the Foundations of Mathematics, V, #33. 43. Stroud, op. cit., pp.493-494. 44. Crispin Wright, op. cit, pp. 364-386. 45. Ibid., pp. 374-375. 46. Ibid., p. 374. 47. Ibid., p. 373. 48. Ibid., p. 379. 49. Ibid., pp. 377-378. 157 50. Ibid., pp. 377; 378-379. 51. Wittgenstein, Philosophical Investigations. #206. 52. Wright, op. cit., p. 379. 53. Wright, op. cit., p. 380. 54. Ibid., p.380. 55. Ibid., p. 380. 56. Ibid., p. 380. 57. Ibid., p. 381. 58. Ibid., pp. 385-386. 59. Wittgenstein, Philosophical Investigations. #240. 60. I have been helped in writing this chapter by G. P. Baker and P. M. S. Hacker, Wittgenstein: Rules. Grammar. ..ancLNeC-essiltt, (New York: Basil Blackwell, 1985). They also express the idea that necessity is the requirement of playing a game by its rules. Chapter. Four: Plato andJM M enstem . "Wittgenstein," according to Professor Kripke, "has invented a new form of skepticism. . .the most radical and original skeptical problem that philosophy has seen to date."1 In this chapter I will argue that Wittgenstein's skepticism is not original, that Plato was working on the same skeptical problem as Wittgenstein. By "skeptic," I mean someone who finds at some point in his career that all the available solutions to a given philosophical problem are inadequate. That such a person eventually discovers an adequate solution to his problem, on this view, does not tell against saying he posed a skeptical problem. Here I part company with Pears who rejects describing Wittgenstein as a skeptic given that Wittgenstein posited the public practice theory of meaning;2 though I agree with him that, as stated above, this theory should not be regarded as a "skeptical solution," as Kripke believes. Taking the Euthyphro as my model of Platonic skepticism, I can formulate Plato's quest for a definition in Wittgensteinian terms. In the Euthyphro Plato is looking for a definition of "piety": It is because I realize this that I am eager to become your pupil, my dear friend. I know that other people as well as this Meletus do not even seem to notice you, whereas he sees me so sharply and clearly that he indicts me for ungodliness. So tell me now, by Zeus, what you just now maintained you clearly knew: what kind of thing do you say that godliness and ungodliness are, both as regards murder and other things; or is the pious not the same and alike in every action, and the impious the opposite of all that is pious and like itself, and 158 1 everything that is to be impious presents us with one form or appearance in so far as it is impious?3 This definition once given can serve as a standard for future predications of 'piety' as well as the explanation of why a number of numerically distinct actions share a common name. It can tell us what all pious actions have in common in virtue of which they can justifiably be termed 'pious'. Tell me then what this form itself is, so that I may look upon it, and using it as a model, say that any action of yours or another's that is of that kind is pious, and if it is not that it is not.4 What is going on here is a questioning of the rationale for using common names. When a number of items are termed by the same name, one naturally asks: Why is this done? What is the justification for such a practice? To reply, "The items in question are the same, or of the same kind," only invites the further question: What makes a number of things 'of the same kind'? Socrates questions whether Euthyphro has a good reason for his predication of 'pious' to a number of acts. If Euthyphro could produce a definition of 'piety' and properly apply it, then we would have reason to believe his applications of 'pious' were justified, i.e., were in accord with a rule. Socrates says that this definition can justify predications of 'pious' by serving as a "standard" for what is pious. Thus Socrates is looking for Euthyphro's guide for using the term 'pious'. We've already seen the essential connection between a guide and an intention.5 Thus we can reformulate Socrates' request in terms that Kripke would accept as capturing Wittgenstein's 1 6 0 skeptical paradox. To wit, "What Euthyphro," Socrates could be taken as asking, "is your paradigm of piety? Why should we think that there is something that points to other justified applications of this term? You call a number of things 'pious', you decide to call any actions like these by the same term. You do so--what makes your predications justified? That is to say, why do you think you've realized your original intention?" Socrates, it is true, asks for a guide that anyone, not just Euthyphro, can use. But this general guide can be given only if Euthyphro himself could produce justification for his practice. Community wide norms will be available only if intentionality is possible, i.e., only if individual guidance is possible. Thus Socrates needs to question the basis of Euthyphro's belief that an informed intention is the genesis of his usage of 'pious'. Does Socrates inquire after such a basis? Though it is hard to see around the request for a universal standard, we can make out an individualistic problem. To wit: Whereas, by Zeus, Euthyphro, you think that your knowledge of the divine, and of piety and impiety, is so accurate that, when those things happened as you say, you have no fear of having acted impiously in bringing your father to trial? I should be of no use, Socrates, and Euthyphro would not be superior to the majority of men, if I did not have accurate knowledge of all such things.6 The connection between Plato's problem of universals and Wittgenstein's problem of rule-following is this: Plato wants to know why a number of things are the same. Wittgenstein, in asking 161 what a rule is, is also inquiring into how things are grouped under a common heading. But there also is an epistemologicai problem in Plato. To wit, what is it about that which links things that enables one to discern their linkage? The theory of Forms is meant to address both concerns. Wittgenstein emphasized the connection between the concepts of sameness and rule-following. According to him, to be the same is to be related by a rule. If X and Y are the same, that can only be because there is a rule determining that they are the same. With this connection established, one can say that someone who strives after an explanation of sameness, like Plato, is trying to validate the concept of a rule, i.e., something that organizes things. This is the problem of universals and it is, thus, the metaphysical concern that Wittgenstein was addressing as well. Their epistemologicai concerns were also the same. For both sought to determine what it was about that which organized things that enabled one who understood it to make out their connections. That is to say, Plato and Wittgenstein were interested in discovering what made guidance possible. For Plato a Form guided by giving necessary necessary and sufficient conditions for its term's use. Wittgenstein thought our training bases gave guidance in virtue of the fact that there is a way people generally go on from them. It is this affinity between their epistemologicai concerns that I am now trying to establish by referring to the Euthyphro. I will later discuss their positions regarding the problem of universals (common names). 162 One can imagine that Euthyphro was trained in the standard Athenian manner in the usage of the term 'pious.' He was shown a number of acts, which were supposedly pious, and then instructed to term like acts 'pious'. Socrates' questions, then, center around Euthyphro's claim that his later applications of this term represent "accurate knowledge" of the import of his training. There is also the further question of whether or not Euthyphro's training base was coherent, i.e., whether all the acts there deserved to share a name. This question, of course, is to be decided by a definition of 'sameness'. But what all this boils down to, then, is the question: Is someone grouping a number of things together according to some rule, that is, according to some intention and its fulfillments, which items could serve as training for the term 'pious', i.e., its guide. Someone must formulate a guide for a community to have one. What we need to know here is are there things grouped together under the term 'pious'? And, if so, how are they grouped, i.e., what groups them? The answer to this last question will provide us with a way of determining which things are to be grouped under this term by giving how one should do this grouping. If Euthyphro's training base is a guide, then Socrates is asking: What makes it so? The answer to this question would provide an explanation of Euthyphro's "accurate knowledge." For it would be the grasping of the significance of his training base, i . e , what its constituents had in common in virtue of which they shared a name, that would justify his later applications of its term. The things he later applied the term 'pious' to would be the same as those in his 163 training base. Thus Socrates' questioning, when pushed a little deeper, does strike at the root of the Wittgensteinian paradox. For Wittgenstein, too, doubts initially that one can be in accord with a training base, i.e., use the term 'same': Suppose for instance that the person who is given the orders in (a) and (b) has to look up a table co-ordinating names and pictures before bringing what is required. Does he do the same when he carries out an order in (a) and the corresponding one in (b)?-Yes and no. You may say: "The point of the two orders is the same". I should say so too.-But it is not everywhere clear what should be called the 'point' of an order. (Similarly one may say of certain objects that they have this or that purpose. The essential thing is that this is a lamp, that it serves to give light; that it is an ornament to the room, fills an empty space, etc., is not essential. But there is not always a sharp distinction between essential and inessential.) Here Wittgenstein questions whether or not there is a principle for deciding the correct, rule-governed way of using a chart. Were one to encounter someone claiming that two charts served the same purpose, how is it possible to verify his claim? That is to say, what would tell one that one is observing rules being followed? 'I am doing the same thing with both charts'. This claim, then, is on the same footing as Euthyphro's 'I am applying the term 'pious' to actions that are the same'. In both cases, one needs a standard against which to measure the respective actions to determine whether or not each one is an example of following a rule. The parenthetical remark is meant to draw attention to closeness of the problems of finding an essence and finding objective justification for calling actions rule-governed. Were we to establish that 'serving to give light' was the essence of being a 164 lamp, then one could say with justification of something that had this property 'it is a lamp'. Unfortunately, as Wittgenstein points out, it has not been possible to find 'essences'. Thus he will later question the Platonic premise that the security of our linguistic practices requires being able to do so, that to give a meaning is to give an essence. In the following passage, Wittgenstein applies the same thinking to the term 'game': Consider for example the proceedings that we call "games", I mean board-games, card-games, ball-games, Olympic games, and so on. What is common to them all?--Don't say: "There must be something common, or they would not be called 'games'"- but look and see whether there is anything common to all.-For if you look at them you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. That is to say, there is no property each game shares with all other games, besides 'being a game'. And that each one is justifiably called 'a game' does not depend on their being such a common property. Instead, this practice is justified by games being "similar" to each other and "related" in a variety of ways: several games may be related by the sharing of a feature not shared by the members of another group of games whose members share another property with some of the members of the original group. In this way are the connections established between those things all of which, because of these connections, we can justifiably call 'games'. To repeat: don't think, but laokl-Look for example at boardgames , with their multifarious relationships. Now pass to card-games; here you find many correspondences with the first 165 group, but many common features drop out, and others appear. When we pass next to ball-games, much that is common is retained, but much is lost.- Are they all 'amusing'? Compare chess with noughts and crosses. Or is there always winning and losing, or competition between players? Think of patience. In ball games there is winning and losing; but when a child throws his ball u the wall and catches it again, this feature has disappeared. Look at the parts played by skill and luck; and at the difference between skill in chess and sksM in tennis. Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! And we can go through the many, many other groups of games in the same way; can see how similarities crop up and disappear. And the result of this examination is: we see a complicated network of similarities overlapping and criss- crossing: sometimes overall similarities, sometimes similarities of detail. A group of people have classified a number of doings under a common heading; they call all of them 'games'. What reason do we have to believe that the proceedings they originally grouped under this heading were grouped according to some intention, so that they could serve as a training base for a rule-governed practice? And if they were so grouped, what reason do we have to believe that their later applications of this term accorded with that intention? These are the questions Wittgenstein is asking here. A Platonic answer to them, he goes on to say, cannot be found: there is nothing common to all games, the discernment of which in any proceeding would justify one in calling it a 'game'. I will return to this point when comparing the solutions of Wittgenstein and Plato to the problem :>f universals. The next remark inquires about a criterion for sameness vis-avis mathematical operations and commitments: 1 Suppose someone gets the series of numbers 1, 3, 5, 7,. . .by working out the series 2x + 1. And now he asks himself: "But am I always doing the same thing, or something different every time?" If froii une day to the next you promise: "Tomorrow I will come and see you"--are you saying the same thing every day, or every day something different?7 I may think that I've been performing a single mathematical operation in deriving a series of numbers. That is to say, I may believe my obtaining a series of numbers was due to my according with the intention to perform operation x a number of times. Similarly, I may believe that i make the same commitment to you every day when I say each day as I leave "tomorrow I will come and see you." In each case, Wittgenstein asks, what reason do i have for holding my belief? I think I've gone on in the same way, i.e., been following a rule, but how could I make this claim to someone who doubted me? Thus, the parallel between Wittgenstein's skepticism and Plato's comes clearly into focus when we turn our attention to their respective discussions of the concept of sameness. Wittgenstein asks why someone would think he was going on in the same way when he applied the same term, like 'game', 'lamp', 'promise', 'order', or 'operation', to a number of different objects or actions. Socrates, Plato's skeptic, asks this question vis-a-vis the term 'pious'. In each case, we have a philosopher questioning whether or not there is a reason for one's usage of common names. Euthyphro believes he does have a reason for using the term 'pious' the way he does. In applying this term, he thinks 'he knows what he's doing'. Socrates is skeptical about this. He does not 167 believe Euthyphro 'knows what he's doing'. That is because Euthyphro cannot tell him what piety is, i.e., give him the essence of piety. This inability, according to Socrates, means Euthyphro has no reason for thinking the actions he has called 'pious' deserve to share a name: So we must investigate again from the beginning what piety is, as I shall not willingly give up before I learn this. Do not think me unworthy, but concentrate your attention and tell the truth. For you know it, if any man does, and I must not let you go, like Proteus, before you tell me. If you had no clear knowledge of piety and impiety you would never have ventured to prosecute your old father for murder on behalf of a servant. For fear of the gods you would have been afraid to take the risk lest you should not be acting rightly, and would have been ashamed before men, but now I know well that you believe you have clear knowledge of piety and impiety. So tell me, my good Euthyphro, and do not hide what you think it is.8 Socrates believes that Euthyphro is "careless and inventive" when it comes to applying 'piety'. In Wittgensteinian terms, he thinks Euthyphro's use of this term isn't rule-governed, since if Euthyphro cannot produce for us his justification for the way he uses the term 'pious' we have no reason to believe there is a rule he's using for his applications of this term. Until such a reason is produced his activity should not be regarded as rule-governed. Euthyphro cannot prove his applications of 'pious' are not random, according to Socrates, because he cannot show he apprehended that which to Socrates' mind could be the only guide to this term's use, viz: the essence of piety. Socrates does, however, make reference to pious acts, as if he has some idea of what instances of piety are.9 These acts could be the Athenian training base for 'piety'. The problem, then, is to find a 168 rule-governed way to go on from this training. This problem will be solved, Socrates thinks, by finding out what the above acts have in common. What they have in common will be the essence of piety; it is the apprehension of this essence and the seeing of it in an act that would justify one in calling said act 'pious'. (Were it to turn out that some of these acts lacked a property shared by most of them, the Athenians would have to revise their training base.) That this :s a problem about intentionality is obscured by Socrates' request for an objective definition of 'piety'; that is, a standard for anyone's applications of this term. On the other hand, Socrates does seek this definition via a questioning of Euthyphro's understanding of piety. And when this individual, who is supposed to be an expert in religious matters, cannot show Socrates that he knows what he's doing in applying 'pious', Socrates comes to believe that everyone's practice is suspect. That Euthyphro has not apprehended what would guide him in his own applications of 'piety' leads Socrates to believe no one knows how to go on from its training base. Socrates is left to search for someone else to provide for him a reason to not be skeptical about whether one could know what one was doing in using 'pious'-whether such a definition is within our understanding. What Socrates is given is a number of acts ail of which have been deemed 'pious'. He does not doubt that at least some of these merit this name. What he is skeptical about is Euthyphro's claim that there he has justification for applying this name to those that deserve it. Socrates doesn't think people know why the acts they call 'pious' merit this name. E.g., his attitude toward Euthyphro is: 169 "You may be right that prosecuting your father for murder is piousbut , if so, why?"10 Presented with acts called 'pious', Socrates wants to know what they share besides being called 'pious' by Euthyphro and his peers. Unless they can give this essence, their practice will be "careless and inventive." Moreover, to be an essence a common property must give the meaning of their practice. Witness Socrates' criticism of Euthyphro's definition of 'pious' as that which the gods love. This may be a necessary and sufficient condition for being pious, he says, but it is not the meaning of 'piety'. For it cannot be used in contexts where 'piety' can. In Wittgensteinian terms, this means that knowing what the gods love would not provide one with guidance in using 'pious': there would be places where the latter would be applicable but knowing what the gods love would not tell one so.11 For the reason that the gods love an action can be 'because it's pious' but not 'because they love it'. So, knowing that they love said action could not guide one to say what is correct about their reasoning, viz., that it involved reference to said action's piety. But if the two terms meant the same thing, then their loving it because it was pious would necessarily involve their loving it because they loved it. The failure of this definition leaves Socrates with a skeptical problem regarding the use of 'pious', and by extension all common names. Thus we see that Wittgenstein is not as original as Kripke asserts. Plato has also approached the question of the nature of guidance. Though Plato focuses on the question of what would be an adequate guide for what a community thinks 'piety' should be, one 170 can see points of contact with Wittgenstein's form of skepticism. For Socrates questions Euthyphro about Euthyphro's supposedly accurate knowledge of piety, thinking that if Euthyphro doesn't understand his own intentions doubt can be cast upon the community's understanding of this concept. A community's norms for the application of a term could be developed only from the understanding individuals in that community have of the way they want to apply said term, it is with this principle in mind that Plato directs his questioning toward an individual's understanding of that individual's concept. Socrates and the skeptic Kripke fashions for Wittgenstein are cut from the same cloth. It will not do to reply here "that Plato has no doubt that once a definition of 'piety' is found, we will have no problem explaining why people are justified (or not) in their judgements, since the judgements will accord (or not) with the definition." This reply would have Plato gaining confidence that a definition of piety will be found from the failure to produce one! While it may be assumed that Plato believed there was a definition of piety to be found, it can not be supposed that he thought that he and his contemporaries would have the benefit of its guidance. Thus, Plato's problem should be seen as akin to Wittgenstein's, since Wittgenstein was also at one time skeptical about people being guided in the way they applied terms. Plato's solution to the problem of common names, of course, was the theory of Forms.12 A group of objects shared a name in virtue of the fact that all of them participated in a single Form. The Form of an object for Plato, was its essence; this essence it shared 171 with all the other things having the same name as it. The question of what made a number of things 'of the same kind', thus, was answered by Plato by reference to the Form that united a number of items into a kind by virtue of the fact that all of them participated in it: two things deserved to be called by the same name if and only if they shared the same Form. On the epistemological side, the Form of an object would provide one with the standard or guide Socrates said was needed to identify other objects of its kind. By apprehending the Form of Piety, for example, one would have before oneself the guide that would enable one to pick out other instances of piety. Faced with a decision to term an act 'pious' or not, one would consult the Form of Piety and then see whether or not the action at hand bore the defining mark of piety that had been given by its Form. If the action did bear this feature, then one could with justification call it 'pious'. In Wittgensteinian terms, one could be said to be following a rule in using a word just in case one was applying it in accordance with the dictates of the Form objects bearing this term shared in, which Form one had apprehended. Wittgenstein, as explained in Chapter Three, criticized this theory, both its epistemology and its metaphysical roots. That Wittgenstein attended to it is further evidence that he and Plato were working on the same skeptical problem. To begin with the metaphysics of Platonism, Wittgenstein is opposed to its essentialist presupposition. That is to say, Wittgenstein does not believe a number of items have to be regarded as sharing a feature that is unique to them in order to justifiably 172 have a name common to all of them. Though the essentialist theory of common names is initially highly plausible, Wittgenstein, following his admonition of "don't think, but look and see," rejects it: Consider for example the proceedings that we call "games". I mean board-games, card-games, ball-games, Olympic games, and so on. What is common to them all?--Don't say: "There must be something common, or they would not be called "games'"--but look and see whether there is anything common to all.--For if you look at them you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. To repeat: don't think, but look! That is to say, the idea that there must he something common to all things justifiably called 'a game', has compelled philosophers to look for an essence here. But it is this assumption that is motivating their search, not the insecurity of our linguistic practices without the discovery of their Forms. Language may work fine without essences. Wittgenstein is admonishing us to disabuse our thought of the assumption that it can't. Instead of searching for the foundation of language "outside" of language, which foundation has proven to be notoriously difficult to secure, we should look at how language has been used in lieu of the securing of this foundation. We might just find that our "surrogate" foundation is all that language needs and could have to successfully function: Look for example at board-games, with their multifarious relationships. Now pass to card-games: here you find many correspondences with the first group, but many common features drop out, and others appear. When we pass next to ball-games, much that is common is retained, but much is lost.