In this essay I shall offer some comments on Wittgenstein’s remarks on rule-following in the Philosophical Investigations (185–242). I share the view voiced by many commentators that these remarks provide a key to the proper understanding of Wittgenstein’s thoughts on the nature of language, meaning and understanding. However, I find myself in disagreement with the way this key role of Wittgenstein’s remarks tends to be construed in a considerable part of the literature. The main reason for what often seems to me to be a misconstrual of the purposes of Wittgenstein’s considerations is a tendency of many interpretations to neglect or disregard what, in my view, is at once the most striking and challenging aspect of the Philosophical Investigations, namely, the view they present of the nature of philosophical problems and their proper treatment. This tendency is by no means a peculiarity of the discussion of Wittgenstein’s remarks on rule-following though, as I hope to show, it is more of a curiosity with regard to them given the frequency and explicitness with which he gives prominence to their methodological purpose. By focusing, more than has been usual, on this aspect of his investigation. I hope to throw a little more light both on Wittgenstein’s rule-following considerations and on his later way of thinking.
Any reader of the Philosophical Investigations must be struck by what Wittgenstein says about ‘the work of the philosopher’ (PI 127):
It was true to say that our considerations could not be scientific ones. […] And we may not advance any kind of theory. There must not be anything hypothetical in our considerations. We must do away with all explanation, and description alone must take its place.
(PI 109)
Philosophy simply puts everything before us, and neither explains nor deduces anything. Since everything lies open to view there is nothing to explain. For what is hidden, for example, is of no interest to us.
One might also give the name ‘philosophy’ to what is possible before all new discoveries and inventions.
(PI 126)
The work of the philosopher consists in assembling reminders for a particular purpose.
(PI 127)
If one tried to advance theses in philosophy, it would never be possible to debate them, because everyone would agree to them.
(PI 128)
Consider also the remark of section 599:
In philosophy we do not draw conclusions. ‘But this must be like this!’ is not a philosophical proposition. Philosophy only states what everyone admits.
Obviously, Wittgenstein’s view of what philosophy is about and how it ought to be practised diverges radically from the images Western philosophers throughout the ages have projected of their own work. For Wittgenstein does not only want to deny that philosophical enquiry is just like scientific enquiry. This denial would be well in accord with one influential traditional view according to which philosophical questions about the nature and possibility of certain phenomena are more fundamental than, or prior to, scientific questions; and hence that the knowledge we need in order to answer these questions is also of a fundamentally different kind than the knowledge science provides of the facts of nature. Thus, for example, on the traditional view, Augustine’s question ‘What is time?’ is not a physical but a metaphysical question, and the knowledge he was looking for is a priori rather than a posteriori knowledge. What Wittgenstein wants to reject is, rather, the assumption of both the scientist and the traditional view that philosophy, like one of the sciences, is a cognitive discipline, namely, a form of inquiry in pursuit of as yet unknown truths about some subject-matter of which a kind of theoretical understanding is needed.
The rationale for Wittgenstein’s rejection of the cognitivist picture of philosophy lies, of course, in Wittgenstein’s conception of the nature of philosophical problems. The business of philosophy, according to Wittgenstein, is not explanation but description, because philosophical questions are not the expression of genuine ignorance at all but of an unclarity about something we do already, in some sense, know and of which we (only) need to remind ourselves (89). Hence, the understanding we need to gain in order to solve philosophical problems does not consist in the discovery of ‘new facts’:
[I]t is, rather, essential of our investigation that we do not seek to learn anything new by it. We want to understand something that is already in plain view. For this is what we seem in some sense not to understand.
(PI 89)
According to Wittgenstein, Augustine’s comment on the question ‘What is time?’ is an apt characterization of the nature of philosophical questions in general: what they ask for is ‘something that we know when no one asks us, but no longer know when we are to explain it’ (PI 89).
What we are unclear about in philosophy, though it is ‘already in plain view’, and of what we need to remind ourselves, Wittgenstein maintains, is the meaning of words, which lies in their use. Thus, philosophy is to be purely descriptive, because the task of removing philosophical unclarity is the task of reminding us of how words are actually used in our language. Rather than to the task of the scientist, Wittgenstein suggests, the task of the philosopher ought to be compared to that of the grammarian. For just like the grammarian, the philosopher seeks to provide an order in ‘our knowledge of the use of our language’ (PI 132). Both the grammarian and the philosopher try to determine what can be ‘said’, the former by clarifying the rules which determine the ways in which we can put words together to construct syntactically correct sentences, the latter by describing which combinations of words have sense. This makes it apt, in Wittgenstein’s view, to call the philosopher’s descriptions ‘rules of grammar’ and to characterize philosophical, conceptual investigations as ‘grammatical investigations’:
Our investigation is therefore a grammatical one. Such an investigation sheds light on our problem by clearing misunderstanding away. Misunderstandings concerning the use of words, caused, among other things by certain analogies between the forms of expression in different regions of language.
(PI 90)
In one of his manuscripts Wittgenstein writes that his methodological reorientation of philosophy consists in the ‘transition from the question of truth to the question of sense’ (MS 105 (Vol. I): 46). This ‘transition’ has often been taken to involve a shift from a concern with the nature of things to a concern with mere words. As a consequence, Wittgenstein’s conception of philosophy as grammar has been criticized for trivializing the task of philosophy by replacing deep and difficult problems by shallow and superficial ones (see Russell 1959: 214). But nothing could be further from the truth. For Wittgenstein does not suggest that we investigate the use of words instead of investigating the essence of the phenomena, to which these words are meant to apply. What he suggests is something else entirely and much more radical, namely, that the puzzlement about essence is in truth a puzzlement about the use of words, and that our inability to see this is, itself, due to grammatical confusions which suggest to us a certain picture of the essence of things and of the nature of philosophy.
