Rating: 
Summary: Excellent, but not for complete beginners
Review: The breadth of this little book is remarkable. In about 110 small pages, Graham Priest touches on truth-functional logic, predicate logic, inductive logic, modal logic, fuzzy logic, temporal logic, conditionals, self-referentiality, identity, paradoxes, probability theory, and much else. As a side-effect, though, this Very Short Introduction can seem a bit dense and choppy. Luckily, I'd already had a year of logic and probability theory at college, so I wasn't confused by Priest's presentation; but I can imagine that someone coming to logic for the very first time might find this book difficult.
Priest begins (and ends) each short chapter with an interesting problem to catch our interest. He then concisely explains the root of the problem and how philosophers have tackled it. He particularly enjoys showing how useful modern logic is in dissecting old theological arguments for the existence of God, because, he says, "philosophers have had a long time to come up with interesting arguments concerning God." (They have also had a long time to thoroughly debunk them, which they've done, as Priest neatly shows. That's why sophisticated modern theologians like Plantinga and Vardy don't waste their time making these arguments any more.)
Priest's book is a bit more technical in its exposition than most popular books on this subject are. In some cases, I felt that other books (by John Hospers and Jamie Whyte, for instance) made identical points more simply and clearly. Nevertheless, it's nice to see these arguments worked out in a more technical yet still accessible manner.
I think this book would work best as a refresher or review for those who have already taken at least a semester of logic and probability theory, years ago, and want to get back into it. As a bonus, Priest scatters intellectual nuggets along the way for the edification of former philosophy students, clearing up those nagging little questions that our own professors couldn't be bothered to answer, such as why the material conditional has the bizarre truth-table it does. At long last, I now know why. Thanks, Graham!
Rating: 
Summary: Very good, essential, compact
Review: This book is a perfect introduction to logic. It is short and goes straight to the point. It features intelligent examples, interesting exercises and a fresh and modern style. It may seem a little too short, but the reader interested in logic is likely to take this book just as an ispiration for buying more complex, specific and comprehensive books on the subject. Some logic dilemmas are left to the reader to interprete, the author just renounces to go in depth in their analysis. This may actually leave a bitter after-taste at the end of each chapter, but it stimulates to further readings in the field of logic and phylosophy of logic.
Rating: 
Summary: Anti-Religious Subtext
Review: This book is bad.
I am not criticizing Mr. Priest's credentials, nor his accomplishments (meticulously catalogued on the back flap). I am, however, critiquing what he is doing. His object is to teach logic, but what he really does is propagandize. His anti-religious devil is in the details of the subtext and examples.
CASE 1: He first quotes Noam Chomsky, who suggests that logic is merely hard-wired into our brain (p. 6). This view of logic, of course, is self-contradictory, and involves the Fallacy of Stolen Concept. If we are evolutionarily determined to believe logic, they why should we trust it? Why should we trust anything that is the end result of random chance?
This position also implies determinisms, which would make the premises themselves determined, and therefore meaningless. The only way we could come to that conclusion is by having a process that was not determined by evolution, but separate and apart of the process.
Logic, in reality, is a description of reality, and must be tied to facts. If it were anything else, it would be meaningless
By the way, Priest and Chomsky also ignore the Anthropic Principle: the universe seems to be made to produce ham life (See Hawking, A Brief History of Time, 128-131). Logic, then would be part of this human-friendly phenomenon, and therefore exist prior to any evolutionary conditioning.
CASE 2: Priest uses a faulty description of the Cosmological Argument in teaching about quantifies (p. 22) By his own admission, it is card-stacking: "[Thomas Aquinas's] version is much more sophisticated than the argument of Chapter 3, and does not suffer from the problem pointed out there" (p. 109). A professor with his stature and resources could have assigned his research assistants to fine a better example, rather than one that betrays an anti-religious bias.
CASE 3: Priest also uses Anselm's Ontological Argument (p. 26). He fails to note that this is just one argument for God, and that it was disputed by Thomas Aquinas (See. Kreeft, Summa of The Summa, 54). Once again, he uses a faulty argument to smear religion.
