The Logic of Provability

As the other reviewers note, this book is remarkable in that it both offers a reasonably gentle introduction to the subject even for those without too much mathematical background (logically-inclined philosophy students come to mind), and at the same time remains to this day an indispensable reference for the specialistâ€"this for example is the only source where you can find the proofs of Solovay's "other" modal completeness results for transitive models of set theory. George Boolos was (is) famous for, among other things, his gift of didactically brilliant exposition. There is only one other book on the subjectâ€"C.Smory'nski's "Self-Reference and Modal Logic", now out-of-print, which provides a nice complement to Boolos with surprisingly small overlap. For an introduction, I would not hesitate to recommend Boolos over Smory'nski. Since 1993 the "baton" has not completely "fallen out of Boolos' hands"â€"the interested reader can follow up on this via e.g. a couple of handbook-chapter expositions, easily found by googling around, that point to current research literature. However, no further textbook-level exposition appears to be forthcoming anytime soon. As a comment to galloamericanus' review, I would note that Boolos does not restrict his monograph exclusively or even primarily to his own results. The reader gets a fair overview of the research field by 1993 as shaped by many contributors.

George Boolos regrettably died too early, at age 56. He was a witty engaging writer, and a brilliant logician. This book, completed not long before his untimely death, is probably the high point of his career. The key insight, that modal logic can be interpreted as a sort of metamathematical algebra, is Godel's from the 1930s. And a key result is due to Martin Lob about 50 years ago. But Boolos built a towering edifice on this slim material. I think that the provability interpretation of the modal operator is the most philosophically and mathematically satisfying of all, and I hope someone comes along to pick up the baton that has fallen from Boolos's hand.

This book is an excelent reference for Logics of Provability.I consider this book a "must have" for anyone in the field, or in the field of Modal Logics.The author is a leader in the field, and this book is frequently cited in the bibliography of papers in the field.