Ludwig Wittgenstein was born in Vienna in 1889 and died in Cambridge in 1951. He studied engineering, first in Berlin and then in Manchester, and he soon began to ask himself philosophical questions about the foundations of mathematics. What are numbers? What sort of truth does a mathematical equation possess? What is the force of proof in pure mathematics? In order to find the answers to such questions, he went to Cambridge in 1911 to work with Russell, who had just produced in collaboration with Whitehead (1861-1947) Principia Mathematica (1910-1913), a monumental treatise which bases mathematics on logic. But on what is logic based? Wittgenstein's attempt to answer this question convinced Russell that he was a genius. During the 1914-8 war he served in the Austrian army and in spare moments continued the work on the foundations of logic which he had begun in 1912. His war-time journal, Notebooks 1914-16 (1961), reveals the development of his ideas more clearly that the final version, Tractatus Logico-Philosophicus, which he published in the early 1920s.
He then abandoned philosophy for a life of a very different kind. He taught in a village school in Austria and after that worked in the garden of a monastery. He returned to philosophy in the late 1920s, drawn back into it by discussions with some of the members of the Vienna Circle and with the Cambridge philosopher Frank Ramsey (1903-30). They wanted him to explain the Tractatus, but their request for elucidations soon produced second thoughts. When he returned to Cambridge, he developed a different philosophy which made its first public appearance in 1953 in his posthumous book, Philosophical Investigations. Before its publication, direct acquaintance with his new ideas had been confined to those who attended his lectures and seminars in Cambridge.
In the second period of his philosophy, as in the first, his notes are the key to his published work. Written continuously from 1929 until his death, they would occupy many metres of shelves if they were all edited and published as books. Philosophers usually intend what they write to be read by others, but these notes are a kind of thinking on paper. It is true that some of the sets are evidently being steered towards publication, but in most of them Wittgenstein is facing problems alone. Since his death many books have been extracted from this material.
2. The General Character of Wittgenstein's Philosophy
Wittgenstein's philosophy is difficult to place in the history of ideas largely because it is anti-theoretical. It is true that in his early work he did produce a theory of logic and language, but it was a theory which demonstrated its own meaninglessness. That was a paradox which he presented, appropriately enough, in a metaphor borrowed from the Greek sceptic, Sextus Empiricus (c.150-c.225): 'Anyone who understands me eventually recognises [my propositions] as nonsensical, when he has used them as steps - to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it)' (Wittgenstein, 1922, 6.54). After 1929 he completely avoided theorising. The task of philosophy, as he now saw it, was never to explain but only to describe. Since western philosophy had mainly been conceived as a search for explanations at a very high level of generality, his work stood to one side of the tradition.
Wittgenstein was not a sceptic. The reason why he rejected philosophical theorising was not that he thought it too risky and liable to error, but because he believed that it was the wrong way for philosophers to work. Philosophy could not, and should not try, to emulate science. That is a point of affinity with Kant, but while Kant's critique resulted in a system in which each of the many forms of human experience found a place, Wittgenstein attempted no such thing. His method was to lead any philosophical theory back to the point where it originated, which might be some very simple routine, observable even in the life of animals but rendered unintelligible by the demand for an intellectual justification. Or it might start from the 'crossing of two pictures' - for example, we construe sensations (pp. 180-2) as objects that are not essentially dependent on their links with the physical world, and so we attribute to them a basic independence modelled on the basic independence of physical objects. His aim was to cure this kind of illusion by a therapy that would gradually lead the sufferer to recognise, and almost to recreate its origin, and so to escape from its domination.
Philosophers are expected to be able to abstract the general from the particular, but Wittgenstein's gift was the opposite - a rare ability to see the particular in the general. He could demolish a theory with a few appropriate counter-examples. His method was to describe an everyday situation which brings a philosophical speculation down to earth. When he used imagery, it was carefully chosen to reveal the structure of the problem under examination. All this helps to explain why his later philosophical writings have been read and appreciated by people with very little philosophical training. However, the explanation of the wide appeal of his later work is not just stylistic. He is evidently taking apart a philosophical tradition that goes back to antiquity. That is a way of treating the past which can be found in many other disciplines today, and even when the scene that he is dismantling has not been precisely identified he can still be read with sympathy and with intuitive understanding.