-Are they all 'amusing"? Compare chess with noughts and crosses. Or is there always winning and losing, or competition between players? Think of patience. In ball 1 games there is winning and losing; but when a child throws his bail at the wall and catches it again, this feature has disappeared. Look at the parts played by skill and luck; and at the difference between skill in chess and skill in tennis.Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! And we can go through the many, many other groups of games in the same way; can see how similarities crop up and disappear. And the result of this examination is; we see a complicated network of similarities overlapping and criss- crossing: sometimes overall similarities, sometimes similarities of detail.13 It is no wonder, Wittgenstein is saying, that Plato could not furnish us with the essence of piety-there is no property common to all pious acts in virtue of which they share a name. When we stop to examine the group of actions we could term 'pious', instead of considering what "must" be the case with them, we see that there are perhaps several features associated with being pious, but that any two pious actions may have none of them in common. If one can accept that such can be the case, then one can disavow the belief that there is an essence of piety. It is then incumbent upon one to provide an alternative metaphysical explanation for why the members of a group can all bear the same name. Wittgenstein doctrine of family resemblances is intended to meet this obligation. More on this later. The salient point here is that we could not justify language by something independent of language, like the Platonic Forms that are purported to be the essences of things. For in justifying anything, language included, we have recourse only to language. Thus the attempt to base language on something more fundamental than 174 language is self-defeating: in attempting to justify this view one would be using that which this view says is not needed to be used to justify it. That something besides the language that we use, that is, something that could be unusable by us, should justify (or not) our linguistic practices is absurd. It is the conceit that we could explain why what makes sense is sensible by understanding nonsense and then detailing why it must be rejected in favor of what makes sense. Wittgenstein would have us, however, view grammar as being stipulated by us so that is suits our purposes in using language. On the epistemological side, Wittgenstein, as we've seen, rejects the idea that an essence, such as a Platonic Form, could function as a guide for the application of a term. For him it's just another rule for interpreting a rule. What Plato has given us in a Form is an idea whose apprehension is supposed to dictate how the term corresponding to it is to be applied. But Wittgenstein, thinking that a Form is just another training base, which is itself in need of an interpretation, does not think that it alone could direct one in the application of its corresponding term. Plato blocks the infinite regress of interpretations that is in the offing here, which would nullify his theory, by declaring that the Forms are self-explanatory. But such a move Wittgenstein would regard as ad hoc: why couldn't a skeptic ask for an interpretation of a Form's dictate? Furthermore, as Colin Strang has shown, Plato himself is forced by the third man paradox to give up the notion that a Form can function as a standard.14 175 Thus the apprehension of a Form is not enough to license the application of a term. That is why Wittgenstein says "that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call 'obeying the rule' and 'going against it' in actual cases."15 The failure of the theory of Forms to explain how to justifiably apply terms is what suggested to Wittgenstein the public practice theory of meaning. One should not attempt here to distinguish Plato's problem from Wittgenstein's by pointing out that the definitions the former sought- the verbal expressions of eternal truths- are not the same as the definitions of Wittgenstein: post hoc generalizations from training bases to enable one to 'go on' from tlsem. For both sought to explain how guidance is possible, though what Plato thought would make guidance possible was not the same as what Wittgenstein placed m this role. To explain how it is that there is one and only one correct way to go on from a training base is to explain how it is possible to start a linguistic practice, which is what Platonic definitions were to explain. For a practice has not been initiated unless there is one and only one way to go on from a purported training base. I say "purported training base" because unless it establishes a practice something can not be a training base: something isn't training unless it's training for something. Wittgenstein's definitions are advanced in light of his discovery that Plato's will not work. One could say that Wittgenstein sought the same things as Plato- eternal truths to guide one- until he realized that they could not be found, thinking only what could not be unusable by us could guide us. Eternal truths--what would hold 176 independently of what we believed-may prove unusable by us. Thus, for guidance we must look to what can not help but make sense to us: our training bases which guide in virtue of the way we would go on from them. Wittgenstein's solution to this epistemoloyical problem has already been given: one is guided in the application of a term just in case one is applying it as anyone would who has been taught by its training base. Here it is not enough tc view a guide and form an interpretation of it in order to qualify as a rule-follower. One must also act with the guide's term--apply it to something-in a manner that is consonant with the usage of the term given by one's linguistic community's practice with it, which practice is given by the way all other community members would go on from the term s training base. It is as if Wittgenstein viewed Plato's project as involving "substitution of one expression of the rule for another" so that no application of the rule resulted, or could result. One is asked, e.g., to define 'piety'. One says apply 'pious' only to acts like these. A skeptic replies: what kind of acts are these? O ;e characterizes these acts. But the skeptic requests further instruction, and so on. Plato posits at this point a self-explanatory Form; but in light of the ~bove mentioned untenabiiity cf ihi? notion Wittgenstein developed the idea that a training base must incline the members of a community to act uniformly when they have run out of interpretations of said training, as they eventually will, in order to qualify as a guide. And being guided is following the course of action that is given by this inclination: 177 If I have exhausted the justifications I have reached bedrock, and my spade is turned. Than I am inclined to say: "This is simply what I do."16 A community can do no more to justify its linguistic practices than to cite its members' agreement regarding doing the right thing when it comes to going on from its terms' guides. But for Wittgenstein this is enough. More on this in the next chapter. The metaphysics that is part and parcel of this theory is given by the concept of "family resemblances." Having rejected the notion that there must be an element common to all things bearing tne same name, Wittgenstein gives the relationship between items having a common name in terms of this concept. When things are grouped under a common heading- called 'the same thing'-this is because the members of the group resemble each other the way the members of a family do. That is to say, there is not oni defining property had by each one of these things. Rather there are a group of properties associated with the members of this group. The members of the group are such that each one has at least one of these properties, but it is not necessarily the case that any two members will share at least one of them: I can think of no better expression to characterize these similarities than "family resemblances"; for the various resemblances between members of a family: build, features, colour of eyes, gait, temperament, etc. etc. overlap and criss- cross in the same way.-And I shall say: 'games' form a family. That is to say, there are a number of characteristics associated with the members of a family. They are what give said family its character. We characterize a family by saying things like 178 'the Smiths all act alike when it comes to sports, except for John' or 'the Smiths all have a dignified bearing, though Sue isn't as stuffy as the rest' and so on. The point here is that, though there is no single property definitive of being a Smith, there can be found characteristics that most of the Smiths share, the exceptions having in common other properties with those 'who fit the mold'. It is visa -vis such a pattern that we understand what it means to be a Smith. Numbers, according to Wittgenstein, are to be viewed in the same way: And for instance the kinds of number form a family in the same way. Why do we call something a "number"? Well, perhaps because it has a-direct- relationship with several things that have hitherto been called number; and this can be said to give it an indirect relationship to other things we call the same name. And we extend our concept of number as in spinning a thread we twist fibre on fibre. And the strength of the thread does not reside in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres. But if someone wished to say: "There is something common to all these constructions- namely the disjunction of all their common properties"- I should reply: Now you are only playing with words. One might as well say: "Something runs through the whole thread- namely the continuous overlapping of those fibres."17 That is to say, we were justified in calling -1, -2, -3 'numbers', e.g., because, like the positive integers, they can be differences between numbers. This is something they have in common; they have, thus, a "direct relationship" with each other. In virtue of bearing this direct relationship with the positive integers, the negative integers then have an indirect relationship to the ordinals, which, like the positive integers, had also been called 'numbers'. 179 Here is an example of how a concept is developed. There is no essence of things sharing a name justifying our decision to call them by the same name. We decide that the properties two things share warrant calling them by the same name or that being related via intermediate things-things having properties in common with each, none of which are shared by all-justifies designating two things by the same term. We needn't posit essences here; the extensions of a concept 'hang together' because of networks of relationships between said extensions. Though the decisions to extend a concept were based on the noticing of different similarities between the things so conceptualized from case to case, the resulting grouping is coherent because of the network of relationships between the things so conceptualized. Wittgenstein will not brook the suggestion that "the disjunction of all (the) common properties" of a concept's extensions is its essence. For this is a distortion of the idea of an essence; an essence isn't a property composed of other properties; it is a single, simple property had by each one of the members of a group. The members of a group of things bearing family resemblances to each other don't each have the disjunction of all the group's common properties, though each one has at least one of the properties that make up the disjunction of common properties. At least they don't have this disjunction in the way each one has at least one of the properties of which said disjunction is composed. And it is in this way that an essence was to be had. 180 Thus Wittgenstein elucidates the concept of sameness by reference to our inclinations regarding what is the same and the examination of what those inclinations has had us group together. What we discover upon examining these groups is that their members resemble each other the way the members of a family do: two members are related to a third, even though they have nothing in common with it, by virtue of having something in common with a fourth member, which does share a property with the third member. A group of