Foreword to Second1 Edition (Full Text)
Introduction (Full Text)
- The main changes in this edition (apart from the correction of many typographic errors and stylistic infelicities) concern chapters 2, 5 and 6. I found my earlier discussion of vagueness very unsatisfactory, in the main because it defined vagueness in such a way as to exclude the epistemic theory. I do not accept this theory, but Timothy Williamson has shown me that I am not able to refute a skilful and determined opponent. Making room for the theory involved some quite widespread changes, including the insertion of three new sections.
- The present version of chapter 5 is better structured, and there is also a change of emphasis. It now seems to me that although some kind of indexicality is involved in the Liar paradox, it is more plausible to locate this in the subject term (in the nature of self-reference) than in the predicate (by means of an indexical truth hierarchy).
- The original version of chapter 6 offered a very superficial criticism of dialetheism. In those days, discussing this topic at all seemed quite adventurous. It is a tribute to dialetheists, and in particular to Graham Priest, that nowadays a book on paradoxes which did not discuss dialetheism would be clearly defective. In this edition, I offer a somewhat more extended, and I hope better, discussion, drawing in particular on a recent exchange between Timothy Smiley and Graham Priest. I find myself, to my regret, in the same frustrating position with respect to dialetheism as to the epistemic theory of vagueness: I do not accept it but cannot refute it.
- In this edition, bibliographical notes have been placed at the end of the relevant chapter. Footnotes are exclusively questions for the reader.
- I would like to thank many people for pointing out mistakes of varying degrees of magnitude in the first edition, either in their reviews or in personal communications: Laurence Goldstein, Anthony Grayling, Masaki Ichinose, Frank Jackson, Anne Kelleher, Bernard Linsky, Vincent Muller, Graham Priest, Robert Seth-Smith and Roy Sorensen. I fear the list may, through inadvertence, be less than comprehensive, and I ask forgiveness of anyone whom I have omitted.
- Paradoxes are fun. In most cases, they are easy to state and immediately provoke one into trying to "solve" them.
- One of the hardest paradoxes to handle is also one of the easiest to state: the Liar Paradox. One version of it asks you to consider the man who simply says, "What I am now saying is false". Is what he says true or false? The problem is that if he speaks truly, he is truly saying that what he says is false, so he is speaking falsely; but if he is speaking falsely, then, since this is just what he says he is doing, he must be speaking truly. So if what he says is false, it is true; and if it is true, it is false. This paradox is said to have "tormented many ancient logicians and caused the premature death of at least one of them, Philetas of Cos". Fun can go too far.
- Paradoxes are serious. Unlike party puzzles and teasers, which are also fun, paradoxes raise serious problems. Historically, they are associated with crises in thought and with revolutionary advances. To grapple with them is not merely to engage in an intellectual game, but is to come to grips with key issues. In this book, I report some famous paradoxes and indicate how one might respond to them. These responses lead into some rather deep waters.
- This is what I understand by a paradox: an apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. Appearances have to deceive, since the acceptable cannot lead by acceptable steps to the unacceptable. So, generally, we have a choice: either the conclusion is not really unacceptable, or else the starting point, or the reasoning, has some non-obvious flaw.
- Paradoxes come in degrees, depending on how well appearance camouflages reality. Let us pretend that we can represent how paradoxical something is on a ten-point scale. The weak or shallow end we shall label 1; the cataclysmic end, home of paradoxes that send seismic shudders through a wide region of thought, we shall label 10. Serving as a marker for the point labelled 1 is the so-called Barber paradox: in a certain remote Sicilian village, approached by a long ascent up a precipitous mountain road, the barber shaves all and only those villagers who do not shave themselves. Who shaves the barber? If he himself does, then he does not (since he shaves only those who do not shave themselves); if he does not, then he indeed does (since he shaves all those who do not shave themselves). The unacceptable supposition is that there is such a barber — one who shaves himself if and only if he does not. The story may have sounded acceptable: it turned our minds, agreeably enough, to the mountains of inland Sicily. However, once we see what the consequences are, we realize that the story cannot be true: there cannot be such a barber, or such a village. The story is unacceptable. This is not a very deep2 paradox because the unacceptability is very thinly disguised by the mountains and the remoteness.
- At the other end of the scale, the point labelled 10, I shall place the Liar. This placing seems the least that is owed to the memory of Philetas.
- The deeper the paradox, the more controversial is the question of how one should respond to it. All the paradoxes I discuss in the ensuing chapters score 6 or higher on the scale, so they are really serious. (Some of those in Appendix I should, I think, score lower.) This means that there is severe and unresolved disagreement about how one should deal with them. In many cases, though certainly not all (not, for example, in the case of the Liar), I have a definite view; but I must emphasize that, although I naturally think my own view is correct, other and greater men have held views that are diametrically opposed. To get a feel for how controversial some of the issues are, I suggest examining the bibliographical notes at the ends of chapters.
- Some paradoxes collect naturally into groups by subject matter. The paradoxes of Zeno which I discuss form a group because they all deal with space, time and infinity. The paradoxes of chapter 3 form a group because they bear upon the notion of rational action. Some groupings are controversial. Thus Russell grouped the paradox about classes with the Liar paradox. In the nineteen twenties, Ramsey argued that this grouping disguised a major difference. More recently, it has been argued that Russell was closer to the truth than Ramsey.
- I have compared some of the paradoxes treated within a single chapter, but I have made no attempt to portray larger patterns. However, it is arguable that there are such patterns, or even that the many paradoxes are the many signs of one "master cognitive flaw". This last claim has been ingeniously argued by Roy Sorensen (19883).
- Footnotes contain questions (though not necessarily in the first sentence). I hope that considering these will give pleasure and will prompt the reader to elaborate some of the themes in the text. Asterisked footnotes are referred to in Appendix II, where I have made a point that might be relevant to an answer.
- I feel that chapter 5 is the hardest and should be left until last. The first is probably the easiest. The order of the middle three is arbitrary. Chapter 6 does not introduce a paradox, but rather examines the assumption, made in the earlier chapters, that all contradictions are unacceptable. I think it would not make much sense to one completely unfamiliar with the topics discussed in chapter 5.
- I face a dilemma: I find a book disappointing if the author does not express his own beliefs. What holds him back from stating, and arguing for, the truth as he sees it? I could not bring myself to exercise this restraint. On the other hand, I certainly would not want anyone to believe what I say without first carefully considering the alternatives. So I must offer somewhat paradoxical advice: be very sceptical about the proposed "solutions"; they are, I believe, correct.
Footnote 1: THere’s now a Third Edition (19th Feb 2009), says Amazon, though I don’t know to what degree it differs from the Second.
Footnote 2: But it’s the popular expression of Russell’s Paradox, which was nearly the death of Frege.
Footnote 3: Blindspots. This is the second reference to this book I’ve recently encountered, so I suspect it’s good (the other was in "Williamson (Timothy) - Vagueness: Preface + Introduction"). But it’s expensive.
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