3. Wittgenstein's Early Philosophy
In spite of the wider appeal of his later work, Wittgenstein was without a doubt a philosopher's philosopher. In the Tractatus he developed a theory of language that was designed to explain something that Russell had left unexplained in Principia Mathematica, the nature of logical necessity. The marginal status of theories in his early philosophy did not deffect this theory from its main goal, which was to show that logically necessary propositions are a kind of by-product of the ordinary use of propositions to state facts. A factual proposition, according to Wittgenstein, is true or false with no third alternative. For he agreed with Russell's theory of definite descriptions: failure of a complex reference simply makes a proposition false. So if two propositions are combined to form a third, compound, proposition, its truth of falsity will simply depend on the truth or falsity of its two components. Now suppose that we want to find out if it really is a contingent, factual proposition, like its two components. What we have to do is to take the two components and run through all their combinations of truth and falsity, and we will find that there are three possible outcomes to this test. The compound proposition may be true for some combinations of the truth-values of its components but false for others, in which case it is a contingent factual proposition. Or it may come out false for all combinations, in which case it is a contradiction. Or, finally, it may be a tautology, true for all combinations. Contradictions and tautologies say nothing. However, they achieve this distinction in two opposite ways, the former by excluding, and the latter by allowing, every state of affairs. So propositions whose truth or falsity are guaranteed by logical necessity are limiting cases, extreme developments of the essential nature of factual propositions.
This explanation of logical necessity answered a question that the axiomatization of logic by Frege and Russell had left unanswered: why should we accept the axioms and rules of inference with which such calculi start? In fact, if every proposition can be tested independently for logical necessity, there does not seem to be any need to promote some of them as axioms and to deduce the others from them. Schopenhauer (1788-1860) had taken the same view of the axiomatization of geometry, which seemed to him to be rendered superfluous by spatial intuition.
Wittgenstein's early account of the foundations of logic relies on semantic insight. If a formula is logically necessary, we can see that it is. There is no need to prove its status from axioms, because a truth-functional analysis will reveal it. If one factual proposition follows from another, we can see that it does, and there is no need to demonstrate that it does by a proof that starts from a logically necessary formula. The two propositions will simply show that their senses are connected in a way that validates our inference. This treatment of logic leaves proof without any obvious utility - a problem that Wittgenstein took up later in his philosophy of mathematics.
The pictorial character of propositions is a theme with many developments in the Tractatus. Not only is it used to explain the foundations of logic and the internal structure of factual language; it also has implications for scientific theories, it yields a treatment of the self which carries the ideas of Hume, Kant and Schopenhauer one stage further, and it allows Wittgenstein to demonstrate that factual language has definite limits.
Wittgenstein believed that Ethics, Aesthetic and religious discourse lie beyond those limits. This has started a long-running controversy about the implications of his placing of the 'softer' kinds of discourse. Was he a positivist, as the philosophers of the Vienna Circle later assume? Or could the opposite conclusion be drawn from what he said about the Tractatus in a letter to L. Ficker: 'The book's point is an ethical one . . . My work consists of two parts: the one presented here plus all that I have not written. And it is precisely this second part that is the important one. My book draws limits to the sphere of the ethical from the inside, as it were' - that is, from inside factual language. If this epigram is taken literally, it appears to put a low value on his solutions to the problems of language and logic. However, nearly all his later work is concerned with the same problems, and there is really no need to subject the Tractatus to such a simple dilemma. Its point is Kantian: ethics (and the whole softer side of discourse, including philosophy itself) must not be assimilated to science.
4. Propositions as Pictures
Wittgenstein's early theory of language was also developed in another direction. If it threw light on the foundations of logic, it ought also to throw light on the structure of ordinary factual discourse. In order to understand this development, we have to go back one step and ask why he thought that factual propositions must be true or false with no third alternative. His reason was that he took them to be a kind of picture. If the points on the canvas of a landscape-painter were not correlated with points in space, no picture that he painted would succeed in saying anything. Similarly, if the words in a factual proposition were not correlated with things, no sentence constructed out of them would say anything. In both cases alike the constructions would lack sense. But, given the necessary correlations, the painting and the proposition have sense and what they say can only be true or false.