Wittgenstein considers this objection in the course of his investigation of the nature of imagination. There one is inclined to protest against Wittgenstein’s methodological instruction: ‘One ought to ask, not what images are or what happens when one imagines something, but how the word “imagination” is used’ (PI 370). For one is tempted to think that the question Wittgenstein wants us to examine is about mere words, while the former question is about the phenomenon of imagination itself. And, surely, one wants to say, it is the phenomenon the word ‘imagination’ is about rather than the use of this word, which is the proper subject of a philosophical analysis. However, Wittgenstein rejects this protest as invalid. He does ‘not want to talk only about words’. He says:
For the question as to the nature of imagination is as much about the word ‘imagination’ as my question is. And I am only saying that this question is not to be decided–neither for the person who does the imagining, nor for anyone else–by pointing; nor yet by description of any process. The first question also asks for a word to be explained; but it makes us expect a wrong kind of answer.
(PI 370)
Essence is expressed by grammar.
(PI 371)
We are inclined to think that the two questions are different. For we presuppose that the words ‘imagine’ and ‘image’ refer, respectively, to a certain mental process or activity and to a kind of object, i.e. to what happens and to what one has when one imagines something. As a consequence, we believe that the answer to the question ‘as to the nature of imagination’ has to tell us what images are or what happens when one imagines something. We then expect that the analysis of the phenomenon of imagination is somehow like a scientific analysis of the process, say, of digestion, that it tells us what goes on when this process takes place; that it gives us an insight into the hidden nature of this process. And we think that imagination is a mysterious process.
According to Wittgenstein, the presuppositions about the essence of imagination are interpretations of the grammar of words, which suggest to us the pictures of a process and a kind of object. And these pictures are grammatical analogies suggested to us by the use of words not explanatory models of certain phenomena. To interpret the grammar of the word ‘imagine’ on the model of a process is to commit oneself to a certain kind of looking at the nature of imagination. It makes us expect a certain kind of answer to the question of what imagination is. Thus, if we interpret the word ‘imagine’ as having the grammar of a process-word like, say, the word ‘digest’, we want to explain what imagination is in the way we explain what digestion is: by showing or describing what happens when a certain process takes place. But this kind of answer to the question of what imagination is will only be appropriate if this interpretation is correct, if the word ‘imagine’ has the grammar of words like ‘digest’. For this reason, then,
We are not analysing a phenomenon (e.g. thought) but a concept (e.g. that of thinking), and therefore the use of a word.
(PI 383)
Some misunderstandings can be removed by analysis, by substituting one form of expression by another one. But to say that what we need in philosophy is the analysis of a concept can be misleading. Because what we think of here is a definition by means of other words, an explicit rule. But most of the words of our language are not learnt this way. And most philosophically relevant misunderstandings do not stem from the lack of a definition. On Wittgenstein’s view, they are, rather, due to a lack of perspicuity, namely, to the fact that the grammar of our words lacks perspicuity (PI 122). In order to remove philosophical misunderstandings, we therefore need not a definition but a perspicuous representation of grammar, which produces the sort of understanding that consists in ‘seeing connections’ (ibid.), which allows us to understand those aspects of the use of words that we were previously prone to misrepresent.
Such misrepresentations of the grammar of words give rise to puzzling ideas (such as, say, that of imagination as a mysterious process) that conjure up the impression of a problem where there is none. Many philosophical problems are, in this way, bogus. The appropriate response to them does not consist in answering the philosophical questions that articulate them, but in making them disappear by achieving the sort of clarity one gains by ‘seeing connections’ in grammar.
[T]he clarity that we are aiming at is indeed complete clarity. But this simply means that the philosophical problems should completely disappear.
(PI 133)
In its aim to make the problem disappear, according to Wittgenstein, the proper treatment of a philosophical question, rather than being similar to a scientific investigation, bears an important similarity to the treatment of a medical or psychological problem:
The philosopher’s treatment of a question is like the treatment of an illness.
(PI 255)
Thus, the methods of philosophical investigations, properly understood, i.e. the methods that enable one to get rid of philosophical problems, are said to be ‘like therapies’ (133). In particular, the therapeutic treatment of a philosophical problem can–in some respects–be fruitfully compared to psychoanalysis, which aims at helping the patient to get rid of his problems by providing him with a certain kind of understanding of the symptoms of his neurotic illness. It seems to me that there are, at least, two such respects. First, on the psychoanalytic view, these symptoms, like dreams, are the expression of repressed emotional conflicts that have their source, in part, in certain phantastic images the patient unconsciously has of himself and his relationship to others. By making him aware (reminding him) of these conflicts and images, through suitable interpretations of his symptoms, the therapy is supposed to enable the patient to abandon these images and cope with his conflicts. Analogously, on Wittgenstein’s view, philosophical problems are the symptoms of a conflict between the pictures misleadingly suggested to us by some aspects of the grammar of a word and its actual use. By making him aware of the source of this conflict, through suitable interpretation, it helps him to abandon the pictures and the inclination to use certain expressions manifesting these pictures. The other respect in which Wittgenstein saw an analogy between the psychoanalytic treatment of neurotic problems and the therapeutic treatment of philosophical problems is constituted by their reliance on the same criterion of correctness for the interpretations offered. Also in philosophy, the interlocutor has to accept the picture or analogy he is being offered as the correct expression of ‘his feeling’, i.e. of the inclination in question; and he has to accept it as the source of ‘his thought’, i.e. as the source of the ideas that conjure up the impression of a problem. Only in this case is the interpretation offered correct (FF 106, UF 121).
