Preface

Summary

The original authors of this work, the late George Boolos and my late colleague Richard Jeffrey, stated in the preface to the first edition that the work was intended for students of philosophy, mathematics, and other fields who desired a more advanced knowledge of logic than is supplied by an introductory course or textbook on the subject, and added the following:

The aim has been to present the principal fundamental theoretical results about logic, and to cover certain other meta-logical results whose proofs are not easily obtainable elsewhere. We have tried to make the exposition as readable as was compatible with the presentation of complete proofs, to use the most elegant proofs we knew of, to employ standard notation, and to reduce hair (as it is technically known).

Such have remained the aims of all subsequent editions, including the present one.

The ‘principal fundamental theoretical results about logic’ are primarily the theorems of Gödel—the completeness theorem and especially the incompleteness theorems—with their attendant lemmas and corollaries. The ‘other meta-logical results’ included have been of two kinds. On the one hand, filling roughly the first third of the book, there is an extended exposition by R.C.J. of the theory of Turing machines, a topic frequently alluded to in the literature of philosophy, computer science, and cognitive studies, but often omitted in textbooks on the level of this one.