Now this runs up against an obvious objection. Many words designate complex things, which do not have to exist in order that the propositions containing them should make sense, and this casts doubt on the analogy between points on a canvas and words. The obvious response would be to claim that such words are complex and that the simpler words out of which they are compounded do have to designate things. Wittgenstein went further and argued that it must be possible to continue this kind of analysis to a point at which no more subdivision would be possible. His argument for this extreme version of logical atomism had nothing to do with empiricism. What he argued was that, if analysis stopped short of that terminus, the sense of a proposition containing a word which designated something complex would depend on the truth of a further proposition. This further proposition would say that things had been combined to form the complex but it would not be part of the sense of the original proposition. That, he argued, was an unacceptable result both for pictures and propositions. Their senses must be complete, self-contained and independent of one another.
The first modification of the system of the Tractatus appeared in 1929 in Wittgenstein's article, 'Some Remarks on Logical Form' (the only other piece of work that he published - everything else is posthumous). He no longer believed in the extreme version of logical atomism for which he had argued in 1922. The requirement, that elementary propositions be logically independent of one another, now struck him as excessive. The reason for his change of mind was simple: singular factual propositions always contain predicates belonging to ranges of contraries. So colour-predicates are incompatible with one another and there is no hope of analysing them into simpler predicates that would not be incompatible with one another. Position, length, velocity, and, in general, all measurable properties, show the same recalcitrance to the analysis required by the Tractatus. He therefore dropped the requirement.
There are two things that make this change of mind important. Firstly, though the Tractatus contains an atomistic theory of language, there are passages that reveal an underlying holism. For example, he says: 'A proposition can determine only one place in logical space: nevertheless the whole of logical space must already be given with it' (1922, 3.42). But the new view of elementary propositions is an open move towards holism. What is now said to be 'laid against reality like a ruler' (1922, 2.1512) is not a single, independent, elementary proposition, but, rather, a set of logically incompatible elementary propositions. For when one predicate in a group of contraries is ascribed to a thing, the others are necessarily withheld. It is plausible to regard this holism as the natural tendency of Wittgenstein's mind, and the atomism as something that he took over from Russell and eventually repudiated.
The change of mind also has a more general importance. The atomism of the Tractatus was offered not as a theory that was supposed to fit the observable surface of factual language, but as a theoretical deduction about its deep structure. Indeed, Wittgenstein was so confident of the validity of the deduction that he was not worried by his inability to produce a single example of a logically independent elementary proposition. This dogmatism evaporated when it occurred to him that the logical structure of language might be visible on its surface and might actually be gathered from the ordinary uses that we make of words in ordinary situations. This was the point of departure of his later philosophy.
6. His Later Philosophy: The Blue Book
The most accessible exposition of the leading ideas of Wittgenstein's later philosophy is to be found in the Blue Book (1958), a set of lecture-notes that he dictated to his Cambridge pupils in 1933-4. What he then did was so far out of line with the tradition that we may at first feel inclined to question whether it really is philosophy. His answer was that it might be called 'one of the heirs of the subject which used to be called "philosophy".' The conspicuous novelty is the absolute refusal to force all the multifarious variety of thought and language into the mould of a single theory. He criticised the 'contempt for the particular case' that any such attempt would involve, and he systematically repressed the craving for generality that has characterised western philosophy since Socrates first instigated the search for the essences of things. We may, of course, ask such questions as 'What is knowledge?', but we must not expect to find the answer wrapped up in the neat package of a definition. There will be many different cases, and though they will show a family resemblance to one another, they will not be linked by the possession of a single set of common properties. Socrates asked for a conjunction of properties, but we must be content with a disjunction.