In 1930 Wittgenstein wrote in his diary: ‘I still find my way of philosophizing new, and am so often struck by its novelty that I must frequently repeat myself. For another generation it will have become part of their very being and the repetitions will seem boring; for me they are essential’ (MS 105 (Vol. I): 46).–Today one can say with some assurance that the generation Wittgenstein was envisaging has not yet arrived. The novelty of his ‘way of philosophizing’ strikes the present reader of his later work as it struck the author. This may account, in part, for the remarkable fact that in the vast literature on Wittgenstein’s Philosophical Investigations comparatively little explicit attention has been paid to the view of philosophy informing his later way of thinking. In contrast to Wittgenstein’s considerations of almost any other philosophical problem, his remarks on the nature of philosophical problems and their proper treatment have only rarely been critically examined, nor do they seem to play a major role in many discussions of Wittgenstein’s thoughts. Beside the novelty, another reason for this apparent neglect of Wittgenstein’s methodology may be a natural unwillingness to engage seriously with thoughts that radically question one’s philosophical self-image. The third and main reason for this, however, is the objective difficulty of understanding Wittgenstein’s remarks on philosophy and of applying them to the rest of his philosophical investigations. One may, indeed, be forgiven for feeling that, on the whole, too little help is offered by Wittgenstein in the way of clarification and justification of the pronouncements he makes on what philosophy is and what it is not, to enable the reader to critically engage with them. To a considerable extent, this difficulty is, of course, also owed to the form in which Wittgenstein is presenting his thoughts in the Philosophical Investigations, a form that gives the book its unique character but evidently defies our usual expectations of how philosophical argument is to be presented and structured. Wittgenstein characterizes it in the preface by comparing his philosophical remarks to ‘a number of sketches of a landscape’ in which ‘[t]he same or almost the same points were always being approached afresh from different directions’. The arrangement of these sketches is meant to give the reader of his book ‘a picture of the landscape’. ‘Thus’, Wittgenstein writes, ‘this book is really only an album’. At least in part he puts this album-like way of presenting his thoughts down to ‘the nature of the investigation itself’ which ‘compels us to travel over a wide field of thought criss-cross in every direction’. And indeed, the comparison of his work to an album of sketches which give us the picture of a landscape is apparently closely connected to Wittgenstein’s view that a main source of philosophical unclarity is that we lack an ‘overview’ of the use of our words.
It is mainly on account of these difficulties that, in dealing with Wittgenstein’s treatment of philosophical problems, many commentators tend to ignore his methodological remarks and proceed as if, whatever Wittgenstein himself might say, what he must have been trying to do is to advance and argue for substantive philosophical doctrines. One example for this tendency is to be found in the discussion of Wittgenstein’s considerations of rule-following. And nowhere, perhaps, is this tendency more evident than in Saul Kripke’s study Wittgenstein on Rules and Private Language which has convinced many philosophers that the remarks on rule-following both play a key role for the proper understanding of Wittgenstein’s later thought and are of great importance to the philosophy of language, mind and mathematics. In fact, I think, Kripke’s achievement is, to a large extent, owed to the fact that it succeeded in offering an interpretation of Wittgenstein’s thoughts which extracts from them a powerful argument for a radical thesis, and in presenting both thesis and argument in a lucid and straightforward form, which abstracts from the peculiarities and obscurities of the style in which Wittgenstein himself presents his thoughts.1
On Kripke’s reading, the aim of Wittgenstein’s remarks on rule-following in sections 185–242 of the Philosophical Investigations is the development of a sceptical problem concerning the possibility of rule-following. In fact, Kripke thinks that it is the fundamental problem of the Philosophical Investigations (Kripke 1982: 78). By developing this problem, Wittgenstein has invented ‘a new form of scepticism’ (Kripke 1982: 62). The conclusion of this sceptical argument is the ‘paradox’ stated by Wittgenstein in section 201:
This was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule. The answer was: if everything can be made out to accord with the rule, then it can also be made out to conflict with it. And so there would be neither accord nor conflict here.
(PI 201)
According to Kripke, Wittgenstein accepts his sceptical argument. However, he does not rest content with it but devises a sceptical solution to the paradox.2 This solution is supposed to be given in section 202:
And hence also ‘following a rule’ is a practice. And to think one is following a rule is not to follow a rule. Hence it is not possible to follow a rule ‘privately’: otherwise thinking one was following a rule would be the same thing as following it.
(PI 202)
On Kripke’s reading, the aim of Wittgenstein’s rule-following considerations is to show that we cannot make sense of the meaningful use of words as an activity of an individual that is guided by rules as long as we consider the individual in isolation from a community. The natural assumption that an individual’s meaning something by his words, which is the reason why he uses them in a certain way, is a fact about his mental state, Wittgenstein wants to show, leads to the paradoxical conclusion that ‘all language, all concept formation’ is ‘impossible, indeed unintelligible’ (Kripke 1982: 63). According to Kripke’s Wittgenstein, one can only be said to follow a rule, if there exists a community whose agreement on what counts as ‘following’ and ‘not following’ a rule sets the standard of correctness against which the behaviour of an individual is measured. As a consequence, one cannot follow a rule privately. Thus, on Kripke’s interpretation, the conclusion of the so-called private language argument is already given in section 202. For, if the meaningful use of language is an activity guided by rules there cannot be a language which only its speaker can understand.
