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

George Boole

Softcover

ISBN 10: 1440066426 ISBN 13: 9781440066429

Publisher: Forgotten Books, 2018

Synopsis

A fresh, symbol-driven take on logic invites you to see reasoning as a precise, mathematical craft.

This edition reveals how logical ideas can be expressed and tested with exact rules.

This work presents a Calculus of Logic that treats propositions as equations and symbols as the language of thought. It argues that the validity of reasoning rests on the laws of symbol combination, not on any fixed interpretation of the signs. By using general symbols, the book shows how a single system can represent arithmetic, geometry, dynamics, and optics, depending on how we interpret the relations.

Readers will learn how complex logical ideas unfold from simple, auditable rules. The text explains the importance of classes and mental distinctions, and how syllogisms can be analyzed with equations. It also discusses cases where traditional middle terms do not appear, and how such cases influence valid inferences. The aim is a universal, mechanical style of reasoning that still respects human insight.

• See how propositions can become solvable equations that mirror logical relations.
• Understand the role of symbols, interpretations, and the laws that govern their use.
• Explore how this approach extends to general theorems in logic and beyond.

Ideal for readers seeking a rigorous, accessible introduction to symbolic logic and its mathematical roots.

About this title

Book Description

In 1847, mathematician George Boole published a pamphlet, The Mathematical Analysis of Logic, which launched him into history as one of the nineteenth century's most innovative thinkers. This work was the first to construct a mathematics of logic and the human intellect, establishing the close relationship between mathematics and philosophy.

About the Author

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.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 1440066426
• ISBN 13: 9781440066429
• Binding: Paperback
• Number of pages: 92