That is an accurate placing of Wittgenstein's new philosophy in the history of ideas, but it leaves an important question unanswered. Why should a catalogue of examples be regarded as a solution to a philosophical problem? Is it not just a collection of the kind of material that poses the problem? The point of these questions is that 'the heir to philosophy' needs to be something more than well-documented negative advice not to theorise: it ought to teach us to see philosophical problems from the inside and to find a more positive way of laying them to rest.
There are, in fact, two discussions in the Blue Book that demonstrate that Wittgenstein's later work was a positive continuation of the philosophy of the past. One is the long investigation of meaning and the other is the treatment of the self. Both are very illuminating.
The discussion of meaning is a development of a point made in the Tractatus: 'In order to recognise a symbol by its sign, we must observe how it is used with a sense' (1922, 3.326). This remark consorts uneasily with the picture theory of propositions, which derives meaning from the original act of correlating name with object. The theory implies that meaning is rigid, because it is based on a single, self-contained connection which, once made, remains authoritative, without any need for interpretation or any possibility of revision. The remark points the way to a more flexible account of meaning which will accommodate all the different uses that we make of words and leaves room for plasticity. This is the difference between treating language as a fossil and treating it as a living organism.
The discussion of meaning in the Blue Book develops the isolated remark in the Tractatus and criticise the rigidity of the theory offered elsewhere in the book. Ostensive definition, which was supposed to attach a word to its object, is shown up as a very inscrutable performance, compatible with many different interpretations of a word's meaning: the underlying assimilation of all descriptive words to names designating objects is rejected; and so too is the assumption that the meaning of a word is something that belongs to it intrinsically, and, therefore, independently of its use. This last point proved to be important. For if meaning never belongs to a word intrinsically, it will never be possible to explain the regularity of a person's use of a word by citing the rule that he or she is following. For the meanings of the words in which the rule is expressed will themselves need to be interpreted. This line of thought is developed in Philosophical Investigations (1953).
The treatment of the self in the Blue Book is very clear and strongly argued. As in the Notebooks and the Tractatus, it is presented as part of an examination of solipsism, but it is much easier to discern the structure of the later version of the argument. The central point is that the solipsist's claim 'Only what I see exists', is not what it seems to be. The solipsist seems to be referring to himself as a person, but really he or she is using the pronoun 'I' to refer to something entirely abstract which is introduced merely as 'the subject which is living this mental life' or 'the subject which is having these visual impressions'. But if the subject is not given any independent criterion of identity, there is no point from which the reference to 'these impressions' can be made. The solipsist constructs something which looks like a clock, except that he pins the hand to the dial, so that they both go round together. Saying what exists, like telling the time, must be a discriminating performance. The idea that the subject is a vanishing point, which was developed by Hume, Kant and Schopenhauer, is here put to a new use.
7. Philosophical Investigations: the Private Language Argument
The so-called 'private language argument' of Philosophical Investigations is closely related to the rejection of a solipsism which is based on an ego without a criterion of identity. What the two critiques have in common is a requirement which was later expressed very concisely by W. V. O. Quine, 'No entity without identity'. The solipsist's ego lacks any criterion of personal identity, and similarly, if the quality of a sensory experience were completely disconnected from everything in the physical world - not only from any stimulus but also from any response - it would lack any criterion of type identity. The parallelism of the two critiques is very close in the lecture-notes in which Wittgenstein first developed the so-called 'private language argument'. Against the solipsist who says, 'But I am in a favoured position. I am the centre of the world', he objects, 'suppose I saw myself in a mirror saying this and pointing to myself, would it still be all right?' (Notes for Lectures on 'Private Experience' and 'Sense-data', 1968, p. 299). Against the phenomenalist who argues for detached sensation-types and says, 'But it seems as if you are neglecting something', he objects, 'What more can I do than distinguish the case of saying "I have tooth-ache" when I really have toothache, and the case of saying the words without having tooth-ache? I am also (further) ready to talk of any x behind my words so long as it keeps its identity' (1968, p. 297).
The interpretation of this important line of thought in his later work is difficult. The parallelism between the two critiques is always a helpful clue, a thread which we must never relinquish in the labyrinth of confusing indications.