Kripke’s sceptical interpretation of the paradox of rule-following has been received with much criticism (see Baker and Hacker 1984, McDowell 1984, Malcolm 1986 and Pears 1988). The main point of this criticism was that Wittgenstein, rather than accepting ‘our paradox’, appears straightforwardly to reject it as being based on a misunderstanding:
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 contented us at least for a moment, until we thought of yet another standing behind it. What this shows is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call ‘following the rule’ and ‘going against it’ in actual cases.
Hence there is an inclination to say: every action according to the rule is an interpretation. But we ought to restrict the ‘interpretation’ to the substitution of one expression of the rule for another.
(PI 201)
Obviously, Wittgenstein wants to say that the view that, paradoxically, it is not possible to follow a rule is based on the misunderstanding that to understand or grasp a rule is to interpret it. Hence, there is no need for Wittgenstein to suggest the desperate remedy of a sceptical solution of the paradox.
However, notwithstanding their rejection of Kripke’s sceptical reading of the considerations that lead to the paradox of rule-following, many commentators agree with Kripke that Wittgenstein’s solution or resolution of this paradox lies in the insight that following a rule is a social practice (see, for instance, Malcolm 1986 and McDowell 1984). Like Kripke, the proponents of this common view believe that we can only make sense of the concept of following a rule by realizing that it necessarily implies the concept of a community: one can only follow a rule if one belongs to a community of rule-followers whose agreement on what counts as ‘following’ and ‘not following’ a rule sets the standard of correctness against which the behaviour of an individual is measured. Like Kripke, they hold that it is this insight that accounts for the key role of Wittgenstein’s discussion of the concept of following a rule. This insight seems of fundamental importance for the understanding of the nature of language and thought, since if it is correct we can only make sense of the meaningful use of language and the application of concepts, as an activity guided by rules, as a necessarily social phenomenon, i.e. the practice of a community.
The debate between the proponents and critics of this ‘social view of rule-following’, both as an interpretation of Wittgenstein’s view and in its own right, has for some time dominated the discussion of Wittgenstein’s considerations of rule-following (see Baker and Hacker 1984 and McGinn 1984 for the minority view). Though I find myself on the side of the critics in this debate, I don’t think that to address the question of whether following a rule essentially requires a community was one of Wittgenstein’s primary concerns. In fact, I believe that to think so is to get the aim of Wittgenstein’s treatment of the problem of rule-following completely wrong, and hence also the role of his considerations of rule-following in the Philosophical Investigations. As I hope will become clear, the aim of Wittgenstein’s investigation is not to argue for a certain contentious conception of the meaningful use of language, as the proponents of the common view have it. Rather, as Wittgenstein’s remarks on the nature of philosophical problems and their proper treatment ought to make us expect, his aim is purely therapeutic.
To show that this is so, we first of all need to have a closer look at those remarks which introduce the problem of rule-following, namely, sections 185 and 186 of the Philosophical Investigations. In section 185 Wittgenstein reverts to a language-game which he had introduced in section 143 and which provides the medium for a large part of the long investigation of the concepts of understanding and meaning (139–242). Like the language-game he had employed in his examination of the Augustinian picture of language at the beginning of the book, it is one of giving and executing orders: when A gives an order B has to write down series of signs according to a formation rule. The first of these series is that of the natural numbers. Wittgenstein had previously used the example to examine what it is to grasp a rule (143–155). Now he sets the stage for investigating the question of what it is to follow a rule. He imagines the following case. Suppose we judge by the usual criteria that the pupil has mastered the series of natural numbers. We now teach him to follow orders of the form ‘+ n’, where the formula constitutes a rule for a series of cardinal numbers. For instance, we give him the order ‘+ 2’ and do successful tests with him up to 1000. But when he proceeds beyond 1000 he writes ‘1000, 1004, 1008, 1012’. No doubt, even though this possibility is clearly conceivable, it provides us with an abnormal case. Normally, when someone satisfies the usual criteria for having mastered a mathematical operation like that of forming a series he will not disappoint our expectations that he will carry on competently. After all, the language-game under consideration is a rather primitive one, the mathematical operation fairly elementary. In the abnormal case the teacher would probably react by saying to the pupil things like: ‘Look what you have done!’ or ‘You were meant to add two: Look how you began the series!’. But what if he does not understand us? What if he answers: ‘Yes, isn’t it right? I thought that was how I was meant to do it?’ or ‘But I went on in the same way’? In that case, Wittgenstein says, it would be of no use to repeat the old examples and explanations. For, obviously, it is these examples and explanations which he has misunderstood. What we could say about this person, Wittgenstein suggests, is that it comes natural to him to understand our order with our explanations, as we should understand the order: ‘Add 2 up to 1000, 4 up to 2000, 6 up to 3000 and so on’. Given the primitive character of the mathematical operation the pupil is to perform, there would be a similarity between our case and that ‘in which a person naturally reacted to the gesture of pointing with the hand by looking in the direction from finger-tip to wrist, not from wrist to finger-tip’ (PI 185). By drawing our attention to this abnormal possibility, what does Wittgenstein want to show? The answer to this question is contained in the ensuing dialogue with his imaginary interlocutor. According to the interlocutor’s interpretation, the abnormal possibility raises an epistemological problem. The problem is: how does one know what one must do to follow a rule, and the interlocutor takes Wittgenstein to suggest that one knows this by intuition.
What you are saying, then, comes to this: a new insight–intuition–is needed at every step to carry out the order ‘+ n’ correctly.
