on 13 July 2014
Priest does a wonderful job in explaining a surprisingly wide spectrum of non-classical logics, with a crystal-clear style, from both the mathematical and the philosophical point of views.
For those who are only used to classical logic, this book is simply illuminating.
Some points need to be improved though : the list of symbols is missing and the index is far from complete...
The difficulty of part II is not due so much to the intrinsic intricacies but mostly to the constant need to review the corresponding chapters of part I... But this is unavoidable if one wants to include quantifiers and identity... And, here again, Priest does a terrific job in unifying the underlying concepts of possible-worlds semantics.
This book now stands in my list of outstanding books on logic :
1. A. Tarski's "Introduction to Logic", a jewel, followed by P. Smith's superb entry-point "An introduction to Formal logic" and the lovely "Logic, a very short introduction" by Graham Priest
2. D. Goldrei's "Propositional and Predicate calculus"
3. Wilfrid Hodges' "Logic", followed by Smullyan's "First-order logic".
4. P. Smith's "An introduction to Gödel's theorems".
5. Kleene's "Introduction to metamathematics" & "Mathematical Logic".
6. G. Priest's " Introduction to non-classical logic".
Hence forgetting altogether Van Dalen's indigestible "Logic & Stucture" as well as
the even more indigestible Enderton, Mendelson & al...