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on 20 December 2003
This is a very short, tersely written book - focusing entirely on the rather narrow subject of first-order logic.
Those who have read Smullyan's later writings such as 'To Mock a Mockingbird' and 'What is the name of this book?' (which are designed to be fun and hence accessible to a general audience) will scarcely recognise the utterly dry, humourless style of the exposition. To be sure, that's exactly the style one expects from a mathematical textbook (with 'we' this and 'we' that) and so if you're a no-nonsense, straight-faced student of logic, who just wants the facts, expressed clearly and concisely in the standard notation and terminology, then you'll be grateful that Smullyan has written the book this way.
This book is to logic what Kernighan & Ritchie's "The C Programming Language" is to programming. What I mean is that it gives the reader a complete and self-contained account of a narrow but fundamentally important part of the subject, but absolutely refuses to stray beyond its self-imposed limits. Indeed, I was a little disappointed that Smullyan 'fenced in' the scope of his book so severely. I'd have liked to get a better idea of the ways in which the theory could be tinkered with and generalised, and how the system of first order logic fits into the wider scheme of things. It would have been interesting to compare its properties with those of its near cousins, such as 'independence-friendly' first order logic. In the event, Smullyan doesn't even go so far as to mention first order logic _with identity_ (which is actually the most common kind).
Despite these reservations, the 'laserbeam' clarity of the writing makes this a very impressive piece of work. Smullyan's "First-Order Logic" is highly recommended to anyone interested in the subject. The mathematical pre-requisites are minimal, but you'll need some familiarity with the basic notions of sets, functions and relations, and enough 'mathematical maturity' not to mind that there aren't any jokes.
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on 28 February 2012
... A thrill if you can cope with the high-speed, no fuss, complete but concise style, i.e. Smullyan's way at its best !

This is the best treatment of tableaux I have come across, nicely covering both propositional logic and first-order logic.

Concerning price, contents and clarity of exposition, one can simply forget about the two unjustifiably-praised "preachers" of the logic world, i.e. Enderton and Mendelson, and use this book instead.

Smullyan covers so much territory and goes so far that the reader -- if not an expert -- will only try to catch the concepts of the last 3 chapters while skipping proofs and details...

Concerning this edition : the book is too small, so the text is packed, i.e. titles, sections, paragraphs, important conclusions are not well separated, hence my rating.
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on 13 March 2005
...but I'll bump it up to full marks.
This is a great book which served as my introduction to tableaus (we forgo the French pluralization here). I think it strikes a good balance between the conciseness of a math text and the verbosity often found in philosophy texts; it's also very reasonably priced. My only complaint is that some exercises are difficult and there are no solutions (the former wouldn't be a problem if the latter weren't the case); it would be nice to be able to confirm one's work, regardless of proficiency. Also, this book isn't for the total rookie--some prior knowledge is assumed. My choice for introductory material would be Copi's Symbolic Logic or even his Introduction to Logic (with Cohen) for those with no or limited background in mathematics; I also think, based on personal experience, that the study of mathematical logic is ultimately more satisfying if the student has a solid grounding in Aristotelian logic.
I don't find Prof. Smullyan's lack of humor in this particular work a problem (I'm lucky enough to have met him several times)--it is, after all, often used as a textbook. Besides, I get jokes a-plenty studying under his student and sometime-collaborator, Mel Fitting.
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