One of the ways of dividing all philosophers into two kinds is by saying of each whether he is an ordinary man's philosopher or a philosophers' philosopher. Thus Plato is a philosophers' philosopher and Aristotle an ordinary man's philosopher. This does not depend on being easy to understand: a lot of Aristotle's Metaphysics is immensely difficult. Nor does being a philosophers' philosopher imply that an ordinary man cannot enjoy the writings, or many of them. Plato invented and exhausted a form: no one else has written such dialogues. So someone with no philosophical bent, or who has left his philosophical curiosity far behind may still enjoy reading some of them.

In the preface to the Philosophical Investigations, written in 1945, Wittgenstein remarks that: ‘It is not impossible that it should fall to the lot of this work in its poverty and in the darkness of this time, to bring light into one brain or another—but, of course, it is not likely’ (PI, viii). There was quite obviously no question for him of endeavouring to dissipate the darkness of the age itself, but at the most of introducing light into a small number of receptive minds, the existence of which he considered, moreover, as problematical. In a rough draft of the preface to the Philosophical Remarks that he wrote in 1930 he says:

I realize … that the disappearance of a culture does not signify the disappearance of human value, but simply of certain means of expressing this value, yet the fact remains that I have no sympathy for the current of European civilization and do not understand its goals, if it has any. So I am really writing for friends who are scattered throughout the corners of the globe. (CV, 6)

In this country, we tend to look at Wittgenstein in a rather ahistorical way. We see his concerns as fundamentally logico-linguistic, following on first from the work of Frege and Russell, and then referring back indirectly to the concerns of the British empiricists, to those of Locke and Hume, say, on such matters as the reference of our talk about sensations and scepticism about the external world. Recently there has been considerable discussion of the extent to which Wittgenstein's own analysis of the private language and of rule-following might not itself be a new version of a fundamentally Humean scepticism: according to Saul Kripke, Wittgenstein's arguments amount to a demonstration that there is no more reason for speakers of a language to follow the rules governing the concepts of that language in the same way than on the Humean account there is any reason for an effect to follow its causes (Kripke, 1981).

In the first and shorter part of this essay I comment on Wittgenstein's general influence on the practice of philosophy since his time. In the second and much longer part I discuss aspects of his work which have had a more particular influence, chiefly on debates about meaning and mind. The aspects in question are Wittgenstein's views about rule-following and private language. This second part is more technical than the first.

To be asked to provide a short paper on Wittgenstein's views on mathematical proof is to be given a tall order (especially if little or no familiarity either with mathematics or with Wittgenstein's philosophy is to be presupposed!). Close to one half of Wittgenstein's writings after 1929 concerned mathematics, and the roots of his discussions, which contain a bewildering variety of underdeveloped and sometimes conflicting suggestions, go deep to some of the most basic and difficult ideas in his later philosophy. So my aims in what follows are forced to be modest. I shall sketch an intuitively attractive philosophy of mathematics and illustrate Wittgenstein's opposition to it. I shall explain why, contrary to what is often supposed, that opposition cannot be fully satisfactorily explained by tracing it back to the discussions of following a rule in the Philosophical Investigations and Remarks on the Foundations of Mathematics. Finally, I shall try to indicate very briefly something of the real motivation for Wittgenstein's more strikingly deflationary suggestions about mathematical proof, and canvass a reason why it may not in the end be possible to uphold them.

We may reflect on language in different ways. There is the way familiar to analytical philosophers. That may take different forms, but most of them are strikingly different from the way of someone like Elias Canetti or F. R. Leavis, whose thought is shaped by their concern with literature. In the latter case language appears as an essentially human phenomenon, not because it is limited to the species Homo sapiens, but because it is essentially connected with the culture and histories of peoples, whose plurality is underdetermined by any elaboration on the nature and environmental conditions of Homo sapiens. It is rare to find analytical philosophers of language for whom that is important or who have tried even to sketch the kind of importance it may have. That is because they assume that it is not important to language as such (to what makes something language) but only to the sophisticated use of language in poetry or literature. They have tended to misunderstand the sense in which a language such as English is a natural language.