things are what they are, according to Wittgenstein, because their multifarious relationships incline us to place them in the same category. I will elaborate upon these thoughts by comparing and contrasting them with other views on this subject. Renford Bambraugh states in "Universals and Family Resemblances" that Wittgenstein has solved the problem of universals.18 I agree with him but wish to question a key point in his exegesis of Wittgenstein's solution. Professor Bambraugh writes: We may classify a set of objects by reference to the presence or absence of features ABODE:. It may well happen that five objects edcba are such that each of them has four of these properties and lacks the fifth, and that the missing feature is different in each of the five cases.19 Even though there is no "common feature" between these objects, Professor Bambraugh says it "would be natural and proper. . .to apply the same word to them."20 This is a good start in expounding the idea of family resemblances, though more needs to be said. The above 181 characteristics are the properties associated with things of a given kind. That is to say, the things of said kind are such that everyone has at least one of these features. (Just as all the members of a family are such that each one of them bears at least one of the family's traits.) That is what makes it natural and proper to give them a common name, though I would say natural thus proper. What I see Wittgenstein doing with the doctrine of family resemblances is providing an explanation for our linguistic practice of using common names. This doctrine is meant to replace Platonism's essentialistic metaphysics. The justification for using common names, on my view, comes from the same source as the justification for other linguistic practices, viz., that human beings are inclined to do so. We have found it natural to call a number of items by the name 'chair', e.g. That we do so is what justifies putting these items in the same category, though we need to be able to explain our decision to do so in terms of the properties associated with being in this group of items. Wittgenstein posits the doctrine of family resemblances, to my mind, to provide a metaphysical explanation for our acting in this way. Looking at these items, we see that they are related as the members of a family are: there are a number of features associated with being a chair-having a seat, being elevated, being made of firm material, etc.-such that every chair has at least one of them. This explains why we have grouped all of them in one category, as opposed to the Platonist's idea that all chairs share a feature that is unique to them. 182 Here is where I may have to part company with Bambraugh, who seems to have disregarded the above point regarding justification. Wishing to distinguish Wittgenstein from the nominalist, who says 'chairs have nothing in common except that they are called chairs', he says Wittgenstein would maintain that 'chairs have only this in common: they are all chairs.' But one could ask: what makes something a chair?. Bambraugh also wants to distinguish Wittgenstein from the realist, who would answer this question by positing an essence of chairs. So he has to develop a middle position. I believe what I've said above would serve this purpose. The nominalist is not completely wrong, on my view, its just that his story is incomplete. There is something about being a chair that is related to 'being called a chair'. It's that being a chair means that a thing would be called a chair by us, given the training base for 'chair'. Had the nominalist included the justification- that a // people call these things 'chairs'-behind the calling in his account, it would have been complete and given Bambraugh what he needs, viz., a way of explaining what it means to say that 'all chairs have ir, common that they are chairs'. The explanation would be that ail chairs have this in common: the property of being something that the rule for 'chair' justifies calling 'a chair'. And that is what it means to be a chair according to Wittgenstein. This way of interpreting Wittgenstein emphasizes the leit motif of his later philosophy: the doctrine that something is an X just in case human beings agree in calling it an X. It does not make it look as if the family resemblances between things of a kind 183 justify the application of a common term to them, which is the initial impression I received from Bambraugh's exegesis. The family resemblances Wittgenstein discovers are simply given as an explanation of why we are inclined to use common names to be opposed to the Platonist's account in terms of essential Forms. But Bambraugh says things at the end of his paper that incline me to believe he wouldn't object to having his views modified in the manner I've suggested. For when it comes time to give principles of categorizing, he utilizes the idea that naturalness should inform our concepts. Bambraugh rightly says that items randomly grouped, such as a knife, a pencil, and a paper clip, and given a common name, say 'alpha', do not make up a group of things deserving a common name.21 That is because, as Bambraugh says, such an arbitrary grouping does not allow for "further application. . .(of) 'alpha'."22 'Alpha' was meant to apply only to the above items. Also, there is no principle behind this selection; one is not looking to group things that we would consider alike. Since there is no such principle, it only stands to reason that the practice could not be extended. The name was not meant to apply to things that accord with a rule, only to the items given the name. Were items grouped because we would find them alike, then it would be possible to find other items deserving the name given to the original things. This entails, as Bambraugh states, "a third and decisive point" regarding the difference between items deserving a common name and those that don't, i.e., between those things purposefully and arbitrarily grouped. And that is that when things are purposefully 184 grouped, it is possible to teach one how to use their term by randomly selecting any of the members of the group.23 I can teach someone how to use the term 'chair' by selecting any group of chairs, things that have been justifiably called a 'chair'. I could not teach one how to use 'alpha' by showing him the paper clip and pencil- the other item is not like them and so couldn't be discerned as requiring the same term. Thus, things arc alike just in case they would be seen to be alike by human beings. That is the conclusion Bambraugh reaches when he says "the nominalist is. . .right in the stress that he puts on the role of human interests and purposes in determining our choice of principles of classification."24 It is unfortunate, however, ihat he does not stress that the "realist's proper insistence on the objectivity of the similarities and dissimilarities on which any genuine classification is based" can be satisfied by our agreement that they obtain. The similarities between things grouped under a common heading, on my view of Wittgenstein, do not justify, but explain our inclination to regard them as similar. But that we agree that there are similarities between things justifies one in regarding them as similar. Having grouped a number of items under a common heading, we notice that they are similar in that a number of features are associated with the members of the group. But these features being so associated are not what "backs up" the practice as Bambraugh puts it, though they do help explain it. Bambraugh comes close to recognizing this when he says: "We know already that our own classification is based on similarities and differences. . .which we 185 can point out to the (uneducated) islanders in an attempt to teach them our language"25 (Italics my own) Our being able to point out the similarities is what makes the trees alike. Our way of seeing things determines how they are grouped. How they are independently of our conceiving them does not determine how we see them, and, thus, how they are grouped. The properties associated with things sharing a term do not associate until we associate them. Thus there is no association of them that determines how we should associate them. Thus the objectivity of our system of classification is not given by 'how things are grouped independently of our grouping of them', as Bambraugh suggests. There is no such grouping. Rather, this objectivity is given by the fact that there is human agreement in how concepts should be extended.26 And that is as objective as something could be. Haig Khatchadourian, in "Common Names and 'Family Resemblances'," makes the same mistake as Bambraugh. He also locates the justification for common term application in the features comprising family resemblances.27 Khatchadourian focuses on the use of a thing or practice as the key feature determining whether or not a given common name is applicable to it: In the case of any given common name SX: (of the kind we are concerned with in this paper) there are certain conditions, fixed by linguistic usage, which determine whether or not 'X' shall properly apply to a given thing T: conditions under which we would refrain from calling a thing an "X" if it did not have a use U the notion of which is implicit in the meaning of 'X'. These conditions may be called the "standard conditions for the use or application of 'X' to a thing I." 28 186 But this interpretation de-emphasizes the roie of community agreement in providing justification for the moves within linguistic practices. As stated above, Wittgenstein posits the doctrine of family resemblances to provide a metaphysical explanation for his epistemology. On this view family resemblances are what we discover- rather than essences- linking the things we've grouped under a single heading. The individual moves of this grouping, though, are justified by our shared inclination to make them, not by that which we see associated with that which we've grouped. To justify an application of a common name one needs only to cite that anyone would apply it to that which one has applied it. One needn't and shouldn't make reference to the similarities between that to which one has applied said name and the other things termed by it, except to explain one's decision. Again, these similarities or family resemblances come into play for Wittgenstein only to explain the results of our grouping inclinations being acted upon, i.e., to give a description of the kind of worldview produced by creatures with our grouping inclination (it is a world whose objects become grouped when they bear family resemblances to each other). In the same way Plato's theory of Forms was to explain why things deserve being grouped: they participated in the same Form. Khatchadourian himself resorts to this analysis when adjudicating a borderline case. The question is, why isn't a log a chair when it does have the use for which chairs are designed? Khatchadourian settles this matter by saying a log cannot be called a chair because "we do not call it a chair."29 Here 'being able to be sat upon', which he'd been treating as If it were the essence of chairs, is 187 put into its proper place. That is to say, its role in determining what is a chair is subordinated to that of our linguistic inclinations. 'Being able to be sat upon' is nothing more than a "criterion" for being a chair: one property amongst others we look for when trying to decide what is and isn't a chair. We will make this decision by following our inclination regarding how one should go on from the training base for 'chair', not by being dictated to by the thing's features, no matter how useful they've proven to be in making similar decisions. And if pressed to give our justification for the decision we've arrived at, we can do no better than to say 'this is how we do things". Thus citing the properties used as criteria is not justifying. Though citing them may help explain the decision to someone who hasn\ understood it, they can never justify it. As Pears has said, "the points in things to which words are related are in the end inaccessible to logicians."30 Something is a chair just in case it is in accord with the rule for 'chair', that is, something we would call a 'chair' given the training for chair. We would point out the similarities we've noticed between something we've decided is a chair and other things so conceptualized only in order to get someone to see aright said something, that is, as a chair. 188 Notes 1. Kripke, op. cit., p. 60. 2. David Pears, The False Prison, pp. 499-501. 3. Plato, Euthyphro. contained in Five Dialogues, translated by G.M.A. Grube (Indianapolis, Indiana: Hackett Publishing Comp. Inc., 1981) p. 9. а. Ibid., pp. 10-11. 5. Cf. p. 7 above. б. Plato, op. cit, p.8. 7. Wittgenstein, Philosophical Investigations. #62, #66, #226. 8. Plato, op. cit, pp. 21-22. 9. Ib id , pp. 9, 10. 10. Ibid., p. 10. 