One source of confusion is hardly Wittgenstein's fault. He himself never used the phrase 'private language argument'. It is his commentators who use it and, by doing so, they have created the illusion that a single, formal argument ought to be extractable from the text of Philosophical Investigations is not the structure of his critique. He argued dialectically, and when his adversary tries to introduce the 'neglected x' behind the words reporting a sensation, he always tries to show his adversary that, if this x is not covered by ordinary criteria of identity based on the physical world, it will not have any criterion of identity at all.
At this point it is a good idea to ask who his adversary is. Evidently, ,his adversary is a philosopher who supports some kind of sense datum theory. B t what kind? One suggestion that has been made is that it is the sense datum theory which he himself adopted in the Tractatus (not very openly). Since he extended his critique to include other mental entities besides sensations, this suggestion has been generalised, and he has been taken to be criticising the 'mentalistic theory of meaning of the Tractatus' (Malcolm, 1986, ch. 4). But a brief review of the development of his philosophy of mind will show that these suggestions are mistaken.
Anyone who compares what Wittgenstein said about simple objects in the Notebooks and in the Tractatus will see immediately that he was uncertain of their category in the former and in the latter was convinced that his uncertainty did not endanger his logical atomism. Maybe they were material particles or perhaps they were Russellian sense data. He did not care, because his argument for their existence did not depend on their category and he did not think that it needed verification by the actual discovery of examples. However, the possibility that they were sense data was worth exploring, especially after his abandonment in 1929 of the extreme version of logical atomism. So when he returned to these problems after the long interval that followed the publication of the Tractatus, he worked out the consequences of identifying them with sense data. This fitted in very well with the programme of the Vienna Circle philosophers. They were interested in the philosophy of science and predisposed to accept a simple stratification of language, with the phenomenal vocabulary on the basic level and the physical vocabulary on the upper level and complete inter-translatability between the two levels.
It is notorious that this kind of phenomenalism looks impregnable until we examine the route that led us into it. That is what Wittgenstein did, and he found an obstacle which seemed to him to make the route impassable. The original position from which it started was supposed to be one in which people spoke a phenomenal language with a vocabulary completely disconnected from the physical world. It is obvious that such a language would be necessarily unteachable, and since Wittgenstein used the word 'private' to mean 'necessarily unteachable', it would be a private language. What is not so obvious is how he thought that he could show that such a language would be impossible.
The primary target of his critique of private language is the sense-datum language that phenomalists claimed that each of us could set up independently; of anything in the physical world and, therefore, in isolation from one another. But the scope of his attack is much wider, because it would show that no mental entity of any kind could ever be reported in such a language. However, neither in its narrow nor in its wide scope is it directed against anything in the Tractatus. For just as there was no commitment to phenomenalism in the early work, so too there was no commitment to the thesis that the meaning of a sentence is derived from the meaning of the thought behind it. If the critique of private language is related to anything in the Tractatus, it is to the critique of ego-based solipsism, but positively, as a further application of the same general demand for a criterion of identity.
It is necessary to distinguish two moves that Wittgenstein made in his dialectical critique of a necessarily unteachable sensation-language. The phenomenalist believes that we can set up this language and use it to report our sense data in complete independence from anything in the physical world. Against this, Wittgenstein's first move was the one that has already been described: he asked for the criterion of identity of the supposedly independent sensation-types. That is a purely destructive demand. His second move was to point out that a report of a sensation will usually contain an expression of the sensory type and seldom a description of it. This move was the beginning of a reconstruction of the situation, designed to lead to a better account of sensation-language.
The destructive move is made most perspicuously in Philosophical Investigations. Suppose that a word for a sensation-type had no links with anything in the physical world and, therefore, no criteria that would allow me ~ to teach anyone else its meaning. Even so, I might think that, when 'I applied it to one of my own sensations, I would know that I was using it correctly But, according to Wittgenstein, that would be an illusion, because in such an isolated situation I would have no way of distinguishing between knowing that my use of the word was correct and merely thinking that I knew that it was correct., Notice that he did not say that my claim would be wrong: his point is more radical - there would be no right or wrong in this case. (Wittgenstein, 1953, § 258).
