Download or read book Augustus De Morgan and the Logic of Relations written by Daniel D. Merrill and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On the Syllogism written by Augustus De Morgan and published by Routledge. This book was released on 2019-09-17 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Formal Logic written by Augustus De Morgan and published by . This book was released on 1847 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Interactive Logic written by J. F. A. K. van Benthem and published by Amsterdam University Press. This book was released on 2007 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book The Laws of Thought 1854 written by George Boole and published by . This book was released on 1911 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the study and difficulties of mathematics by A De Morgan written by Augustus De Morgan and published by . This book was released on 1831 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Elements of Arithmetic written by Augustus De Morgan and published by . This book was released on 1854 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Relational Methods in Computer Science written by Chris Brink and published by Springer Science & Business Media. This book was released on 1997-04-23 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Equations from God written by Daniel J. Cohen and published by JHU Press. This book was released on 2007-04-08 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This illuminating history explores the complex relationship between mathematics, religious belief, and Victorian culture. 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.
Download or read book Language in Action written by Johan van Benthem and published by MIT Press. This book was released on 1995 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities.
Download or read book A Survey of Symbolic Logic written by Clarence Irving Lewis and published by . This book was released on 1918 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Budget of Paradoxes written by Augustus De Morgan and published by . This book was released on 1915 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Trigonometry and Double Algebra written by Augustus De Morgan and published by . This book was released on 1849 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Concise Introduction to Logic written by Craig DeLancey and published by Open SUNY Textbooks. This book was released on 2017-02-06 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Augustus De Morgan Polymath written by Karen Attar and published by Open Book Publishers. This book was released on 2024-09-04 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Foundation Mathematics for Computer Science written by John Vince and published by Springer. This book was released on 2015-07-27 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Vince describes a range of mathematical topics to provide a foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author's visual approach will greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications. Each chapter includes full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will consolidate comprehension of abstract mathematical concepts. Foundation Mathematics for Computer Science covers number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus, and reveals the names of the mathematicians behind such inventions. During this journey, John Vince touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barycentric coordinates, transfinite sets and prime numbers. Whether you intend to pursue a career in programming, scientific visualisation, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts.
Download or read book Syllabus of a Proposed System of Logic written by Augustus De Morgan and published by . This book was released on 1860 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