11. Ibid., p. 16. 12. Plato, Phaedo. in Five Dialogues, p. 102. 13. Wittgenstein, PhiIosoohicaI In vestio alio ns, #66. 14. Colin Strang, "Plato and the Third Man," in Plato J . ed. by Gregory Vlastos (Douuleday: Garden City, New York, 1971) p.198. 15. Wittgenstein, Philosophical Investigations. #201. 16. Ibid., #217. 17. Ibid., #67. 189 18. Renford Bambraugh, "Universals and Family Resemblances," in Wittgenstein: The Philosophical Investigations, p. 186. 19. Ibid., p. 189. 20. Ibid., p. 189. 21. Ibid., p. 199-200. 22. Ibid., p. 200. 23. Ibid., p. 200-201. 24. Ibid., p. 201. 25. Ibid., p. 202. 26. Wittgenstein, Remarks on the .Foundations of Mathematics, p. 184. 27. Haig Khatchadourian, "Common Names and 'Family Resemblances'," in Wittgenstein: The Philosophical Investigations, p. 220. 28. Ibid., p. 220. 29. Ibid., p. 221 n. . 30. David Pears, "Universals," in Logic and Language, ed. by Anthony Flew (New York: Philosophical Library, 1953) p. 63. Chapter Five: Wittgenstein. ancLKani To sum up my dissertation: Chapter One's main insight was that one must provide the fact of the matter of guidance in order to show what it means to have an intention vis-&-vis a rule's training. How is it possible to have an intention? This question, it was demonstrated above, will be answered just in case one answers the question 'how can something be a guide?'. Thus, contrary to what some have thought, Humphries and Kripke give equivalent formulations of Wittgenstein's going on problem, the former conceiving it as a point to be solved in explaining the possibility of guidance, the latter as paradox concerning the possibility of having an intention. But these problems are at root the same. One who is pressed to show 'what he intended to do with a case at hand' will ultimately cite his training for some rule and say 'can't you see that this training guides me to do this-what I claimed I intended to do?'. The skeptic who maintains that he can't see how this training could guide one to do what the above person claims he intended to do will, thus, be denying that it is possible to form an intention vis-^-vis this rule's training base. The generalization of this skepticism is Wittgenstein's going on problem. It was also argued in Chapter One that 'how one is disposed to go on from a training base' does not give the intention formed vis-avis it. Simply because one is disposed to go on one way rather than 190 191 another from a training base does not mean one is being guided by it, i.e., following an intention. As the private language argument shows, such a response fails to meet the skeptic's demand for the justification behind one's application of a rule. For this response does not allow for a distinction between what seems right to a person and what is right: on this account what one is disposed to do is what one should do. Thus the individual disposition theory of intentionality does not address the normative concerns that motivate Wittgenstein's going on problem. The heart of Wittgenstein's later philosophy is the idea that one is following a rule just in case one is going on from its training as anyone who took its training would. In Chapter Two, i showed how this idea was used by Wittgenstein to solve his going on problem. Someone pressed by the skeptic described above can respond by citing the fact that he is applying the rule in question in the way that anyone who took its training would. This response gives the fact of the matter of being guided, i.e., according with an intention. In being trained, one is trying to decide what the training is supposed to guide one to do, that is, how one should intend to apply it. That one is going on from a case of training as anyone who took that training would demonstrates, according to Wittgenstein, that one is being guided by it, that is, according with the intention formed vis-&-vis it, the intention to follow its guidance, whatever one takes that to be (though it must be possible, on this account, to explain to others just what one's practice is, i.e., how to accord with one's intention, e.g., one could use green and blue patches as a 1 9 2 training base for a single color concept, 'grue\ just so long as one could teach others the usage of this notion. Though this practice would be odd; it would still be rule-governed given that it is teachable). Wittgenstein used this theory, as I argued in Chapter Three, to give mathematical standards, that is, to answer the question 'what justifies us in practicing mathematics as we do?'. We are justified in going on from mathematical training as we do, e.g., in answering '12' when asked the sum of '7' and '5', because the ways we go on are natural, that is, practices, given our nature, that we can't help but follow. As with color terms, our agreement in actions vis-ci-vis mathematical practices is what makes mathematical discourse possible, and, hence provides its foundation. Not its agreement with what obtains in a world independent of our own, but its agreement with what we find it natural to do, is what makes the above answer correct. In fact, Wittgenstein rejects the Platonic idea that one is stating a fact in answering '12' when giving the sum of '7' and '5'. Giving this answer is "just the way we do things," according to him; it is neither true nor false but is justified because, since it is what is natural for us to do- usable-- -it serves the purpose for which it was intended: helping us to order our experience. Chapter Four saw us questioning Kripke's claim that Wittgenstein discovered a radically new form of skepticism. There it was argued that Plato also sought the fact of the matter of guidance. He too questioned whether there could be a standard for the correct application of a term. It was the grasping of a form and 193 the application of its term to said Form's particulars that constituted guidance for Plato. But it took the discovery of this theory to allay the skeptical concerns he shared with Wittgenstein. Wittgenstein's skepticism arose out of seeing the inadequacy of this theory and empiricist accounts. Here I parted company with Pears who does not take Wittgenstein's rejection of Platonism and empiricism to be an indication of skepticism on his part. It was my contention that Wittgenstein, like Plato, allayed skeptical concerns regarding rule-following only by developing what he could consider an adequate account of guidance. We also saw in Chapter Four Wittgenstein's rejection of Platonic essentialism, the metaphysics that is part and parcel of the theory that Forms are guides. Though his skeptical problem wasn't radically new, Wittgenstein's solution to it bore the stamp of originality. No longer would it be the sharing of an essence that linked a group of items having a common heading. Wittgenstein reasoned, instead, that we should come to view the world in terms of our grammar, i.e., norms of representation. To be sure, others had made human beings "the measure of all things." That is, had said, Pears puts it, "there are no independent, objective points outside of man's world view of support (for) meaning and necessity."1 Hume, e.g., based the existence of causal connections on the habits of human psychology. But it remained for Wittgenstein to focus on the linguistic aspect of our existence as that which will give reality. This approach to metaphysics is akin to the one taken by Kant, who deduced the structure of reality from the requirements of our 194 conceptual scheme. Why must there exist "objects in space outside us?" According to Kant, such objects must exist because they are a prerequisite for the possibility of human beings having intelligible experience.2 Giving his answer to this question a linguistic twist, Wittgenstein would say there has to be a material world because such a world is required for us to use the term 'sameness', i.e., follow linguistic rules. Thus how things must be for man to follow the rules required by him to understand his experience becomes the measure of all things. Thus there is an affinity between the systems of Kant and Wittgenstein, the fleshing out of which will provide the conclusion to this dissertation. Kant argued against Berkeley that the world could not possibly be such that all it contained is sensations. For the possibility of our having intelligible experience requires that there be objects whose existence is not dependent upon their being perceived.3 What is the basis Kant had for linking the existence of a material world to our being able to have intelligible experience? Here I will fellow the lead of Jonathan Bennett, though my exegesis will deviate from his at points. Kant says: I am conscious of my own existence as determined in time. All determination of time presupposes something permanent in perception. This permanent cannot, however, be something in me, since it is only through this permanent that my existence in time can itself be determined. Thus perception of this permanent is possible only through a thing outside me and not through the mere representation of a thing outside me; and consequently the determination of my existence in time 195 is possible only through the existence of actual things which I perceive outside me. Now consciousness (of my existence) in time is necessarily bound up with consciousness of the (condition of the) possibility of this time-determination; and it ss therefore necessarily bound up with the existence of things outside me, as the condition of the time-determinaticn. In other words, the consciousness of my existence is at the same time an immediate consciousness of the existence of other things outside me.4 In other words, I am aware that I am the owner of various experiences, i.e., "determined in time" as that being who experienced seeing a chair, smelling a rose, hearing a knock, etc. The totality of these experiences is my being. But I cannot lay claim to any of these experiences unless there are things existing independently of them, to which said experiences correspond as 'the experiences of them'; "something permanent in perception," which is what is perceived. Why, though, must the things required for the determinations of my self exist "outside me"? Jonathan Bennett would flesh out Kant's argument here in a Wittgensteinian fashion. It is normative considerations, he argues, with which Kant would have filled this lacuna.5 To ascertain the experiences which determine my being, I must have standards to mark the difference between what seems right to me and what is right. Without such standards there is no sense in talking about right and wrong. But, as Wittgenstein points out, it is only by using things outside of me, viz., public training bases, that I can develop adequate standards of correctness. For without them I have only my own inclinations to rely on, and then whatever seems right to me is right. 196 In this connection one should recall Berkeley's method for distinguishing between ideas of sense and ideas of imagination.6 Ideas of sense, which give real sensible objects, were to be distinguished by their being connected to the ideas preceding and following them. Ideas of imagination, which were of unreal things, had no connection to the ideas around them. The connections Berkeley had in mind were those established by the laws of nature. E..g. , if one is really seeing a dagger before oneself then, by the laws of nature, one should bs able to reach out and touch said dagger. Thus, to see whether or not an idea is an idea of sense, one must test whether or not it obeys certain laws of nature. In our example this would mean determining whether or not that which is seen is also touchable. Unfortunately for Berkeley, however, any such determination can be made only if one can have more than one experience of an object. Berkeley will not allow for this: with only sensations in the world nothing can be experienced more than once; each sensation qua experience at a given time will be unique and without anything besides sensations there can be nothing two or more sensations could have in common as that of which all of them are sensations. Thus Berkeley's own system does not provide him with the means whereby he can perform the tests required to see whether or not an object obeys the laws of nature, and hence is an idea of sense, a sensible object. Indeed, in Berkeley's system laws of nature themselves could not be established, since their establishment requires seeing how the same object works on a number of occasions. 