Augustus De Morgan And The Logic Of Relations
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Augustus De Morgan And The Logic Of Relations
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Author : Daniel D. Merrill
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Augustus De Morgan And The Logic Of Relations written by Daniel D. Merrill and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Philosophy categories.
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.
On The Syllogism
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Author : Augustus De Morgan
language : en
Publisher: Routledge
Release Date : 2019-09-17
On The Syllogism written by Augustus De Morgan and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-17 with Philosophy categories.
Originally published in 1966 On the Syllogism and Other Logical Writings assembles for the first time the five celebrated memoirs of Augustus De Morgan on the syllogism. These are collected together with the more condensed accounts of his researches given in his Syllabus of a Proposed System of Logic an article on Logic contributed to the English Cyclopaedia. De Morgan was among the most distinguished of nineteenth century British mathematicians but is chiefly remembered today as one of the founders of modern mathematical logic. His writings on this subject have been little read, however since apart from his Formal Logic, they lie buried for the most part in inaccessible periodicals. De Morgan’s own later amendments are inserted in the text and the editorial introduction gives a summary of the whole and traces in some detail the course of the once-famous feud with Sir William Hamilton of Edinburgh.
Aristotle S Syllogism And The Creation Of Modern Logic
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Author : Lukas M. Verburgt
language : en
Publisher: Bloomsbury Publishing
Release Date : 2023-01-26
Aristotle S Syllogism And The Creation Of Modern Logic written by Lukas M. Verburgt and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-26 with Philosophy categories.
Offering a bold new vision on the history of modern logic, Lukas M. Verburgt and Matteo Cosci focus on the lasting impact of Aristotle's syllogism between the 1820s and 1930s. For over two millennia, deductive logic was the syllogism and syllogism was the yardstick of sound human reasoning. During the 19th century, this hegemony fell apart and logicians, including Boole, Frege and Peirce, took deductive logic far beyond its Aristotelian borders. However, contrary to common wisdom, reflections on syllogism were also instrumental to the creation of new logical developments, such as first-order logic and early set theory. This volume presents the period under discussion as one of both tradition and innovation, both continuity and discontinuity. Modern logic broke away from the syllogistic tradition, but without Aristotle's syllogism, modern logic would not have been born. A vital follow up to The Aftermath of Syllogism, this book traces the longue durée history of syllogism from Richard Whately's revival of formal logic in the 1820s through the work of David Hilbert and the Göttingen school up to the 1930s. Bringing together a group of major international experts, it sheds crucial new light on the emergence of modern logic and the roots of analytic philosophy in the 19th and early 20th centuries.
Syllabus Of A Proposed System Of Logic
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Author : Augustus De Morgan
language : en
Publisher:
Release Date : 1860
Syllabus Of A Proposed System Of Logic written by Augustus De Morgan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1860 with Logic categories.
Relations Concrete Abstract And Applied An Introduction
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Author : Herbert Toth
language : en
Publisher: World Scientific
Release Date : 2020-06-22
Relations Concrete Abstract And Applied An Introduction written by Herbert Toth and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-22 with Mathematics categories.
The book is intended as an invitation to the topic of relations on a rather general basis. It fills the gap between the basic knowledge offered in countless introductory papers and books (usually comprising orders and equivalences) and the highly specialized monographs on mainly relation algebras, many-valued (fuzzy) relations, or graphs. This is done not only by presenting theoretical results but also by giving hints to some of the many interesting application areas (also including their respective theoretical basics).This book is a new — and the first of its kind — compilation of known results on binary relations. It offers relational concepts in both reasonable depth and broadness, and also provides insight into the vast diversity of theoretical results as well as application possibilities beyond the commonly known examples.This book is unique by the spectrum of the topics it handles. As indicated in its title these are:
Formal Logic
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Author : Augustus de Morgan
language : en
Publisher: Legare Street Press
Release Date : 2022-10-27
Formal Logic written by Augustus de Morgan and has been published by Legare Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-27 with History categories.
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 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. 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.
The Rise Of Modern Logic From Leibniz To Frege
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Author : Dov M. Gabbay
language : en
Publisher: Elsevier
Release Date : 2004-03-08
The Rise Of Modern Logic From Leibniz To Frege written by Dov M. Gabbay and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Mathematics categories.
With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century.
Interactive Logic
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Author : J. F. A. K. van Benthem
language : en
Publisher: Amsterdam University Press
Release Date : 2007
Interactive Logic written by J. F. A. K. van Benthem and has been published by Amsterdam University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Philosophy categories.
Traditionally, logic has dealt with notions of truth and reasoning. In the past several decades, however, research focus in logic has shifted to the vast field of interactive logic—the domain of logics for both communication and interaction. The main applications of this move are logical approaches to games and social software; the wealth of these applications was the focus of the seventh Augustus de Morgan Workshop in November 2005. This collection of papers from the workshop serves as the initial volume in the new series Texts in Logics and Games—touching on research in logic, mathematics, computer science, and game theory. “A wonderful demonstration of contemporary topics in logic.”—Wiebe van der Hoek, University of Liverpool
Relational Methods In Computer Science
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Author : Chris Brink
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-04-23
Relational Methods In Computer Science written by Chris Brink and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-23 with Computers categories.
The calculus of relations has been an important component of the development of logic and algebra since the middle of the nineteenth century, when Augustus De Morgan observed that since a horse is an animal we should be able to infer that the head of a horse is the head of an animal. For this, Aristotelian syllogistic does not suffice: We require relational reasoning. George Boole, in his Mathematical Analysis of Logic of 1847, initiated the treatment of logic as part of mathematics, specifically as part of algebra. Quite the opposite conviction was put forward early this century by Bertrand Russell and Alfred North Whitehead in their Principia Mathematica (1910 - 1913): that mathematics was essentially grounded in logic. Logic thus developed in two streams. On the one hand algebraic logic, in which the calculus of relations played a particularly prominent part, was taken up from Boole by Charles Sanders Peirce, who wished to do for the "calculus of relatives" what Boole had done for the calculus of sets. Peirce's work was in turn taken up by Schroder in his Algebra und Logik der Relative of 1895 (the third part of a massive work on the algebra of logic). Schroder's work, however, lay dormant for more than 40 years, until revived by Alfred Tarski in his seminal paper "On the calculus of binary relations" of 1941 (actually his presidential address to the Association for Symbolic Logic).
The Principles Of Science
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Author : William Stanley Jevons
language : en
Publisher:
Release Date : 1892
The Principles Of Science written by William Stanley Jevons and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1892 with Logic categories.