Paradoxes

Author: R. M. Sainsbury

Edition: Third

Publisher: Cambridge University Press

Pages: 190

Price: £45.00 and £15.99

ISBN: 9780521896320 and 720793

Bertrand Russell once wrote: "A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible" - and that certainly seems to be the aim and strategy in this popular little book. The (inadequate) index offers 36 paradoxes ranging from evergreen Ancient Greek ones such as the Liar, the Lawyer and Zeno's various efforts, to more recent paradoxes, such as the Grue or the Believer ones. Few will have heard of the last - it seems to be Sainsbury's own invention. Enthusiastically developing its logical implications, he springs into an 11-stage argument set out in logical notation of Bs and not Bs.

But hang on! Students may complain that they thought this book was going to be a collection of intriguing philosophical puzzles. If so, they will be disappointed. Because formalism is very much the subtext of the book - it is an attempt to examine paradoxes through converting them into logical notation. Furthermore, the great majority of paradoxes that do not lend themselves to such a treatment are excluded.

So here is a primer not so much in paradoxes but in elementary philosophical logic. In this small pond, the book is well placed to snap up any passing students. But, particularly in this third edition, the attempts to move into the areas of "moral paradoxes", or dilemmas, into paradox as a trigger for paradigm change in science or into general epistemological questions of the applicability of the rules of classical logic are less well served.

In the lifeboat dilemma, for example, Sainsbury sees the moral rule that it is wrong to throw innocent people overboard as negated ("annulled") by the situation. But one could equally well have asserted that the obligation to save the boat is "annulled" by the duty not to throw innocent people overboard. Sainsbury's text only hints at the richness of his theme as it presses on to more mathematically satisfying problems, such as the Prisoner's dilemma and the Monty Hall problem. Nor is the book wholly satisfying in its treatment of logic. The last chapter, for example, is devoted to a discussion of what Sainsbury calls "rational dialetheism", and whether it is ever possible that a statement that is both true and false could have any "intelligible context". After all, in classical logic, Sainsbury notes, contradictions have a dangerous role. Put one into any argument as one of the premises, and any conclusion may validly be derived. As soon as one contradictory statement is allowed, "one would be committed to holding that everything is true".

Who is it for? Not for the general reader, but attractive as an adjunct to an introductory logic course.

Presentation: Efficient summaries of popular paradoxes with occasional witty asides, alongside technical discourses.

Would you recommend it? Certainly for introductions to philosophical logic - and to my enemies!