The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. Philosophical Logic provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading. Philosophical Logic addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis. The tree method is elaborated in manageable steps over five chapters, in each of which its adequacy is reviewed; soundness and completeness proofs are extended at each step, and the decidability proof is extended at the step from truth functions to the logic of nonoverlapping quantifiers with a single variable, after which undecidability is demonstrated by example.
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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. On the one hand, filling roughly the first third of the book, there is an extended exposition by R. On the other hand, there is a varied selection of theorems on in definability, un decidability, in completeness, and related topics, to which G.
The special aim of the present edition has been to increase the pedagogical usefulness of the book by adding a selection of problems at the end of each chapter, and by making chapters more independent of each other, so as to increase the range of options available to the instructor or reader as to what to cover and what to defer.
Pursuit of the latter aim has involved substantial rewriting, especially in the middle third of the book. Otherwise, the changes in the present edition are the sole responsibility of J. The book runs now in outline as follows. An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while. Computability and Logic By George S.
Boolos, John P. Burgess, Richard C. No cover image. Read preview. Synopsis This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book has become a classic because of its accessibility to students without a mathematical background, and because it covers not simply the staple topics of an intermediate logic course such as Godel's Incompleteness Theorems, but also a large number of optional topics from Turing's theory of computability to Ramsey's theorem.
John Burgess has now enhanced the book by adding a selection of problems at the end of each chapter, and by reorganising and rewriting chapters to make them more independent of each other and thus to increase the range of options available to instructors as to what to cover and what to defer.
Excerpt 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.
Computability and Logic
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View Larger Image. Computability and Logic is a classic because of its accessibility to students without a mathematical background. This fifth edition was first published in Dimension: x x Weight in Grams: Weight: Bookseller Inventory V