197 Thus Berkeley's system is open to the Wittgensteinian objection that within it there is no way to distinguish what seems right from what is right. Confronted by what appears to be a dagger, e.g., I have no choice but to accept this appearance-what seems to be the case-as what is the case, to conclude that I am seeing a dagger. There is nothing else I can appeal to to dispel the doubts that could arise regarding the veracity of this impression. (After all I have been the victim of perceptual errors before.) Thus, to get back to the original Kantian concern, I would have no way in a Berkeleian world to know, as Bennett puts it, what my peisonal history has been-just how my self has been determined, to use Kant's terminology. Am I really someone who saw a dagger a moment ago? Professor Bennett focuses on the unanswerability in Berkeley's system of questions like this, those regarding one's past. But one could equally fault Berkeley for faili.ig to provide a way to answer questions about one's present state. Am I now seeing a dagger? No less than with the former case, I am reduced to deciding this matter on the basis of what appears to me to be the case. Moreover, Bennett's emphasis is misplaced since Kant himself speaks of "all grounds of determinations of myself in time," not just those determinations that constitute my past. But he is right that at the heart of Kant's Refutation of Idealism lie normative considerations akin to those Wittgenstein employed in his private language argument. There is, however, a deeper problem with Berkeley's idealism. To wit, it not only leaves us unable to justifiably apply concepts, it 198 precludes their very formation. The latter, of course, follows from the former- since one must be able to justifiably apply a concept in order to devnlop it-but, leaving the problem of the untestability of objects aside, it is apparent that without the possibility of their being identical things, concept formation would be impossible. That is to say, Berkeley not only has a problem with perceptual error- so that were we somehow to be given concepts we would not be sure how to apply them-he also cannot explain how one could learn. Imagine someone in a Berkeleian world where, as Berkeley himself admits, there is no such thing as 'the experience of sameness'.7 Then any "concepts" one would have would be as unique in their applicability as the experiences from which they were culled. The concept of identity itself would never be formed, if concepts can be formed only from experiences. Thus "words," as Berkeley puts it, would be "of arbitrary imposition."8 We really would have no reason to call-what we thought was-the same thing by the same name on different occasions, let alone form kinds whose members share a term. Berkeley is not troubled by this result, but surely it is the picture of intellectual chaos. Kant had this in mind when he said: There (could not) be an empirical synthesis of reproduction, if a certain name were sometimes given to this, sometimes to that object, cr were one and the same thing named sometimes in one way, sometimes in another, independently of any rule to which appearances are in themselves subject.9 Wittgenstein will echo this thought when he points out that "the use of the word 'rule' and the use of the word 'same' are interwoven." So Kant has another way that he could defend the claim 199 that determinations of self presuppose the existence of a Berkeleian material world: without such a world I would have no way to develop the concepts with which to characterize what happens to me. But both this way and the one sketched before it draw on the idea that Wittgenstein would make a cornerstone of his later philosophy: the idea that a philosophical system must allow fcr the possibility of distinguishing between 'seeming right to me' and 'being right' vis-&-vis the application of concepts (or rules, to use Wittgenstein's term for concept). Whether it is because of not allowing for fallible creatures to test objects, or because it does not provide the means for developing concepts, the radical empiricism of Berkeley does not allow for this distinction. Thus Kant could dismiss Berkeley's system. In a world where appearance cannot be distinguished from reality and words are of arbitrary imposition, we could not come to know ourselves. We could not tell just what our experiences are. I will now point out how £ nnett misdescribes the affinity between Kant's and Wittgenstein's philosophies. The fundamental error he makes, to my mind, is fleshing out Wittgenstein's private language argument in a way that is unnecessary. Bennett says of this passage from Wittgenstein: In the present case I have no criterion of correctness. One would like to say: whatever is going to seem right to me is right. And that only means that here we can't talk about 'right'.10 that "it is too casual to be assessed."11 2 0 0 But the matter really is as simple as that: in a private language, which is what the radical empiricist leaves one with, one has no way of marking the difference between 'what seems to him in the final analysis to be right' and 'what is right'. But it is obvious that a language needs a means of making this distinction, given that one can make a mistake even regarding one's intentions. Without this distinction not only would an individual himself have no standard for correctness-'I think this is right' won't do- but others would have no way of telling a genuine mistake-an error that takes place in the context of a rule-governed practice-from merely random behavior. Faced with what we thought was a misapplication of a term, we could not give one who stubbornly refused to admit it any reason for changing his mind. His bizarre ways would have to be accepted as following a rule. But clearly this result is unacceptable. (Unlike an individual, the community's final decision regarding its intentions is not open to a challenge: there are no higher sources in relation to it. Were an individual or group to maintain we were wrong in this situation, we could not understand him or them: he or they would be declared bizarre, like the above mentioned obstinate person. We cannot declare ourselves bizarre, for what we do is only what comes naturally to us. It is those who don't conform to our ways who are not understandable, not speaking a language.) Earlier Bennett dismissed an attempt to use Wittgenstein's considerations regarding the "trustworthiness of memory" to flesh out Kant's Refutation.12 In seeing what my experiences have been, "what is achieved, Bennett asks, by checking recollections against objective states of affairs?'." Why can't one simply decide to trust one ■* memory? Here the answer is, of course, that objective states of affairs provide a standard independent of what seems right to an individual, who can't "simply trust his memory" because of its known fallibility. Objective states of affairs give a way whereby one could be wrong, viz., by not corresponding in one's judgement to what they are. (By objective states of affairs I take Bennett to mean things existing independently of anyone's perception of them. These things could be of two sorts: things themselves like, to use Bennett's example, "heaps of ashes," or reports on them.) Without them, .what is possibly fallible- one's memory- can never be declared faulty. (In the same way, Berkeley's perceivers have no reason to say that what appeared to be a crooked oar has turned out to be straight.) Bennett says objective states of affairs, like a newspaper report, may also turn out to be deceptive and, moreover, have to be interpreted in light of what one's memory has to say about them, so that epistemically one is on no surer ground with them than one was with one's own memory.13 But this misses Wittgenstein's point. He is not saying all objective sources of information are inevitably veracious and clear whereas one's memory is useless. It's just that one's memory couldn't be the sole source of knowledge, for then 'what seems right to one' is 'what's right'. This conflation flies in the face of basic intuitions regarding 'rightness'. (The situation where one newspaper's reports had to be taken as gospel truth would be equally untenable.) Were one newspaper's reports fishy, one could always check another's. But were one's memory the sole source of knowledge regarding one's past, then it could never be checked. With 2 0 2 misremembering being a distinct possibiiity, this consequence is a reason for rejecting that from which it follows: the possibiiity of a private language. Bennett misses this point because he is inclined to add superfluities to Wittgenstein's argument. Its main point, as just shown, is that a language can't necessarily conflate seeming right to a person and being right. This follows from considering the possibility that an individual could be wrong. Thus it is not just the trustworthiness of memory ihat is at issue in the private language argument. There is also what follows from considering the possibility of misremembering. It is the combination of this conclusion- that there must be a way of distinguishing what seems right to a person from what is right-with the known fallibility of memory that yield the conclusion that a private language is impossible. Nevertheless, I believe Bennett would have seen the importance of the point regarding the trustworthiness of memory had he focused his exegesis of the private language argument on what follows from this point: "(where) whatever seems right to me is right . . . we can't talk about 'right'." Instead of focusing on this conclusion, Bennett chooses to point out that in a private language "the distinction between 'I was . . .' and 'I recollect . . .' is literally idle, "thus obviating the need for the former notion. It is this obviation, according to Bennett, that makes a private language untenable.14 But Bennett fails to notice that in a private language, the distinction between 'I was . . .' and 'I recollect . . .' is idle because there is no way one can be wrong about what one recollects. 2 0 3 With only 'what one recollects' to work with in recalling, there is nothing that could belie one's remembrances. Thus the problem Bennett points out boils down to the one I focus on. There is no need for him, therefore, to introduce the idea that 'i was . . is superfluous in a private language, an idea which doesn't suit Kant's needs anyway, since he is attempting to show that all determinations of self are impossible in a private language, not just past ones. Later Bennett criticizes Wittgenstein for "(implying) that a language which was de facto private could not be used according to rules."15 Norman Malcolm is then taken to task for defending this implication by saying "on the private language hypothesis no one can teach me what the correct use of 'same' is . . . But a sound that I can use as I please is not a word."16 But this is exactly right and at the heart of the private language argument. That a language is "unteachable"--this is the non-modal feature Bennett is looking for in Wittgenstein's argument.17 This is the "reason" that Wittgenstein believes a private language is impossible: it is unteachable. As before with "things," Bennett does not think people can provide "memory-independent checks:" their words have to be interpreted no less than what things mean.18 But again he is missing Wittgenstein's point. That other people's words have to be interpreted does not prevent them from providing what is critically missing in a private language: a way to distinguish what seems right to the private "language" user from what is right. 204 Professor Malcolm has this in mind when he says "a sound I can use as / please is not a word ." For were someone to capriciously use a term, its meaning would be unteachable to others. And they, seeing this capricious behavior, would have no reason to regard it as rule-governed. It couldn't be called a 'language'. It is to rule out such behavior as language that others are needed. Granted, their words are useless as a means for ascertaining what is correct, what one meant to do with one's training, until they are interpreted. Still, that an interpretation is in the offing provides the chance that caprice can be seen as caprice- the possibility of distinguishing what seems right from what is right. If someone maintained that his behavior with a term was rule-governed when other human beings saw it as capricious, he could not be called a language user. Bennett goes on to say that Wittgenstein's main point is that "our public reports of our inner states are logically connected with the objective causes of inner states and with their objective manifestations in non-linguistic behavior."19 This is something Wittgenstein wants to show; however, it is not his main point. His main point is, as I've argued above, that a private language is impossible because it provides no distinction between seeming right to a person and being right, since it is unteachable. What Bennett believes is Wittgenstein's main point, however, follows from this: since an "inner object" is unobservable to others, its appearances must connect with that which is observable, viz., objective causes and its manifestations in non-linguistic behavior. 