(PI 186)
It is natural that being struck by the possibility of understanding the order ‘+ 2’ in an abnormal way causes disquiet. For the case of expanding a series of cardinal numbers seems to be a paradigm example of an operation guided by a mathematical law, i.e. a strict rule which determines a unique successor for the indefinitely many numbers in the series. While it often requires interpretation to apply the rules or criteria for the use of non-mathematical concepts (e.g. legal or moral concepts), the rules that constitute the meaning of mathematical symbols seem to determine their application with logical necessity. As a consequence, we are inclined to explain the perfect certainty with which almost all of us will carry out the order ‘+ 2’ by continuing the initial segment of the series ‘2, 4, 6, 8’ by writing down ‘10’ by our grasp of a rule from which we derive the knowledge of which step is the correct one. It seems that, on the basis of just a finite number of examples and explanations, we come to understand the meaning of the sign ‘+ 2’, i.e. grasp the rule that guides and justifies the use we subsequently make of that sign.
All this, in the interlocutor’s view, takes on a disturbingly problematic aspect in the light of the abnormal possibility. For how, when ordered ‘+ 2’, can one know how to continue the initial segment of ‘2, 4, 6, 8’, if the expression ‘+ 2’, like any other sign, can be variously interpreted, i.e. as the expression of different rules which require and justify different ways of expanding the series? Since the explanations that can be given of the sign ‘+ 2’ do not provide compelling reasons for choosing one interpretation rather than the other, for they too can be variously interpreted, it seems, our knowledge of how to follow the rule ‘+ 2’ cannot ultimately be based on reasons. There appears to be a gap between the order ‘+ 2’ and its execution which, at every step, must be bridged by a new insight or intuition as to which step is the correct one (cf. 431). Hence, the interlocutor concludes that ultimately our knowledge of how to execute the order at each step must be based on a new intuition.
Wittgenstein responds to this suggestion by asking how it is decided what is the correct step at any particular stage, if this is not determined by the rule ‘+ 2’ and the examples by which it is explained? For even though intuition may be the way in which we know which step is correct, it is not what makes it correct. Which step is correct must be determined independently of intuition, if there is anything for intuition to intuit. The interlocutor now makes the natural suggestion that ‘The right step is the one that accords with the order as it was meant’. After all, the order ‘+ 2’ is a sign with a particular meaning, it does not merely consist of meaningless sounds. And to carry out the order one must know what is meant by it. Thus, ‘1002’ is the right step after ‘1000’ because of the rule the teacher meant by ‘+ 2’. This is what one must intuit. But what did this meaning consist in and how did it determine the step that accords with the order? When giving the order ‘+ 2’, did the teacher mean an infinite number of particular propositions, among them ‘that he should write 1002 after 1000’. No, says the interlocutor, what he meant was a general proposition from which all the particular propositions follow: ‘… what I meant was, that he should write the next but one number after every number that he wrote; and from this all those propositions follow in turn.’ However, if the rule ‘+ 2’ does not by itself determine which step is correct, since it can be variously interpreted, neither does the proposition which specifies what was meant by ‘+ 2’. For this proposition is just a paraphrase of the rule ‘+ 2’. Hence, it remains an open question how what is meant by the rule ‘+ 2’ can provide a criterion of correctness for its application. Therefore, if the interlocutor is right in taking the abnormal possibility to raise the problem of how we know what course of action is in accord with the rule, and if the solution to this problem presupposes such a criterion of correctness, then we have not come closer to a solution of this problem. Pending that solution, the way we apply the rule seems to be completely arbitrary. Wittgenstein therefore suggests that ‘It would almost be more correct to say, not that an intuition was needed at every stage, but that a new decision was needed at every stage’ (PI 186).
Were it not for the careful choice of words (‘almost more correct’), the point of Wittgenstein’s critical remark, considered on its own, might be taken to be the rejection of an ‘intuitionist’ epistemology of rule-following in favour of a ‘decisionist’ one. On such a reading, by drawing our attention to the abnormal possibility, Wittgenstein sets the stage for mounting an argument designed to show that, paradoxically, a rule cannot determine what course of action is in accord with it, because any course of action can be brought in accord with it by some interpretation; in particular, what is meant by a sign cannot determine its use. That such a reading is wrong is, however, decisively shown by the progress of Wittgenstein’s exchange with his interlocutor to whose protest, ‘But I already knew, at the time when I gave the order, that he ought to write 1002 after 1000’, he responds, ‘Certainly, and you can also say you meant it then’. According to Wittgenstein, there is nothing wrong with using these forms of words, any more than with saying ‘The steps are determined by the formula’ (189) or ‘The way the formula is meant determines which steps are to be taken’ (190).
What, then, is the point of Wittgenstein’s criticism? The answer is that he wants us to see that there is something wrong with the ‘idea’ or ‘picture’ the interlocutor has of how meaning something by an order or rule determines what must be done to carry it out or follow it. But it is important to be clear about what kind of error the interlocutor is guilty of. Not that Wittgenstein leaves us in any doubt about this. The source of this error, he suggests, is a misunderstanding of the use of the forms of words whose legitimacy the interlocutor is so eager to defend. For one thing, the interlocutor is ‘misled by the grammar of the words “know” and “mean”’ (187) to think that the forms of words ‘I already knew at the time…’ and ‘When I gave the order “+ 2” I meant…’ are used to refer to a certain act which was performed at the time the order was given, an act accompanying the order, like thinking of the step. Against this Wittgenstein first of all suggests that the use of ‘know’ in the past tense ought to be interpreted not to the actual performance of an act in the past but counterfactually:
When you said ‘I already knew at the time…’ that meant something like: ‘If I had then been asked what number should be written after 1000, I should have replied “1002”’.
