The Unprovability of Consistency: An Essay in Modal Logic
(The Unprovability of Consistency is concerned with connec...)
The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has persisted for at least thirty years between the followers of C. I. Lewis and W. V. O. Quine. The author employs semantic methods developed by Saul Kripke in his analysis of modal logical systems. The book will be of interest to advanced undergraduate and graduate students in logic, mathematics and philosophy, as well as to specialists in those fields.
(Computability and Logic has become a classic because of i...)
Computability and Logic 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. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems.
(A text for a second course in logic for graduate and adva...)
A text for a second course in logic for graduate and advanced undergraduate students. This third edition has been corrected and contains thoroughly revised versions of the chapters on Ramsey and provability, with new exercises provided for three other chapters. There are also two new chapters dealing with undecidable sentences and on the non-existence of non-standard recursive models of Z.
Studies in Logic and Probability (Dover Books on Mathematics)
(From one of the founders of symbolic logic comes this col...)
From one of the founders of symbolic logic comes this collection of writings on logical subjects and related questions of probability. George Boole invented Boolean logic, the basis of modern digital computer logic, for which he is regarded as a founder of the field of computer science. This authoritative compilation of his papers features his most mature thinking on Boolean logic and includes previously unpublished material.
Appropriate for upper-level undergraduates and graduate students, the contents range from The Mathematical Analysis of Logic to Boole's final works, including The Laws of Thought, the most systematic statement of his ideas on logic and probability. Boole had intended to create a follow-up volume but did not survive to fulfill his ambition; this volume features his further studies on the subject.
An Investigation Of The Laws Of Thought: On Which Are Founded The Mathematical Theories Of Logic And Probabilities
(This scarce antiquarian book is a facsimile reprint of th...)
This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.
An Investigation of the Laws of Thought: On which are founded the mathematical theories of logic and probabilities
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An Investigation of the Laws of Thought
On which are f...)
An Investigation of the Laws of Thought
On which are founded the mathematical theories of logic and probabilities
By George Boole
The Laws of Thought, more precisely, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, was an influential 19th century book by George Boole, the second of his two monographs on algebraic logic. It was published in 1854. Boole was Professor of Mathematics of then Queen's College, Cork in Ireland.
The following work is not a republication of a former treatise by the Author, entitled, “The Mathematical Analysis of Logic.” Its earlier portion is indeed devoted to the same object, and it begins by establishing the same system of fundamental laws, but its methods are more general, and its range of applications far wider. It exhibits the results, matured by some years of study and reflection, of a principle of investigation relating to the intellectual operations, the previous exposition of which was written within a few weeks after its idea had been conceived.
That portion of this work which relates to Logic presupposes in its reader a knowledge of the most important terms of the science, as usually treated, and of its general object. On these points there is no better guide than Archbishop Whately’s “Elements of Logic,” or Mr. Thomson’s “Outlines of the Laws of Thought.” To the former of these treatises, the present revival of attention to this class of studies seems in a great measure due. Some acquaintance with the principles of Algebra is also requisite, but it is not necessary that this application should have been carried beyond the solution of simple equations. For the study of those chapters which relate to the theory of probabilities, a somewhat larger knowledge of Algebra is required, and especially of the doctrine of Elimination, and of the solution of Equations containing more than one unknown quantity.
Preliminary information upon the subject-matter will be found in the special treatises on Probabilities in “Lardner’s Cabinet Cyclopaedia,” and the “Library of Useful Knowledge,” the former of these by Professor De Morgan, the latter by Sir John Lubbock; and in an interesting series of Letters translated from the French of M. Quetelet. Other references will be given in the work. On a first perusal the reader may omit at his discretion, Chapters x., xiv., and xix., together with any of the applications which he may deem uninviting or irrelevant.
Studies in Logic and Probability (Dover Phoenix Editions)
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Boole's earlier work, The Mathematical Analysis of Logi...)
Boole's earlier work, The Mathematical Analysis of Logic, appears here, together with an account of the notes Boole made on his own interleaved copy. Appendices contain relevant papers by contemporaries with whom the author engaged in discussion, making it possible to trace interesting developments in Boolean reasoning. 1952 edition.
An Investigation Of The Laws Of Thought, On Which Are Founded The Mathematical Theories Of Logic And Probabilities (Afrikaans Edition)
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This is a reproduction of a book published before 1923....)
This is a reproduction of a book published before 1923. This book may have occasional imperfections
such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact,
or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections,
have elected to bring it back into print as part of our continuing commitment to the preservation of printed works
worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
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The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to ensure edition identification:
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An Investigation Of The Laws Of Thought, On Which Are Founded The Mathematical Theories Of Logic And Probabilities; Volume 2 Of George Boole's Collected Logical Works; Volume 28 Of DoverBooks On Advanced Mathematics. S
George Boole
Walton and Maberly, 1854
Mathematics; Logic; Logic, Symbolic and mathematical; Mathematics / Logic; Philosophy / Logic; Probabilities; Thought and thinking
George Stephen Boolos, American philosophy educator. National Endowment of the Humanities fellow, 1984; Fulbright scholar, 1961-1963; Guggenheim Foundation fellow, 1996; National Science Foundation grantee, 1986, 88-89. Fellow American Academy Arts and Sciences; member Association Symbolic Logic (president 1995-1996), American Philosophical Association, Mathematics Association American.
Background
Boolos, George Stephen was born on September 4, 1940 in New York City. Son of Stephen George and Blanche (Salomon) Boolos.
Education
Bachelor, Princeton University, 1961;Bachelor of Philosophy, University of Oxford, England, 1963;Doctor of Philosophy, Massachusetts Institute of Technology, 1966.
Career
Assistant professor philosophy, Columbia University, 1966-1969;assistant professor philosophy, Massachusetts Institute of Technology, 1969-1973;associate professor, Massachusetts Institute of Technology, 1973-1980;professor, Massachusetts Institute of Technology, 1980-1996.
Author: The Logic of Probability, 1993, The Unprovability of Consistency, 1979, (with R.C. Jeffrey) Computability and Logic, 1974. Editor: Journal Symbolic Logic, 1987, Meaning and Method, 1990.
Membership
Fellow American Academy Arts and Sciences. Member Association Symbolic Logic (president 1995-1996), American Philosophical Association, Mathematics Association American.
National Endowment of the Humanities fellow, 19...National Endowment of the Humanities fellow, 1984. Fulbright scholar, 1961-1963. Guggenheim Foundation fellow, 1996.