The common objection to this criticism is that it simply fails to allow for the ability to recognise recurring types of things. This, it is said, is a purely intellectual ability on which we all rely in the physical world. So what is there to stop a single person relying on it in the inner world of his mind? Perhaps Carnap was right when he chose 'remembered similarity' as the foundation of his Logical Structure of the World (1967).
Here Wittgenstein's second move is needed. If the ability to recognise types really were purely intellectual, it might be used in the way in which Carnap and others have used it, and it might be possible to dismiss Wittgenstein's objection by saying, 'We have to stop somewhere and we have to treat something as fundamental - so why not our ability to recognise sensation types?' But against this Wittgenstein argues that what looks like a purely intellectual ability is really based on natural sequences of predicament, behaviour and achievement in the physical world. Pain may seem to be ~a"clea example of a sensation-type which is independently recognisable, but the word is really only a substitute for the cry which is a natural expression of the sensation (1953, ~~ 244-6). Or, to take another example, our ability to recognise locations in our visual fields is connected with the success of our movements in physical space. Our discriminations in the inner world of the mind are, and must be, answerable to the exigencies of the physical world.
At this point we might begin to regret Wittgenstein's refusal to theorise. If he had offered a more systematic account of the dependence of our sensory language on the physical world, the so-called 'private language argument' might have carried more conviction. In fact, many philosophers have been convinced by it, but there is a large opposition, containing few doubters and consisting almost entirely of philosophers who feel sure that the argument is invalid. The dialectical character of Wittgenstein's argument has contributed to this result.
8. Philosophical Investigations: Meaning and Rules
Another, similar-sounding, but in fact very different, question is discussed in Philosophical Investigations. Could a person speak a language that was never used for communication with anyone else? Such a language would be private in the ordinary sense of that word, because it would be unshared; but it would not be necessarily unteachable, because it would be a language for describing the physical world, and so it would not be private in Wittgenstein's sense. The question is important, but we have to go back to the theory of meaning of the Tractatus in order to see why it is important.
A rough, but useful, distinction can be drawn between two kinds of theory of meaning, the rigid and the plastic. The theory offered in the Tractatus is rigid. Once names have been attached to objects everything proceeds on fixed lines. The application of the names is settled once and for all, and propositions and truth-functional combinations of propositions, including the two limiting cases, namely tautology and contradiction, all unfold without any more help from us. The theory does not actually treat the meaning of a name as something intrinsic to it, because we do have to correlate the name with an object. If we want an example of a theory that does take the further step and treats meaning as an intrinsic feature of a symbol, there is the theory that a mental image automatically stands for things that it resembles. That illustrates the extreme degree of rigidity: we would have no options.
A plastic theory of meaning would reject the analogy between a descriptive word and a name, and it would deny that the meaning of a descriptive word can be fixed once and for all by ostensive definition. Both these moves are made in Philosophical Investigations. It is, of course, not denied that our use of a descriptive word will exhibit a regularity: what is denied is that it is a regularity that is answerable to an independent authority. We do have options. We may say, if we like, that we are following a rule, but that will not be an explanation of the regularity of our practice, because it is our practice that shows how we are interpreting the words in which the rule is expressed. Are there, then, no constraints? Is the use of descriptive language pure improvisation? Evidently, there must be some limit to plasticity, and one obvious possibility is that it is imposed by the need to keep in step with other people. That is how the question, 'Does language require exchanges between members of a community of speakers?' comes to be important in Philosophical Investigations. When we trace the line of development from Wittgenstein's early to his late theory of meaning, we need to know how far he moved in the direction of plasticity.