Asked about Wittgenstein's contribution to aesthetics, one might think first of all of his discussion of ‘family resemblance’ concepts, in which he argued that the various instances of games, for example, need not have any feature or set of features in common, in virtue of which they are all called games; the concept of a game can function perfectly well without any such set of conditions. This insight was soon applied to the much debated quest for a definition of the word ‘art’, and it was claimed that here too the various instances of art were related by way of family resemblance, so that it was futile to look for a condition or set of conditions, which works of art, and only works of art, had in common. Wittgenstein himself did not extend his argument to the concept of art. Although he was deeply interested in the arts, especially music, he wrote very little on aesthetics, his most sustained treatment of the topic being available for us only in the form of notes taken of a set of his lectures on aesthetics (LC).

There is a well-known remark in Wittgenstein's Philosophical Investigations which even some philosophers sympathetic to his work have found very hard to accept. It reads:

Philosophy may in no way interfere with the actual use of language;

it can in the end only describe it.

For it cannot give it any foundation either.

It leaves everything as it is. (PI, I, 24)

Surely, it is said, that is carrying matters too far. Wittgenstein's hyperbole should be excused as a harmless stylistic flourish.

My aim in this paper is to consider the suggestion, made in an unpublished paper by Peter Hobson, a psychoanalytic colleague, that psychoanalysis is a form of life. Hobson is impressed by the peculiarity of psychoanalytic thinking, by its specialness, by the fact that its concepts are embedded in a system of practices and beliefs such that an outsider to all this may be unable to understand what the analyst says, whether to his patient or to another analyst. Hobson uses Wittgenstein's notion of a form of life to refer to this system of practices and beliefs, but he does not criticize or examine the notion itself.

The ‘abominable mess’ of which Wittgenstein complains is that of confounding reasons and causes. What does Wittgenstein mean to call attention to by this contrast and why does he think himself entitled to hold that Freud confounded them? Sometimes by reasons he means just what someone says on being asked why he did what he did or reacted as he reacted, and sometimes what an experience meant to a subject on further reflection upon it—its ‘further description’.

We must do away with explanation, and description alone must take its place. And this description gets its light, that is to say its purpose, from … philosophical problems. These are, of course, not empirical problems; they are solved, rather, by looking into the workings of our language, and that in such a way as to make us recognize those workings: in spite of an urge to misunderstand them. The problems are solved, not by giving new information, but by arranging what we have already known. Philosophy is a battle against the bewitchment of our intelligence by means of language. (PI, I, 109)

The work of the later Wittgenstein has had a vast influence in the field of social science. This is hardly surprising as the effect of that philosophy has been an emphasis on the priority of the social. Empiricist philosophy started with the private experience of the individual and from there built up an inter-subjective picture of the world. Wittgenstein, on the other hand, began with the rule-governed practices of a community. Both the nature of private experience, and of an objective world, was deemed to depend on concepts all could share. Society is the source of such concepts and thus becomes the key notion in our understanding of ourselves and our relation to the world.

So is this it: I must recognize certain authorities in order to make judgments at all? (OC, 493)

I want in this paper to consider Wittgenstein's great posthumous work On Certainty in a different perspective from the usual: from the point of view of certain deep questions in political philosophy. These questions concern the nature of the state's authority and the citizen/s obligation to it; the notion of legitimacy and the role of consent in this context. Such issues have many dimensions; but they arise in part out of difficulties in reconciling the application of such concepts with our understanding of human rationality, especially practical rationality. I think it has been, and remains, characteristic of the main tradition of discussion of such issues to leave certain important questions about the nature of practical rationality unasked. I believe that these questions are asked, though in a different context, in Wittgenstein's On Certainty.

‘Where two principles really do meet which cannot be reconciled with one another, then each man declares the other a fool and a heretic’ This sentence from Wittgenstein's On Certainty (OC, 611) is the source of my title. A passage in George Orwell's Shooting an Elephant might have prompted the same choice: ‘The Catholic and the Communist are alike in assuming that an opponent cannot be both honest and intelligent. Each of them tacitly claims that “the truth” has already been revealed, and that the heretic, if he is not simply a fool, is secretly aware of “the truth” and merely resists it out of selfish motives’ (Orwell, 1950, 177).