CASE 4: He mentions Russell's Paradox (P. 34), but misses the broader point. If any system comes up with a paradox, or an absurdity, then the system is faulty. This paradox shows that the system of symbolic logic has a hole in it that needs to be resolved.
CASE 5: Priest says "Truth, then, comes by degrees." (p. 73). He is confusing truth with facts and data. Facts and data change from time to time, and day to day, but truth is eternal and constant. If truth changes, then it is absurd.
CASE 6: He discusses "The Best Possible Worlds," and uses this to disprove the Argument From Design.
He says, "Similarly with god [sic]. Conceivably there are many different way the cosmos could have been. And intuitively, relatively few of those are significantly ordered: order is something special. That, after all, is what gives the Argument From Design its bite. But there are relatively few possible cosmoses in which there is an orderer, so a priori, it is much more likely that there is no creator than there is." (p. 90)
Priest is blowing smoke. He divorces the symbolic logic from the obvious fact that we have only one universe. Any discussion about an hypothetical other cosmos is just a flight of fancy. This is formally called the Fallacy of Hypostatization: a hypothetical is taken for a reality. In other words, Priest's point only makes sense if you abandon common sense.
CASE 7: The Coin Toss In Hell example is his most obvious anti-religious dig (p. 99-101) He makes the error of Discarded Differentia: he ignores the essential difference between heaven and hell. True if all you focus on is the probably of the coin toss, but you ignore the nature of hell (which comes from our own choices and character) and the nature of heaven (also dependant upon our choices and character), the argument is sound.
This book is gross propaganda. As I read it, I felt like C. S. Lewis reading The Green Book mentioned in "The Abolition Of Man." To paraphrase him, anyone reading Priest will learn about logic precisely nothing. He is not teaching logic: teaching logic is easy, and what he is actually doing, namely propagandizing in the subtext, is much easier. And the nocive reader will be worse off.
Rating:
Summary: A Very Good Introduction to Logic
Review: This is a lucid introduction to logic, ideal to introduce the interested high-school student or non-specialist in the field, or as a refresher for anyone who has already dipped a toe into the field. It contains plenty of interesting examples and puzzles, and as always, with Priest's work, points you to important philosophical issues tied up with the notions of logical consequence. It's short, it's clear, it's written by an expert, and it contains pictures! What more could you want?Graham Priest taught me logic (so perhaps I'm biased), and I'm delighted that his clarity and expertise are made available to a really wide audience with this book. If you want to know what's been going on in logic in the last few hundred years, and you don't know where to start, I'd unhesitatingly recommend this book.
Rating:
Summary: Excellent brief introduction to logic
Review: This is just the book to whet one's appetite for a deeper engagement in logic. Priest's little book has short, clearly written chapters on validity, truth functions, quantifiers, descriptions, self-reference, modal operators, conditionals, tenses, identity, vagueness, inductive logic, and decision theory. Virtually every chapter shows how interesting philosophical problems arise from or are tied in with logic. The only possible drawback to the book is that new initiates to the philosophical foundations of logic are likely to never again have a good night's sleep after Priest introduces them to some of the classic puzzles.
Rating:
Summary: Though an intro, certainly not easy
Review: This was a very good and hard book on logic. I had to re-read all the chapters, up to four times on some, to get a good grasp of the concepts. I learned some interesting things. For example, not only can statements be either true or false, statements can also be neither true nor false, both true and false, or have various degrees of truthness combined with various degrees of falseness. The book also contains nice and serious logical refutations on a couple of famous arguments for the existence of god that will make any believer a non-believer. Simply Excellent!
Rating: 
Summary: Not for me . . .
Review: To put things in context, while I view myself as a logical person, I find formal logic difficult to follow. (On the other hand, someone who is wired for formal logic may find this book a breeze.)
I got this book to help me brush up for my logic final exam at university. Unfortunately, it didn't clarify anything for me, and in fact my text book explains things in a much simplier way. So, even with my prior knowledge (having studied university-level philosophy in the past, just having studied formal logic for a term and reading a text book on the subject), I still thought this book was confusing.
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