An Investigation of the Laws of Thought
Author | : George Boole |
Publisher | : |
Total Pages | : 688 |
Release | : 1854 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : |
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Author | : George Boole |
Publisher | : |
Total Pages | : 688 |
Release | : 1854 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : |
Author | : George Boole |
Publisher | : |
Total Pages | : 476 |
Release | : 1854 |
Genre | : Investigation |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 446 |
Release | : 1854 |
Genre | : |
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Author | : George Boole |
Publisher | : |
Total Pages | : 454 |
Release | : 1854 |
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ISBN | : |
Author | : George Boole |
Publisher | : |
Total Pages | : 476 |
Release | : 1911 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : |
Author | : George Boole |
Publisher | : Literary Licensing, LLC |
Total Pages | : 436 |
Release | : 2014-08-07 |
Genre | : |
ISBN | : 9781498138741 |
This Is A New Release Of The Original 1854 Edition.
Author | : George Boole |
Publisher | : Palala Press |
Total Pages | : 462 |
Release | : 2018-02-24 |
Genre | : |
ISBN | : 9781378574911 |
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author | : George Boole |
Publisher | : Courier Corporation |
Total Pages | : 452 |
Release | : 2012-07-26 |
Genre | : Philosophy |
ISBN | : 0486157504 |
"A classic of pure mathematics and symbolic logic ... the publisher is to be thanked for making it available." — Scientific American George Boole was on of the greatest mathematicians of the 19th century, and one of the most influential thinkers of all time. Not only did he make important contributions to differential equations and calculus of finite differences, he also was the discoverer of invariants, and the founder of modern symbolic logic. According to Bertrand Russell, "Pure mathematics was discovered by George Boole in his work published in 1854." This work is the first extensive statement of the modern view that mathematics is a pure deductive science that can be applied to various situations. Boole first showed how classical logic could be treated with algebraic terminology and operations, and then proceeded to a general symbolic method of logical interference; he also attempted to devise a calculus of probabilities which could be applied to situations hitherto considered beyond investigation. The enormous range of this work can be seen from chapter headings: Nature and Design of This Work; Signs and Their Laws; Derivation of Laws; Division of Propositions; Principles of Symbolical Reasoning; Interpretation; Elimination; Reduction; Methods of Abbreviation; Conditions of a Perfect Method; Secondary Propositions; Methods in Secondary Propositions; Clarke and Spinoza; Analysis, Aristotelian Logic; Theory of Probabilities; General Method in Probabilities; Elementary Illustrations; Statistical Conditions; Problems on Causes; Probability of Judgments; Constitution of the Intellect. This last chapter, Constitution of the Intellect, is a very significant analysis of the psychology of discovery and scientific method.
Author | : George Boole |
Publisher | : Courier Corporation |
Total Pages | : 514 |
Release | : 2012-01-01 |
Genre | : Mathematics |
ISBN | : 0486488268 |
Authoritative account of the development of Boole's ideas in logic and probability theory ranges from The Mathematical Analysis of Logic to the end of his career. The Laws of Thought formed the most systematic statement of Boole's theories; this volume contains incomplete studies intended for a follow-up volume. 1952 edition.
Author | : George Boole |
Publisher | : Createspace Independent Pub |
Total Pages | : 336 |
Release | : 2013-06-03 |
Genre | : Mathematics |
ISBN | : 9781490335933 |
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. Boole's work founded the discipline of algebraic logic. It is often, but mistakenly, credited as being the source of what we know today as Boolean algebra. In fact, however, Boole's algebra differs from modern Boolean algebra: in Boole's algebra A+B cannot be interpreted by set union, due to the permissibility of uninterpretable terms in Boole's calculus. Therefore algebras on Boole's account cannot be interpreted by sets under the operations of union, intersection and complement, as is the case with modern Boolean algebra. The task of developing the modern account of Boolean algebra fell to Boole's successors in the tradition of algebraic logic (Jevons 1869, Peirce 1880, Jevons 1890, Schröder 1890, Huntingdon 1904). In Boole's account of his algebra, terms are reasoned about equationally, without a systematic interpretation being assigned to them. In places, Boole talks of terms being interpreted by sets, but he also recognises terms that cannot always be so interpreted, such as the term 2AB, which arises in equational manipulations. Such terms he classes uninterpretable terms; although elsewhere he has some instances of such terms being interpreted by integers. The coherences of the whole enterprise is justified by Boole in what Stanley Burris has later called the "rule of 0s and 1s", which justifies the claim that uninterpretable terms cannot be the ultimate result of equational manipulations from meaningful starting formulae (Burris 2000). Boole provided no proof of this rule, but the coherence of his system was proved by Theodore Hailperin, who provided an interpretation based on a fairly simple construction of rings from the integers to provide an interpretation of Boole's theory (Hailperin 1976).