His first two steps were taken soon after his return to philosophy in 1929. The meaning of a symbol can never be one of its intrinsic features, and even an ostensive definition cannot saddle it with a single, definite meaning, because an ostensive definition is always compatible with many different sequels. Meaning, then, must depend on what we do next with a word - on our use of it. What limit to plasticity did Wittgenstein recognise? Did he treat agreement with the responses of other people as an absolute constraint? And did he recognise any other absolute constraints? It is difficult to extract definite answers to these questions from his later writings. Both in Philosophical Investigations and in Remarks on the Foundations of Mathematics (1978) he says that agreement in judgements is required if people are going to communicate with one another. But that does not rule out the possibility that a wolf-child might develop a language solely for his own use. It would, of course, be a language of written signs with which he would communicate with himself across intervals of time. But it would not require the co-operation of other people. So it looks as if Wittgenstein went no further than maintaining that, if there are other people around and if the language-user is going to communicate with them, the plasticity of his language will be limited by the exigencies of agreement with them. This squares with the fact that in several of his texts dating from the 1930s he allows that a person might set up a system of signs solely for his own use. However, though Wittgenstein does not deny this in Philosophical Investigations or in Remarks on the Foundations of Mathematics, he does not re-assert it either. There seems to be some ambivalence.
In any case, there is another, more important, constraint on plasticity which really is absolute. If we are going to discover regularities in nature, our language must exercise a certain self-discipline: it must follow routines which allow us to collect evidence, to make predictions and, later, to understand them. Sheer improvisation will not put us in a position to do these things. This obvious constraint is overlooked by those who attribute to Wittgenstein a 'community theory of language'. It is hardly likely that he overlooked it.
9. The Authority of Rules
Wittgenstein's next step in the development of his theory of meaning was to argue by reductio ad absurdum. Given that the meaning of a word is never contained in the word itself, either intrinsically or after an ostensive definition, it must be a mistake to hold that someone who follows a linguistic rule is obeying an independent, external authority. For any basis that we might propose for the so-called 'authority' will always leave it open what the speaker should do next, and, what is more, open between many different alternatives. If we try to remedy this situation by offering a more explicit statement of the rule that he is supposed to be following, he will still be able to interpret that statement in many different ways. So when we try to fix the right use of a word purely by precept and past applications, we fail, because we end by abolishing the distinction between right and wrong. We feel that the distinction requires a rigid external authority and so we eliminate all plasticity, but, when we do that, we find we have lost the distinction.
It would be absurd to suggest that the meaning of a particular instruction is determined by what a person does when he tries to obey it. If the instruction did not already stand there complete with its meaning, there would be no question of obedience. But when the same suggestion is made about a general instruction, or rule, it is not absurd but only paradoxical. In order to understand Wittgenstein's argument, we have to elucidate the paradox.
It shocks us, because in daily life there is no doubt about what counts as obeying the instruction, 'Always take the next left turn'. However, there is an important grain of truth in the paradox. For the reason why there is never any doubt about what counts as obeying this instruction is that in the ordinary course of our lives nobody ever does take it to mean anything bizarre, like, 'Always take the opposite turn to the one you took last'. But if someone did understand it in this eccentric way, a verbal explanation of what it really meant might well fail to put him right. For he might give our verbal explanation an equally eccentric interpretation. Now because this sort of thing never happens in real life, we find Wittgenstein's argument paradoxical. It simply does not fit our picture of the independent authority of a rule. However, his point is that it could happen, and that indicates something important. It indicates that our use of language to give general instructions and state rules depends on our shared tendency to find the same responses natural. We have to agree in our practice before rules can have any independent authority. The independent authority is limited by the requirement that makes it possible. Wittgenstein's argument is not concerned with the real possibility of linguistic crankiness but with the logical structure of the situation.
It appears, then, that the intellectual performance of following a linguistic rule is based on something outside the realm of the intellect. Its basis is the fact that we, like other animals, find if natural to divide and classify things in the same way as other members of our species. This line of thought runs parallel to the line that Wittgenstein took about sensation-language. For there too the intellectual achievement of reporting sensations was based on pre-established natural responses and behaviour of a more primitive kind.
10. Wittgenstein's Philosophy of Mathematics
Wittgenstein's Philosophy of Mathematics is another development of the same general idea. For here too our most elaborate intellectual constructions are said to be founded on basic routines that cannot be justified intellectually. When we count, we feel that we are using footholds already carved for us in a rock-like reality. 'But counting . . . 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, and merciless exactitude. . . . "But is this counting only a use, then? Isn't there also some truth corresponding to this sequence?" . . . it can't be said of the series of natural numbers - that it is true, but that it is useful, and, above all, it is used' (Wittgenstein, 1978, I, 4).
