*Logic: A very short introduction*is very short and is about logic. But it is not an introduction. That is not to say that it is too hard to be introductory, it is not, if you are even the slightest bit bold in the face of a little bit of symbolism and mathematics. But the topic it introduces is not standard logic.

This is a book more about its author than its subject. Graham Priest is well known amongst logicians and philosophers to have an agenda, and it comes out strongly in this book - too strongly. For example chapter 7 suggests that "->" might not be truth-functional. This is true, but it is not introductory stuff. I'll explain why in a moment. Exploiting the ambiguities in natural language for its counterexamples, or apparent counterexamples in logic is annoying and is a bad way to introduce modern conjunctions. For example when he exploits the ambiguity of "and" to sometimes mean "and then" and ignores canonical logical conjunction which has no such ambiguity. Paradoxes (and drawings of such - as Priest has done in earlier papers) appear to be interpreted as a problem whose real solution appears to be a Priestian paraconsistent logic. This is hardly standard or accepted.

In another place Priest endorses the use of fuzzy logic to solve the sorities paradox. (Perhaps I am being hard on him here, as this may just be an "in" to fuzzy logic.) He then shows how it must fail as a solution. But of course there are a number of ways to diagnose and solve the problem, fuzzy logic being only one of them.

In short he presents too many controversial issues as solved problems with one bad answer that does not work. Letting Priest write an introductory book on logic is like letting Dembski teach a course on introductory evolutionary theory. It becomes a course on each and every alleged problem with the theory - which is fascinating - but barely scratches the surface when it comes to offering a clear report on the going paradigm in logic. This is bad for two reasons: 1) Some problems are only big problems for Priest, who likes to "solve" them with his own version of logic, and 2) it leaves the reader wondering what good logic is if it is just as system full of holes and problems. On the whole logic is a profound system allowing for all sorts of useful stuff from digital watches to artificially intelligent robots. It is not too bad as a system to base philosophy or mathematics on either.

On the positive side it does at the end cover a very nice and judiciously chosen range of topics, though I did not like how they were handled. And while he does have a specific agenda that comes out on every page, he is eminently qualified to write a book of this kind. He is a top-notch writer and thinker.

It is also nice that the book ties in many of the logic exercises with some classic problems in philosophy, especially the philosophy of religion. I especially liked the discussion of Pascal's Wager in the section on decision theory.

I would highly recommend this book to someone who has learned a bit of logic and now wants to go deeper. It is a good and quick read and very rewarding. I would not recommend this book to someone who wants to learn for the first time what logic is. This is for someone who wants to know for the second time.