(PI 187)
Since, in fact, the teacher had not been asked at the time there was nothing with which the actual step of continuing the series could have been in agreement or disagreement. Nonetheless we would not doubt that he knew, i.e. was able to say, what was the correct step, any more than we would doubt someone’s word when he said: ‘If he had fallen into the water then, I should have jumped after him.’ That is to say, we would not doubt the assumption that the teacher possessed the necessary elementary mathematical competence, any more than we would doubt his moral competence.
Wittgenstein thinks that we are now able to understand what was wrong with the interlocutor’s idea of how meaning the order in a particular way determined what one has to do to carry it out.
Here I should first of all like to say: your idea was that the meaning of the order had in its own way already traversed all those steps: that when you meant it your mind as it were flew ahead and took all steps before you physically arrived at this or that one.
Thus you were inclined to use such expressions as: ‘The steps are really already taken, even before I take them in writing or orally or in thought.’ And it seemed as if they were in some unique way predetermined, anticipated–as only the act of meaning can anticipate reality.
(PI 188)
It seems obvious that, in Wittgenstein’s view, the interlocutor’s idea is not wrong in the sense in which a theoretical idea can be wrong. For it is not an explanatory model at all but a kind of mythological picture. Misled by grammar the interlocutor is under the illusion that the explanation of how the rule ‘+ 2’ determines its application in advance lies in the hidden nature of a mysterious mental act. The effect of this illusion is his inclination to use such expressions as ‘The steps are really already taken, even before I take them in writing or orally or in thought’. Is the interlocutor aware of this mythological picture? I don’t think so. Its role is rather that of an interpretation of his inclination which is to make him aware of the illusion of which his inclination is the effect. Its function, I want to suggest, is in an important respect similar to that of an interpretation given in psychoanalysis of a symptom which is to help the patient to understand, become aware of, the emotional conflict of which his symptom is the expression. The purpose of the interpretation in both cases is to help the patient to liberate himself from his problem, in the psychological case from the emotional conflict, in the philosophical case from the disquiet produced by a misleading aspect of grammar. To accept the mythological picture as the correct interpretation of his inclination to use such expressions is to accept that this inclination has its source in a grammatical confusion and ought to enable one to give up its use.
The way the interlocutor understands Wittgenstein’s argument, however, contrasts sharply with the interpretation I have suggested of it. Far from recognizing the therapeutic character of Wittgenstein’s criticism of his idea of how meaning something by the algebraic formula determines the steps to be taken, the interlocutor takes him to question that the steps are determined by the formula at all. ‘But are the steps then not determined by the algebraic formula?’, he asks (189). To which Wittgenstein responds with the comment that the interlocutor’s question ‘contains a mistake’ (189). The mistake consists in the presupposition that there must be an explanation of how the algebraic formula determines the steps; that otherwise we must conclude that they are not determined by the formula. And since Wittgenstein’s argument, as it strikes the interlocutor, aims to show that the most natural explanation of this fact is wrong, he takes Wittgenstein to draw precisely that conclusion. Thus, he mistakes Wittgenstein’s rejection of his interpretation of the grammar of the sentence ‘The way the formula is meant determines which steps are to be taken’, for a denial of a metaphysical truth, namely, that a rule, meant or understood in a particular way, determines the course of action in accord with it. This he does because he finds his own interpretation natural. In effect, he wants to defend the legitimacy of this form of expression, but he does so in the belief that he is defending a philosophical claim. In Wittgenstein’s view, however, the legitimacy of our ordinary use of this form of expression is not in question at all. Nor is there anything wrong with saying: ‘The way the formula is meant determines which steps are to be taken’ (190). What Wittgenstein does question is, as I said, the legitimacy of the interpretation put upon those words by the interlocutor. That interpretation manifests itself in the ‘metaphysical use’ of such expressions as ‘The steps are in a unique way predetermined by the act of meaning’, which try to capture the elusive essence of the way in which the steps are determined.
What we have to do, according to Wittgenstein, is ‘to bring words back from their metaphysical to their everyday use’ (116). For we do use the expression: ‘The steps are determined by the formula…’. We can either use it to make a causal statement about how people are brought by education (training) to apply an algebraic formula like ‘y = 2x’ in the same way, i.e. that they all work out the same value for ‘y’ when they substitute a number for x. By making such a statement we may want to distinguish these people from others who apply the formula in different ways. Or we can use this expression to make a grammatical statement about a kind a formula, say ‘y = 2x’, in contrast to one that does not, e.g. in the context of teaching someone the different kinds of formulae. Equally, the sentence ‘The way the formula is meant determines which steps are to be taken’, has a legitimate use. But the criteria for the way the formula is meant are not provided by a description of how a certain act of meaning is performed but by describing the way we always use such a formula: the way we are taught to use it.
Having clarified the perfectly ordinary senses in which we can say, ‘The way the formula is meant determines which steps are to be taken’, Wittgenstein now turns to examining a related problem about understanding. It seems undeniable that someone who understands a sign, i.e. grasps its meaning, knows its use. There can be no doubt about this, any more than one can doubt that the way a sign is meant determines its use. But just as we may be puzzled by how this is done, so we may also be puzzled by how one can grasp the whole use of a sign when we understand it:
‘It is as if we could grasp the whole use of the word at a stroke’. Like what for example?–Can’t the use–in a certain sense–be grasped at a stroke? And in what sense can it not?–The point is, that it is as if we could ‘grasp it at a stroke’ in yet another and much more direct sense than that.–But have you a model for this? No. It is just that this expression suggests itself to us. As the result of the crossing of different pictures.