The application of this idea to the philosophy of mathematics has proved less fruitful than its application to the philosophy of language. The reason for this may only be the greater distance between the superstructure and the proposed basis in this case. Or some would argue that mathematics is really not amenable to this treatment. It is, for example, questionable whether it can yield a convincing account of proof in mathematics.
Inevitably people ask what message can be extracted from Wittgenstein's philosophy. If a message is a theory, then, as we have seen, the message is that there is no message. Like any other philosopher, he pushed the quest for understanding beyond the point at which the ordinary criteria for understanding are satisfied. However, unlike others, he believed that philosophical understanding is more like the experience of a journey than the attainment of a destination. He regarded philosophy as an activity that is like Freudian therapy. You relive all the temptations to misunderstand and your cure recapitulates the stages by which it was achieved.
So it is not the restoration of a state of unreflective health. In fact, rather than aiming to re-establish any kind of state, philosophy is concerned with the process.
If there is a single structure discernible in his philosophy, it is his rejection of all illusory, independent support for our modes of thought. Rigid theories of meaning treat linguistic rules as independent authorities to which we who follow them are supposed to be wholly subservient. But he argues that this is an illusion, because the system of instruction and obedience involves a contribution from each individual and presupposes a basic like-mindedness. Similarly, the necessity of mathematics is something which we project from our practice and then mistakenly hail as the foundation of our practice. Evidently, he was rejecting realism, but his treatment of rules shows that he was not recommending conventionalism in its place. Certainly, his investigations have a structure, but it is not the structure of traditional philosophy.
11. Further Reading
There are several ways in which Wittgenstein's writings may be approached for the first time. Someone unfamiliar with philosophy might read Culture and value. This is a collection of remarks that are not direct contributions to philosophy; they are about art, religion, Wittgenstein's own life and especially about what it is like to be a philosopher.
A closer approach would be to read his Cambridge Lectures 1930-1932 or The Blue Book (1958), which was written 1933-4. In the former he explains the leading ideas of the Tractatus to an audience of Cambridge students; the latter deals with the nature of his later philosophy and with two specific philosophical problems: meaning and the self. Both are easier to follow than his other works, because they are written in the continuous, consequential way in which treaties are usually written, unlike the major part of his oeuvre which consists of independent remarks, which are carefully, but not always perspicuously, arranged.
In the Preface to Philosophical Investigations he compares his remarks to sketches made by an artist on many different journeys, crossing and recrossing the same terrain. This work can be appreciated only by someone who travels on the same routes, following in his footsteps - that is, only by someone who can read his remarks as contributions of the philosophical problems with which they are concerned. Reading a book of this kind is not like ordinary reading. It is, of course, partly a matter of taking in what he writes, but it is also much more than that. You have to stop and think after reading a remark, and sometimes you have to follow up a long train of thought before going on to his next remark. But how can you get into a position to read Wittgenstein's texts in this way? That is the problem.
One solution is to use A Wittgenstein Workbook (compiled by Coope, Geach, Potts and White; Oxford: Blackwell, 1970). This helpful companion takes 18 topics of central importance in Wittgenstein's thought, and for each of them gives references to his writings and to related discussions by other philosophers, and a list of questions to which the reader can work out answers.
Another solution is to use one of the many books about Wittgenstein's philosophy in a similar way. Instead of reading it through from beginning to end, take a chapter dealing with a particular topic, read it and then look up all the references to Wittgenstein's work in the footnotes. The chapter will help you to understand Wittgenstein's remarks and, in the reverse direction, the remarks will serve as a check on the accuracy of the interpretation offered in the chapter.
In general, his earlier philosophy is more difficult to penetrate than his later philosophy, because it is directly and immediately related to the work of Frege and Russell. But though it is easier to find points of entry into the dialectical discussions of Philosophical Investigations, a full understanding of them requires familiarity with the theories under criticism, whether they are those of other philosophers or of Wittgenstein's earlier persona.
In The Blackwell Companion to Philosophy, 1996, pp. 685-701.