205 To use Bennett's terminology, the inner object "idles" in a "public language."20 But it is not only public Slanguage that is at stake here. It is all language. The inner object by itself is as useless for an individual in setting up a language as it would be for a group of persons. For its appearances, contrary to what Bennett believes,21 could not be described according to rules. Wittgenstein does have grounds, as I've shown above, for believing "a rule cannot be obeyed privately." Private behavior, action that is indescribable to others, could be capricious without being known as such, since its performer must regard what he thinks is correct as correct. Therefore, it cannot involve the use of language. I will now point out how Wittgenstein's work draws upon Kant's. Specifically, I want to show how Wittgenstein's use of the ideas of human ability and Identity is similar to Kant's. We have just seen how Kant uses the idea of human ability: certain propositions, like 'there is a material world', are to be regarded as synthetic a priori truths because we would not be able to characterize our experience if they were false. Given that our perceptual organs are fallible, we cannot ascertain what things are by observing them only once. That one was being appeared to by a crooked oar, e.g., one could never be certain of: for all one knows, given only one perception of it, it may be an optical illusion. To gain justification for our judgements of experience, then, we need to be able to perceive objects more than once, so that we can "test" for how they should be conceived. But being able to do such testing requires, as we've seen, that there be more to the world than sensations, since each one of them is nonrepeating. There must 206 be objects existing independently of anyone's sensation of them, any one of which could be the object of numerous sensations. This is Kant's conditional proof of a material world, as defined by Berkeley.22 And given that no one can seriously deny that we can characterize our experience, it follows that there is a material world. We can see Wittgenstein citing the same consideration in discussing the correctness of our answers to mathematical problems. E.g., Wittgenstein tells us that it is correct to answer '12' when asked the sum of '7' and '5' because this is the answer we can't help but giving: if we are to calculate.23 In other words, our abilities are such that we can add only by answering '12' here. Thus Wittgenstein, like Kant, fixes what is necessary by considering what human beings have to do to perform cognitive functions. In both cases we have a philosopher saying that certain things are necessary conditions- in Kant's case synthetic a priori propositions, in Wittgenstein's our mathematical rules- of our being able to do something whose performance could not be given up. And Wittgenstein, to complete the analogy, would declare our mathematical practices correct, given that we cannot abdicate the wherewithal to calculate. They are correct and necessary, on this view, given that without them we lose the ability to calculate, which, of course, we could not lose. As Kant himself argued, our mathematical rules are justified because they "make experience in general possible."24 The private language argument, as we saw above, also brings out this tendency in Wittgenstein'^ thought. We are simply not able 207 to describe our sensations without, as Bennett says, "logically (connecting their reports) with the objective cause (of them) and with their objective manifestations in non-linguistic behavior." This must be done here because, given one's fallibility, one cannot be the sole arbiter of success. Therefore, the language game of describing sensations must be set up so that something besides an individual's final description gives the correct description: viz., as Bennett describes it, so that others' judgements provide a standard whereby what may oniy seem right to an individual can be seen as incorrect. In having a sensation, one is inclined to characterize it, to categorize it with other sensations that one believes are like it. One places it in the category of painful sensations, e.g.. Does it belong there?, one could ask. Is it really like the other sensations I've classified as 'painful'? What is hard for some to see is that this is a normative question. They will object that according with an intention vis-avis the description of a sensation is not like the practice of describing public objects. To accord with one's intention here, one just has to do what one thinks accords with it. To classify a sensation, one has only to feel it. One could say, to use the above example, "it feels like other sensations I've called 'painful' so it deserves to be classified with them. What do I need the judgements of others for? I don't need to test this thing more than once to ascertain its identity, for there is no possibility of deception here (as there is with classifying things like tables and chairs). My sensation just is what I think it is." 208 But Wittgenstein would seize upon this last statement to bring out the inadequacy of this objection. Any time that something just is what I think it is we have a situation where "we can't talk about right or wrong." Even when trying to accord with one's intention vis-sk-vis the description of a sensation, one could go wrong; one's practice could become haphazard, due to a memory failure, e.g.. ("I'd thought I was having a headache, but I'd forgotten how bad that feels.") Thus one needs an arbiter of identity besides one's inclination to think two sensations a"e identical. Otherwise, what is haphazard could never be discovered to be so, so that a skeptic, perhaps oneself, could not become justified in believing that one was engaging in a rule-governed practice, i.e., according with one's intentions. Pressed to prove that what one was doing wasn't haphazard, one would be at a loss: having no way to spot randomness, and knowing that it could be about, one couldn't single out correctness either-reject the charge of haphazard use. Here, as with other practices, the public is brought in to lend its judgement as that which can distinguish what is right from what only seems right to an individual. Our judgements of what is rulegoverned and what is haphazard, then, provide the standards for determining these things. Would someone maintain that his behavior, which we regarded as haphazard, was rule-governed, we would have no way of agreeing with him, though it may suit his purposes and would suit ours were we but like him. To make the final determination, it would be necessary to discover the difference between him and us that is responsible for divergence in our practices and alter accordingly ourselves. Were we then able to 209 comply with his practice, we could call it rule-governed. But until such time as this alteration was possible, we would be justified in regarding his practice as haphazard. With the public serving as the arbiter of regularity, it follows that 'what is going on' in one's practices must be teachable to others. That is why the occurrence of sensations, the "raw feels" that can't be had by anyone but him to whom they happen, must be logically connected to public observable phenomena: their causes and behavioral effects. These phenomena will sen/e as the training bases for the practice of describing sensations. And going on from them as anyone would will constitute correct use of sensation terms. Thus we see that Kant would flesh out his Refutation of Idealism using Wittgensteinian normative considerations while Wittgenstein drew on Kant's ideas regarding human ability to show that the experience of our feelings could not be described without a public and material condition intrinsically associated with our feelings. So Wittgenstein really just applied Kant's Refutation to the discussion of sensation language and added that which will provide the standard for all correct term application, viz., public practice. Here again, we see that Wittgenstein was not as original as has been thought, a fact he himself acknowledged.25 The second similarity between Kant's and Wittgenstein's philosophies is the importance both place on the concept of identity. Berkeley's idea that no two sensations give identical objects, that "words are of arbitrary imposition" was unacceptable to Kant. To believe we can intelligibly picture our experience, Kant argued, we 2 1 0 must reject thiu idea and posit that which would make such a rejection possible, viz., a material world.26 Wittgenstein also stressed the importance of the idea of identity, saying it is "interwoven" with the idea of "rule." We need linguistic rules to understand our experiences and to develop these rules we need to understand first that training bases are identical to themselves and, secondly, what other things are 'of the same kind' as a given training base. Thus Wittgenstein, like Kant, would reject any system where "words are of arbitrary imposition." (Kant would accept the first understanding as required because of the necessity 'of testing the same object several times to ascertain its identity'. He would accept the second because of the necessity of having concepts with which to characterize experience'.) But Wittgenstein has more to say than Kant about what a system would need to give us the possibility of understanding our experience.27 That is to say, though Kant stresses the need for concepts, he does not do the work Wittgenstein does in explaining what kind of concepts we need or how to develop epistemically adequate linguistic rules. The concepts we should have, Wittgenstein tells us, are those we develop from going on as we do from rules' training bases. We go on from rules' training bases in the ways that are natural for us, that work for us. Thus the concepts we should have are those that come naturally to us, i.e., those we find it natural to work with. How should we go about characterizing experiences as 'of the same kind'? Wittgenstein tells us that our principle here should be: which experiences are people inclined to treat as 'of the same kind'? 21 The experiences that are so grouped by most human beings are those we should regard as having the same concept applicable to them. There is precedent for this move in Kant. There it's argued that the concept of "causality" is justifiably used because it is a way human beings naturally and unavoidably use to characterize their experience.28 Wittgenstein makes this into a general principle: a concept is justified as usable just in case it is one that human beings find natural to use. Why shouldn't this principle guide us? After all, our concepts are supposed to help US understand our experience. Thus how can we help using that which helps us? The purpose of our concepts is to enable us to get an intellectual handle on our experience. Thus we should cultivate those notions that give us this handle. Is our concept of addition correct? Have we gone on in the proper fashion from its training base? This question is nonsensical, Wittgenstein tells us, because our way of going on is usable by us, that is, suits the purpose for which we have concepts: it enables us to characterize our experience- it works. The question is nonsensical because it presupposes the existence of a practice-independent standard by which one could assess the correctness of our practices, as if their usefulness shouldn't be the sole arbiter of their worth. But a practice of ours, defined by what its rules tell one to do, could be neither correct nor incorrect, it is either helpful or needs improvement. It is only the moves mace in trying to follow a practice that are properly said to be correct or incorrect, depending on whether or not its rules have been followed. 