The Mathematical Analysis of Logic (Classic Reprint): Being an Essay Towards a Calculus of Deductive Reasoning - Couverture souple

George Boole

Couverture souple

ISBN 10 : 1440066426 ISBN 13 : 9781440066429

Editeur : Forgotten Books, 2018

Synopsis

A bold rethinking of logic, treating deductive reasoning as a calculable system of symbols.

In this work, logic is shown as a branch of mathematical analysis. The author argues that propositions can be expressed exactly with symbolic rules, and that their meaning comes from how the symbols combine, not any fixed interpretation of their signs. The book aims to establish a Calculus of Logic that uses general, well‑defined laws to derive conclusions, much like ordinary mathematics does with numbers.

Readers are guided through how transparent symbolism can model syllogisms, propositions, and logical inferences. The text links logic to language, showing how mental operations can be formalized, tested, and extended to broader mathematical ideas. It presents a systematic method for converting complex logical problems into equations and solving them with rigor.

• Learn how logical propositions can be turned into exact equations and manipulated with general rules.


• See how syllogisms fit into a broader algebra of symbols, including cases with and without a middle term.


• Explore how the method aims to express universal conclusions, multiple premises, and hypothetical statements.


• Understand the link between logic, language, and mathematical analysis, with an eye toward wide applications.

Ideal for readers interested in the foundations of logic, mathematical analysis, and the philosophy of reasoning.

A propos du livre

Biographie de l'auteur

George Boole (1815 – 1864) was an English mathematician, philosopher and logician. He worked in the fields of differential equations and algebraic logic, and is now best known as the author of The Laws of Thought. Boole said, ... no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise ... those universal laws of thought which are the basis of all reasoning ... Boole was born in Lincolnshire, England. His father, John Boole (1779–1848), was a tradesman in Lincoln, and gave him lessons. He had an elementary school education, but little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin; which he may also have learned at the school of Thomas Bainbridge. He was self-taught in modern languages. At age 16 Boole became the breadwinner for his parents and three younger siblings, taking up a junior teaching position in Doncaster, at Heigham's School. He taught briefly in Liverpool. Boole participated in the local Mechanics Institute, the Lincoln Mechanics' Institution, which was founded in 1833. Edward Bromhead, who knew John Boole through the Institution, helped George Boole with mathematics books; and he was given the calculus text of Sylvestre François Lacroix by Rev. George Stevens Dickson, of St Swithin Lincoln. Without a teacher, it took him many years to master calculus. In 1841 Boole published an influential paper in early invariant theory. He received a medal from the Royal Society for his memoir of 1844, On A General Method of Analysis. It was a contribution to the theory of linear differential equations, moving from the case of constant coefficients on which he had already published, to variable coefficients. The innovation in operational methods is to admit that operations may not commute. In 1847 Boole published The Mathematical Analysis of Logic , the first of his works on symbolic logic. At age 19 Boole successfully established his own school at Lincoln. Four years later he took over Hall's Academy, at Waddington, outside Lincoln, following the death of Robert Hall. In 1840 he moved back to Lincoln, where he ran a boarding school. With E. R. Larken and others he set up a building society in 1847. He associated also with the Chartist Thomas Cooper, whose wife was a relation. From 1838 onwards Boole was making contacts with sympathetic British academic mathematicians, and reading more widely.

Présentation de l'éditeur

( 20 ) OF EXPRESSION AND INTERPRETATION. A Proposition iB a sentence which either affirms or denies, as, All men are mortal, No creature is independent. A Proposition has necessarily two terms, as men, mortal; the former of which, or the one spoken of, h culled the subject; the latter, or tha! which is affirmed or denied of the subject, the predicate. These are connected together by the copula w, or m not, or by some other modification of the substantive verb. The substantive verb is the only verb recognised in Logic; all others are resolvable by means of the verb to be and a participle or adjective, e. g. " The Romans conquered"; the word conquered U both copula and predicate, being equivalent to "were (copula) victorious" (predicate). A Proposition must either be affirmative or negative, and must be also either universal or particular. Thus we reckon in ail, four kinds of pure categorical Propositions. 1st. Universal-affirmative, usually represented by A, Ex. All Xs

About the Publisher

Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.

Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the difficult to read text. Read books online for free at www.forgottenbooks.org

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1440066426
• ISBN 13: 9781440066429
• Reliure: Broché
• Nombre de pages: 92
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