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physical terms what it takes to be an inscription (intended or unintended) in a given font of a proof of “0 = 1” in a given formal system of Peano Arithmetic; a physical theory could predict that an event of a specified physically possible type would cause there to be such an inscription. Less directly, psychological experiments might in principle reveal levels of human unreliability in proof-checking that would undermine current mathematical practice. To conclude on that basis alone that mathematics should become an experimental discipline would be hopelessly naïve. In practice, most of mathematics will and should remain an armchair discipline, even though it is not in principle insulated from experimental findings, because armchair methods, specifically proof, remain by far the most reliable and efficient available. Although the matter is less clear-cut, something similar may well apply to many areas of philosophy, for instance, philosophical logic. In particular, on the account in this book, the method of conducting opinion polls among non-philosophers is not very much more likely to be the best way of answering philosophical questions than the method of conducting opinion polls among non-physicists is to be the best way of answering physical questions.

Although this book is a defense of armchair philosophy, it is not written in a purely conservative spirit. Our ideas about philosophical methodology, however inchoate, are liable to influence the methodology we actually employ; bad ideas about it are liable to tilt it in bad directions. A reasonable hypothesis is that our current methodology is good enough to generate progress in philosophy, but not by much: ten steps forward, nine steps back. Nevertheless, we can improve our performance even without radically new methods. We need to apply the methods we already have with more patience and better judgment. A small increase in accuracy of measurement may enable scientists to tackle problems previously beyond reach, because their data lacked sufficient resolution. Similarly, small improvements in accepted standards of reasoning may enable the philosophical community to reach knowledgeable agreement on the status of many more arguments. Such incremental progress in philosophical methodology is a realistic prospect, for current standards in the profession exhibit large variations significantly correlated with differences between graduate schools. Philosophical methodology can be taught – mainly by example, but fine-tuning by explicit precept and discussion also makes a difference. For instance, the level of rigor in philosophical statement and argument which Frege achieved only by genius (with a little help from his mathematical training) is now available to hundreds of graduate students every year: and we know how to do even better. That is not to imply, of course, that we must strive for maximum rigor at all times, otherwise this impressionistic introduction would be self-defeating. At any rate, if the philosophical community has the will, it can gradually bring up a much higher proportion of practice to the standard of current best practice, and beyond. Such progress in methodology cannot be relied on to happen automatically; not all of us love the highest at first sight. Although the envisaged incremental progress lacks the drama after which some philosophers still hanker, that hankering is itself a symptom of the intellectual immaturity that helps hold philosophy back. No revelation is at hand; any improvement in accepted standards of philosophical discussion will result from collective hard work and self-discipline. One hope with which this book is written is that by contributing to the current tendency towards increasing methodological self-consciousness in philosophy it will play some role, however indirect, in raising those standards. Philosophizing is not like riding a bicycle, best done without thinking about it – or rather: the best cyclists surely do think about what they are doing.

      This book is an essay. It makes no claim to comprehensiveness. It does not attempt to compile a list of philosophical methods, or of theories about philosophical methods. It touches on historical matters only glancingly. Instead, it explores some interrelated issues that strike me as interesting and not well understood. It starts by inquiring into the nature of philosophical questions. It proceeds in part by detailed case studies of particular examples. Since all examples have their own special characteristics, generalizations from them must be tentative. But many long-standing misconceptions in philosophy are helped to survive by an unwillingness to look carefully and undogmatically at examples, sometimes protected by a self-righteous image of oneself and one’s friends as the only people who do look carefully and undogmatically at examples (some disciples of the later Wittgenstein come to mind).

It is difficult to displace one philosophical picture except by another. Although discussion of philosophical methodology is itself part of philosophy, it is less often conducted with a clear view of the theoretical alternatives than is usual in philosophy. David Lewis once wrote that “what we accomplish in philosophical argument” is to “measure the price” of maintaining a philosophical claim; when his remark is cited as an obvious truth, it tends not to be noticed that it too is subject to philosophical argument, and has its price – not least the danger of infinite regress, since claims about the price of maintaining a philosophical claim are themselves subject to philosophical argument.² Another hope for this book is that it will clarify an alternative to widespread assumptions about the nature of philosophy.

      Notes

      1 ¹In this respect Hilary Kornblith seems to misunderstand the claim that philosophy can be done in an armchair (2006: 19). I have even dabbled in experimental philosophy myself (Bonini, Osherson, Viale and Williamson 1999).

      2 ²See his 1983a: x. Lewis himself gives a brief philosophical argument for his claim about measuring the price, based on the premise that ‘[o]ur ‘intuitions’ are simply opinions,’ against a foundationalist alternative. He also qualifies the claim, allowing that Gödel and Gettier may have conclusively refuted philosophical theories, and that perhaps the price of a philosophical claim ‘is something we can settle more or less conclusively’.

1 The Linguistic Turn and the Conceptual Turn

      The Linguistic Turn is the title of an influential anthology edited by Richard Rorty, published in 1967. He credited the phrase to Gustav Bergmann (Bergmann 1964: 3; Rorty 1967: 9). In his introduction, Rorty (1967: 3) explained:

      The purpose of the present volume is to provide materials for reflection on the most recent philosophical revolution, that of linguistic philosophy. I shall mean by “linguistic philosophy” the view that philosophical problems are problems which may be solved (or dissolved) either by reforming language, or by understanding more about the language we presently use.

      “The linguistic turn” has subsequently become the standard vague phrase for a diffuse event – some regard it as the event – in twentiethcentury philosophy, one not confi ned to signed-up linguistic philosophers in Rorty’s sense. For those who took the turn, language was somehow the central theme of philosophy.

      The word “theme” is used with deliberate vagueness. It does not mean “subject matter,” for the linguistic turn was not the attempted reduction of philosophy to linguistics. The theme of a piece of music is not its subject matter. Those who viewed philosophy as an activity of dispelling confusions of linguistic origin did not see it as having a subject matter in the sense in which a science has a subject matter. But merely to regard linguistic analysis as one philosophical method among many is not yet to have taken the linguistic turn, for it is not yet to regard language as central. We will be more precise below.

      There is an increasingly widespread sense that the linguistic turn is past. We will ask how far the turn has been, or should be, reversed.

Language has been regarded as central to philosophy in many different ways, which cannot all be treated together. A history of the many different forms that the linguistic turn took would be a history of much of twentieth-century philosophy. That is a task for another book, by another author. Self-indulgently, I will use a thin slice through history to introduce the contemporary issues by briefly considering some of my predecessors in the Wykeham Chair of Logic at Oxford.

A. J. Ayer was the first holder of the Chair to take the linguistic turn.¹ In 1936, back from Vienna and its

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