(PI 191)
You have no model of this superlative fact, but you are seduced into using a super-expression. (It might be called a philosophical superlative.)
(PI 192)
If Wittgenstein is right, however, the puzzle about how we can grasp the whole use of a word at a stroke is no more a problem that calls for a kind of theoretical explanation as a solution than was the former puzzle about meaning. When in the course of ordinary life we use the expression ‘I grasped the whole use of the word at a stroke’, it does not seem to us as if there was something astonishing or hard to understand about what happened. It is not as if there were some process whose mechanism we don’t understand or some super-human act we see in a movie. According to Wittgenstein, it is only when we look at that form of expression (‘grasping the whole use of a word at a stroke’), that what happened may come to assume a problematic aspect. For then we may well form the idea of a ‘queer process’, a ‘superlative fact’ of which we have ‘no model’. There is only a ‘super-expression’, namely the sentence ‘It is as if we could grasp it at a stroke in yet another much more direct sense’, which we are ‘seduced into using’.
But let us look closer at what is going on here. Wittgenstein says that the ‘super-expression’ results from the ‘crossing of different pictures’. If I am not mistaken, these pictures are, on the one hand, that of a mental process which occurs when one grasps the whole use of a word at a stroke and, on the other, that of the use of the word as a future process. The ‘crossing’ of these pictures produces the idea of a ‘queer process’ in which the future use must in some way be present and yet cannot be itself present. This reading is suggested by the following remarks:
In our failure to understand the use of a word we take it as the expression of a queer process. (As we think of time as a queer medium, of the mind as a queer kind of being.)
(PI 196)
‘It’s as if we could grasp the whole use of a word at a stroke.’–And that is just what we say we do. That is to say: we sometimes describe what we do in these words. But there is nothing astonishing, nothing queer, about what happens. It becomes queer when we are led to think that the future development must in some way already be present in the act of grasping the use and yet isn’t present.
(PI 197)
Wittgenstein continues this remark by suggesting the source of this thought:
For we say that there is no doubt that we understand the word, and on the other hand, its meaning lies in its use.
(PI 197)
This brief diagnosis harks back to the very beginning of Wittgenstein’s investigation of the concept of understanding (138–142). The nature of understanding can seem puzzling because, on the one hand, we understand the meaning of the words spoken to or by us ‘when we hear or say them’, i.e. we grasp their meaning ‘at a stroke’, while on the other hand the meaning of a word is its use or is at least determined by its use, and to understand the meaning of a word is to know its use. But how is this possible, if the use of a word is something ‘which is extended in time’? (138). For while, on the one hand, grasping the meaning at a stroke seems to require the presence of what is grasped, what is present cannot be literally identical with the future use of the word. On the other hand, by grasping the meaning of a word one grasps how it must be used. It is therefore a natural thought that what one grasps when one grasps the meaning of a word (i.e. the meaning of the word qua what we grasp) is internally related to the word’s correct use (i.e. the meaning qua use), namely, that the former is related to the latter by determining which use of the word is in accord with it and thus explains one’s knowledge of the use of the word.
On this way of looking at the problem, we must look for a model of something that constitutes the meaning of a word qua what one grasps and, like a rule, determines its use. In section 139 Wittgenstein considers one natural suggestion for such a model of what is meant by a word, namely that the meaning of a word qua what one grasps is a kind of picture which comes before our mind when we hear a word and understand it, for instance the picture of a cube when we hear the word ‘cube’. Suppose I am given the order ‘Bring me a cube!’. Then, according to the present view, my understanding of the order (i.e. my knowing of what I am ordered to do), consists in part in my having before my mind something like a picture of a cube which shows me what I have to bring. And what I do will either agree or disagree with that picture. Thus, if I bring a cube, what I do is in accord with it, while if I bring a triangular prism it is not.
In his criticism of this suggestion, Wittgenstein draws our attention to the possibility of imagining a method of projection according to which the application of the word ‘cube’ to triangular prisms does after all fit the picture that may come before our mind when we hear the word ‘cube’. Thus, in this case, when I am given the order ‘Bring me a cube!’ and I bring a prism I can be said to have executed the order. The picture of a cube does suggest a certain use to us, but with a different method of projection a different application will be in accord with it. Since it is the method of projection that determines what is to be called ‘agreement’ or ‘disagreement’ between picture and application, one is tempted to think that to understand a word is to have a picture plus the method of projection before one’s mind. But Wittgenstein’s argument applies equally to any mental representation of a given method of projection, since any schema representing the rule of projection (‘say a picture of two cubes connected by lines of projection’) could also be applied in a number of ways. But if the same mental representation can come before our mind when we hear a word, and yet the use of this word be different, then the word in those cases cannot have the same meaning; and so the suggested solution of the puzzle must be rejected.
This criticism is, of course, well known. Nonetheless, it deserves a closer look from a methodological point of view, since it is instructive to note what Wittgenstein has to say about the kind of error his criticism is directed at and the nature of his argument:
Then what sort of error did I make? The error which one would like to express by saying: I should have thought the picture forced a particular use on me. How could I think that? What did I think? Is there such a thing as a picture, or something like a picture, that forces a particular application on us; so that my mistake lay in confusing one picture with another?–For we might also be inclined to express ourselves like this: we are at most under a psychological, not a logical, compulsion. And now it looks quite as if we knew of two kinds of case.
