The Boole-De Morgan Correspondence, 1842-1864
Author : George Boole
Publisher : Oxford University Press, USA
Page : 164 pages
File Size : 46,4 MB
Release : 1982
Category : Language Arts & Disciplines
ISBN :
The Boole-De Morgan Correspondence
Author : Augustus De Morgan
Publisher :
Page : 156 pages
File Size : 43,77 MB
Release : 1982
Category :
ISBN :
Book Description
Augustus De Morgan, Polymath
Author : Karen Attar
Publisher : Open Book Publishers
Page : 234 pages
File Size : 40,32 MB
Release : 2024-09-04
Category : Mathematics
ISBN : 1805113291
Book Description
When Augustus De Morgan died in 1871, he was described as ‘one of the profoundest mathematicians in the United Kingdom’ and even as ‘the greatest of our mathematicians’. But he was far more than just a mathematician. Because much of his voluminous written output on various subjects was scattered throughout journals and encyclopaedias, the breadth of his interests and contributions has been underappreciated by historians. Now, renewed interest in De Morgan’s life and work has coincided with the digitization of his extensive library, revealing the extent to which he pioneered and influenced the development of not merely mathematics but also logic, astronomy, the history of mathematics, education, and bibliography. This edited collection celebrates De Morgan as a polymath. Drawing together multiple elements of his activity from a range of publications and archives, its contributors re-assess his academic work, his place in his intellectual environment, and his legacy. The result offers new insight into De Morgan himself as well as the wider circles in which he moved, including his family life.
Augustus De Morgan and the Logic of Relations
Author : Daniel D. Merrill
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 45,54 MB
Release : 2012-12-06
Category : Philosophy
ISBN : 9400920474
Book Description
The middle years of the nineteenth century saw two crucial develop ments in the history of modern logic: George Boole's algebraic treat ment of logic and Augustus De Morgan's formulation of the logic of relations. The former episode has been studied extensively; the latter, hardly at all. This is a pity, for the most central feature of modern logic may well be its ability to handle relational inferences. De Morgan was the first person to work out an extensive logic of relations, and the purpose of this book is to study this attempt in detail. Augustus De Morgan (1806-1871) was a British mathematician and logician who was Professor of Mathematics at the University of London (now, University College) from 1828 to 1866. A prolific but not highly original mathematician, De Morgan devoted much of his energies to the rather different field of logic. In his Formal Logic (1847) and a series of papers "On the Syllogism" (1846-1862), he attempted with great ingenuity to reformulate and extend the tradi tional syllogism and to systematize modes of reasoning that lie outside its boundaries. Chief among these is the logic of relations. De Mor gan's interest in relations culminated in his important memoir, "On the Syllogism: IV and on the Logic of Relations," read in 1860.
A Boole Anthology
Author : James Gasser
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 33,46 MB
Release : 2013-11-11
Category : Philosophy
ISBN : 940159385X
Book Description
Modern mathematical logic would not exist without the analytical tools first developed by George Boole in The Mathematical Analysis of Logic and The Laws of Thought. The influence of the Boolean school on the development of logic, always recognised but long underestimated, has recently become a major research topic. This collection is the first anthology of works on Boole. It contains two works published in 1865, the year of Boole's death, but never reprinted, as well as several classic studies of recent decades and ten original contributions appearing here for the first time. From the programme of the English Algebraic School to Boole's use of operator methods, from the problem of interpretability to that of psychologism, a full range of issues is covered. The Boole Anthology is indispensable to Boole studies and will remain so for years to come.