2 1 2 There could be no practice-independent standard by which to assess the correctness of a practice like addition because we could not jnderstand its being wrong, which is a "possibility" we'd have to believe in if something besides how we do addition determined how to do it. Given that we could not believe this "possibility," we could not believe in a practice-independent standard of correctness for addition. And if we could not believe in such a standard we could have no reason to think that the practice of addition is incorrect or correct. And not being able to have a reason why addition is correct or incorrect means that it couldn't be correct or incorrect. Thus asking whether or not addition is correct is nonsensical. Thus Wittgenstein rejected the idea that there were facts in a Platonic grid that authorized or didn't warrant the concepts we use. Our concepts were answerable, he believed, to no authority besides ourselves. Does it „ Ip us organize our experience?, that is the only question we need to ask when assessing the epistemic worth of a concept.29 Moreover, Wittgenstein believed there were three other reasons why Platonic Forms could not authorize the concepts we use, besides the fact that the Platonic theory fails to consider the purpose for which we form concepts, viz., to help creatures like US understand the world in which WE live. It posits the Forms as the terms in which we should view the world, regardless of whether or not they suit our needs. The first of these reasons was that there could be no such thing as a Form whose meaning would be so evident as to require no interpretation by its user. If these Forms are to help us conceive 213 our world, thei< we must figure out how to use them. But then we would not be conceiving the world in terms of the Forms but rather in terms of our interpretations of the Forms. Thus the Platonic theory fails to give that which it promises: mind-independent standards for conceiving the empirical world.30 Secondly, were the Platonist to argue that we needn't interpret the Forms-that they and all the directions for their use were instantaneously known, then we couldn't misapply a term, unless conditions were not ideal. What is being imagined here is that understanding involves having all and only the correct uses one will make of a term in one's mind before one makes the actual applications of it, so that one needn't interpret it at each potential application to see if it applies. This one could not disobey a rule: but it was the disobeying of rules that induced the Platonist to posit his theory to explain what made for disobedience. If one cannot know a form without not having to interpret it, i.e., if apprehending a form essentially involves having every application of it, with each one of these being deemed 'correct' in one's mind before said form is used, then there can be no distinction between right and wrong applications, for there will be none of the latter, under ideal circumstances. Each application, by being an application, will be correct. Misapplications could be made only by those who never understood the form in question.31 Finally, there is the problem of specifying "ideal conditions" for applying a rule. The Platonist has told us that under favorable conditions one's intentions "play themselves out"; one doesn't act according to them, at most one merely recalls the case at hand. But 214 how are we to know when favorable conditions have been met so that one's cognitive machinery can be ascertained to have functioned properly? The Platonist could tell us to distinguish them by contrasting cases where mistakes have occurred with them. But this will only beg the question: 'given that mistakes can occur only under unfavorable circumstances, how can we discern them without knowing favorable conditions?'. The Platcnist asks us to make out errors before we know what is doing right. Given these three problems and the fact that his solution is more appropriate for the problem at hand, Wittgenstein rejects Platonism. That our concepts are or are not in line with a Platonic grid does not matter. Our concepts are the only ones we can use, so if they didn't correspond to Platonic Forms, we could not be faulted epistemically. If they do correspond, we are not any better off epistemically than if they aren't: for our justification would still remain 'they work for us'. Platonism is superfluous. So we are equipped with a set of epistemic standards of our own making. These standards are our concepts into which we try to fit our experiences so that we can understand them. As our constructs, these concepts do not necessarily correspond to a preestablished order of things. As Wittgenstein says, they are neither true nor false but only usable. But, then, what is truth?32 A first stab would be-truth, in this system, is that which is given by a correspondence between a concept and that which is said to fall under it. When and only when our epistemic standards, i.e., the paradigms for determining the identity of things are met by 215 experiences which are judged to meet them, does truth become realized. But what is it for our epistemic standards to be met? Our epistemic standards are met- our concepts are correctly used- Wittgenstein says, just in case we agree that they are met by that which is said to meet them. Does such a theory preserve the essential objectivity of truth? That is, in this system is there room for truth to be independent of that which we think is the case, a possibility there must be an allowance for given our known fa llib ility ? It should be first said that for the paradigmatic cases with which we initiate a practice, there could be no such thing as congruity between truth and what is agreed to be the case. Otherwise, concepts could never be developed. This is a corollary of the private language argument. Grammar does not determine what is true, but what can be true and under what conditions what can be true is true. And one must determine what can be true before one determines what is true. What we are concerned about here, then, is the extension of a practice from its paradigmatic cases. Having been given the training for the use of a concept, when can one be said to have made a true judgement by the application of it? The world is not inscrutable, but conditions sometimes prevail that make it difficult for us to ascertain the truth, that is, just how things stand in relation to our concepts. All of us can agree that certain things are the case which we would later say aren't. Are we forced by Wittgenstein's system to recognize those mistaken 216 judgements as true? Of course not: since we don't agree that our epistemic standards have been met. In such cases it can be said that, though our concepts were applied correctly, their application did not yield a true judgement. They were applied correctly because things greatly appeared to fall under the concepts we took them to fall under. From the standpoint of following a rule, one is not to be faulted for being compliant here. In fact, unless one has good reasons to offer his contemporaries for being contrary in such situations, reasons that would get them to see the error of their ways, one is to be regarded as not following a rule. The agreement, then, that yields the truth is that which is produced under ideal circumstances. But what are these? Those situations where nothing is deceiving us? But that only begs the question 'what is a situation where deception can't occur?'. This result, it should be pointed out, is not damaging to our system. For we never proposed to single out what is true by citing community agreement. Our only project here was to determine when a rule was being followed. This occurs, we have said, when someone goes on from a training base as his peers would. Our application of terms is justified, according to this theory, when they are applied as anyone in our linguistic community would apply them. It can only be our hope that such applications yield true judgements. And they will- under ideal circumstances. It's just that we are not always aware when these obtain. So we advance cautiously our conclusions, knowing our assertions are justified if not veracious. Really, this doesn't tell against the view that truth is agreement under ideal circumstances. Truth is agreement under 217 ideal circumstances, but we are hard pressed to discern the latter. So it isn't the nature of truth that we can't specify, but how we are to know that we are in possession of it. This difficulty, it should be said, is not unique to our system. Plato also, as we saw above, had problems specifying when one could be said to know one had apprehended a Form, so that it could guide one in making truthful statements about its particulars. Yet in that system it could still be said: truth is realized when a particular is called by the name of its Form. We have a d if^ent standard but we proceed likewise in determining when we £ 'iould say we have met it. Our rule-following standard is following our intentions vis-a-vis a guide. The question is 'when should we agree that we have gone on correctly?'. In one sense, the answer is 'when we do agree'. For we are concerned with only what strong' appears to be the case when it comes to following rules. But we strive for truth as well. That will be achieved when we agree that we should agree that we've gone as we intend to, i.e., when we see that nothing has kept us from doing what we intended to do with a training base. For this achievement, more is required than just epistemic responsibility: we must also strive to recognize and make out ways of discerning the existence of the possible sources of error. 218 Notes 1. David Pears, Wittgenstein, p. 184. 2. Immanuel Kant, Critique of Pure Reason, translated by Norman Kemp Smith, St. Martin's Press: New York, 1965) p. 244. 3. Ibid., p. 244. 4. Ibid., p. 245. 5. Jonathan Bennett, Kant's Analytic. (Cambridge University Press, 1966) pp. 206-214. 6. George Berkeley, Three Dialogues Between Hvlas and Phiionous (Hackett Publishing Company: Indianapolis, 1988) p. 68. 7. Ibid., p. 78. 8. Ibid., p. 80. 9. Kant, op. cit., p. 132. 10. Bennett, op. oil, p. 206. 11. Ibid., p. 206. 12. Ibid., p. 205. 13 14 15 16 Ibid., p. 205. Ibid., p. 207. Ibid., p. 213. Ibid., p. 213. 17. Wittgenstein, The Philosophical Investigations. #258, #265, #293, #294. 219 18. Bennett, op. cit., p. 212. 19. Ibid., p. 213. 20. Ibid., pp. 213-214. 21. Ibid., p. 214. 22. Kant, op. cit., p. 245. 23. Wittgenstein, Remarks on the Foundations of Mathematics. I #155, #156, #162; II #70-#78. 24. Kant, Prolegomena to. Any Future Metaphysics. (Bobbs-Merrill: New York, 1950) p. 60. 25. Wittgenstein, Culture and Value, pp. 20, 36, 60. 26. Kant, Critique of Pure Reason, p. 244. 27. Professor William Stine, lectures on Kant's epistemology, April 1990. 28. Kant, PmlegomenaJto_Any Future Metaphysics, pp. 59-60. 29. David Pears, The False Prison. Oxford: Clarendon Press, 1987, p. 60. 30. Ibid., pp. 469-470. 31. Ibid., pp. 474-489. 32. What follows is taken largely from Professor Humphries' "Wittgenstein and Public Practice." 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ABSTRACT LANGUAGE GAMES: AN EXPOSITION AND DEFENSE OF WITTGENSTEIN'S LATER PHILOSOPHY by ROBERT ALLEN December, 1991 Adviser: Professor Barbara Humphries Major: Philosophy Degree: Doctor of Philosophy This dissertation is an exposition and defense of Wittgenstein's later philosophy. In it, I take Wittgenstein to be posing in his later philosophy a paradox of guidance. That is, I understand him to be questioning the possibility that rules' training give directions for their application. A result of reading Wittgenstein this way is a reconciliation of two opposing views of Wittgenstein's problem: the view that he sought the fact to the matter of guidance and the view that he sought the fact to the matter of intentionality. For those who hold the latter view take it that to have an intention is to have directions for doing something. Wittgenstein's solution to this problem, I argue, is the community disposition theory of guidance: the idea that one is being guided by his training just in case one is going on from it as anyone who took it would. What is the fact that lends credence to claims of 223 224 rule-following? According to Wittgenstein, it is the fact that people would agree regarding the way one should go on from the training in question. Pressed to justify his application of a rule one should say, on this view, that one is following its training as anyone would. Wittgenstein's philosophy of mathematics is taken in this dissertation to be an extension of this theory to foundational questions in mathematics. To justify one's way of doing arithmetic one should appeal to the fact that people agree regarding how to follow arithmetical training. One's being in line with this uniform practice shows that one's arithmetic has a standard, i.e., is a justified way of doing arithmetic. In this connection, Wittgenstein is seen as taking the necessity of our mathematical practices as coming from the fact that we must practice in the way we do or abdicate the doing of mathematics. Mathematics is constituted by necessary rules, not necessary truths. It is not the correspondence between necessary facts and our practices that makes them necessary. Rather, it is our inability to work with other rules. The final two chapters are devoted to comparing Wittgenstein's later philosophy with the work of Kant and Plato. I take Plato to be trying to solve the same skeptical paradox as that which Wittgenstein posed. Plato's essentialism is seen as an inadequate solution to it. Kant, on the other hand, is viewed as anticipating Wittgenstein's views and giving in his refutation of idealism the kernel of Wittgenstein's private language argument. Autobiographical ..Statement I was born in 1959. From 1977 to 1981 I attended the University of Michigan where I majored in psychology and minored in history. Since 1983 I've studied philosophy in the graduate school at Wayne State University. I held a teaching assistantship at Wayne State from 1985 to 1990. From 1988 to 1990 I was President of Wayne State's Graduate Philosophy Club. I plan on pursuing a career as a university professor.