What did my argument consist in? It called our attention to (reminded us of) the fact that there are other processes, besides the one we originally thought of, which we would under certain circumstances be prepared to call ‘applying the picture of a cube’. So, our ‘belief that the picture forced a particular application upon us’ consisted in the fact that only the one case and no other occurred to us. ‘There is another solution as well’ means: there is something that I am also prepared to call a ‘solution’; to which I am prepared to apply such-and-such a picture, such-and-such an analogy, and so on.
What is essential is to see that the same thing can come before our minds when we hear the word and the application still be different. Has it the same meaning both times? I think we shall say not.
(PI 140)
We are inclined to think that the error in the suggested solution to the puzzle about understanding which Wittgenstein wants to point out consists in the mistaken belief that the picture logically compels me to use the picture in a certain way. On this way of looking at it, his argument shows that the ‘picture-theory’ of how the meaning of a word determines its use rests on a confusion between psychological and logical compulsion. On this view, what the proponent of the ‘theory’ doesn’t realize is that ‘we are at most under a psychological, not a logical compulsion’. But, as Wittgenstein indicates, this is not the right way of looking at what his argument is supposed to show and what kind of argument it is. For the erroneous ‘belief that the picture forced a particular application upon us’, says Wittgenstein, just ‘consisted in the fact that only the one case and no other occurred to us’. And the argument that shows this is not a demonstration that our belief was false, since that would presuppose that we knew two kinds of compulsion that we confused. But there is no such thing as logical compulsion. The argument consists, rather, in calling to our attention a fact concerning the use of words, namely, the fact that there are other processes, besides the one we originally thought of, which we would under certain circumstances be prepared to call ‘applying the picture of a cube’. Thus, the error in the ‘picture-theory’ of meaning which Wittgenstein’s argument is designed to bring out is a grammatical confusion. To be sure, the point of Wittgenstein’s argument is to show something about the essence of what is meant or understood by a word, namely, ‘that the same thing can come before our minds when we hear the word and the application still be different’, and that, as a consequence, the word has not the same meaning in this case. However, it does so not by telling us something new, but by a grammatical reminder.
Here, as in the sections 185–186 previously discussed, Wittgenstein does not seek to establish that ‘There is no logical compulsion’ forcing us to put down ‘1002’ after ‘1000’ in response to the order ‘+ 2’ or compelling us to apply the drawing of a cube precisely to cubes. Rather, he wants to make us realize how we arrive at the picture of a mysteriously inexorable kind of compulsion, a compulsion that forces us with the inexorability of logic, by the quasi-mechanistic means of an inner ‘psychological’ process. We arrive at this picture, i.e. at the idea that the drawing of a cube or the rule ‘+ 2’ ‘force a particular application upon us’ in this mysterious way, by misinterpreting the responses that come natural to us, as driven by some peculiarly inexorable process, quite simply because no other application occurs to us than the one that strikes us as natural. In reminding us of that, namely, of what abnormal responses we would still be willing to accept as applications of the picture or rule, Wittgenstein thus wants to show us how we came to endorse a mysterious picture that is in conflict with the ways in which we actually speak of ‘grasping a word’s meaning or a rule’. This, then, may enable us to shed this picture. And this resolves the conflict of which the problems we discussed are the symptoms.
With section 197 we have only reached the thirteenth of fifty-eight remarks on rule-following. But, I hope, it has already become clear that at least in these remarks Wittgenstein is practising exactly what he is preaching in his remarks about the nature of philosophy. A reading that takes seriously the therapeutic aspect of Wittgenstein’s investigation would therefore, I believe,
ERICH AMMERELLER also provide a promising perspective for the remainder of his considerations. In particular, the debate on the question of what thesis Wittgenstein is arguing for (be it sceptical or social) may appear in a new light. For if Wittgenstein’s aim is purely therapeutic, he is not arguing for any thesis whatsoever.
1. Kripke is, of course, aware that his way of presenting Wittgenstein’s argument is at odds with Wittgenstein’s own ‘philosophical style’ (Kripke 1982: 5). He therefore suggests that ‘the present paper should be thought of expounding neither “Wittgenstein’s” argument nor “Kripke’s”: rather Wittgenstein’s argument as it struck Kripke’. He also believes that his attempt to present Wittgenstein’s precisely is ‘to some extent to falsify it’ (Kripke 1982: 5).
2. A sceptical solution similar to Hume’s solution of his sceptical doubts about causation.
Baker, G. and Hacker, P.M.S. (1984) ‘On Misunderstanding Wittgenstein: Kripke’s Private-Language Argument’, Synthese 58: 407–50.
Cavell, S. (1979) The Claim of Reason, Oxford: Oxford University Press.
Diamond, C. (1991) The Realistic Spirit. Wittgenstein, Philosophy and Mind,Massachusetts: MIT Press.
Kripke, S.A. (1982) Wittgenstein on Rules and Private Language, Oxford: Blackwell.
McDowell, J. (1984) ‘Wittgenstein on Following a Rule’, Synthese 58: 325–63.
McGinn, C. (1984) Wittgenstein on Meaning, Oxford: Blackwell. Malcolm, N. (1986)
Wittgenstein: Nothing is Hidden, Oxford: Blackwell.
Pears, D. (1988) The False Prison. A Study of the Development of Wittgenstein’s Philosophy, Vol. 2, Oxford: Oxford University Press.
Russell, B. (1959) My Philosophical Development, London: Allen & Unwin.