Hyperidentities: Boolean And De Morgan Structures
Author : Yuri Movsisyan
Publisher : World Scientific
Page : 561 pages
File Size : 34,19 MB
Release : 2022-09-20
Category : Mathematics
ISBN : 9811254931
Book Description
Hyperidentities are important formulae of second-order logic, and research in hyperidentities paves way for the study of second-order logic and second-order model theory.This book illustrates many important current trends and perspectives for the field of hyperidentities and their applications, of interest to researchers in modern algebra and discrete mathematics. It covers a number of directions, including the characterizations of the Boolean algebra of n-ary Boolean functions and the distributive lattice of n-ary monotone Boolean functions; the classification of hyperidentities of the variety of lattices, the variety of distributive (modular) lattices, the variety of Boolean algebras, and the variety of De Morgan algebras; the characterization of algebras with aforementioned hyperidentities; the functional representations of finitely-generated free algebras of various varieties of lattices and bilattices via generalized Boolean functions (De Morgan functions, quasi-De Morgan functions, super-Boolean functions, super-De Morgan functions, etc); the structural results for De Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras, bilattices, among others.While problems of Boolean functions theory are well known, the present book offers alternative, more general problems, involving the concepts of De Morgan functions, quasi-De Morgan functions, super-Boolean functions, and super-De Morgan functions, etc. In contrast to other generalized Boolean functions discovered and investigated so far, these functions have clearly normal forms. This quality is of crucial importance for their applications in pure and applied mathematics, especially in discrete mathematics, quantum computation, quantum information theory, quantum logic, and the theory of quantum computers.
British Logic in the Nineteenth Century
Author : Dov M. Gabbay
Publisher : Elsevier
Page : 751 pages
File Size : 17,17 MB
Release : 2008-03-10
Category : Mathematics
ISBN : 0080557015
Book Description
The present volume of the Handbook of the History of Logic is designed to establish 19th century Britain as a substantial force in logic, developing new ideas, some of which would be overtaken by, and other that would anticipate, the century's later capitulation to the mathematization of logic. British Logic in the Nineteenth Century is indispensable reading and a definitive research resource for anyone with an interest in the history of logic. - Detailed and comprehensive chapters covering the entire range of modal logic - Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic
Equations from God
Author : Daniel J. Cohen
Publisher : JHU Press
Page : 274 pages
File Size : 23,56 MB
Release : 2007-04-08
Category : History
ISBN : 9780801885532
Book Description
Throughout history, application rather than abstraction has been the prominent driving force in mathematics. From the compass and sextant to partial differential equations, mathematical advances were spurred by the desire for better navigation tools, weaponry, and construction methods. But the religious upheaval in Victorian England and the fledgling United States opened the way for the rediscovery of pure mathematics, a tradition rooted in Ancient Greece. In Equations from God, Daniel J. Cohen captures the origins of the rebirth of abstract mathematics in the intellectual quest to rise above common existence and touch the mind of the deity. Using an array of published and private sources, Cohen shows how philosophers and mathematicians seized upon the beautiful simplicity inherent in mathematical laws to reconnect with the divine and traces the route by which the divinely inspired mathematics of the Victorian era begot later secular philosophies.
The Logician and the Engineer
Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 245 pages
File Size : 23,95 MB
Release : 2017-04-04
Category : Biography & Autobiography
ISBN : 0691176000
Book Description
Third printing. First paperback printing. Original copyright date: 2013.
Generations of Reason
Author : Joan L. Richards
Publisher : Yale University Press
Page : 456 pages
File Size : 27,74 MB
Release : 2021-10-26
Category : Science
ISBN : 0300262574
Book Description
An intimate, accessible history of British intellectual development across the eighteenth and nineteenth centuries, through the story of one family This book recounts the story of three Cambridge-educated Englishmen and the women with whom they chose to share their commitment to reason in all parts of their lives. The reason this family embraced was an essentially human power with the potential to generate true insight into all aspects of the world. In exploring the ways reason permeated three generations of English experience, this book casts new light on key developments in English cultural and political history, from the religious conformism of the eighteenth century through the Napoleonic era into the Industrial Revolution and prosperity of the Victorian age. At the same time, it restores the rich world of the essentially meditative, rational sciences of theology, astronomy, mathematics, and logic to their proper place in the English intellectual landscape. Following the development of their views over the course of an eventful one hundred years of English history illuminates the fine structure of ways reason still operates in our world.
