Augustus De Morgan and the Logic of Relations


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


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.




Neutrosophy, Paradoxism and Communication


Book Description

There are people for whom are too few things they do not know how to do, to approach them, to understand them. There are people who is enough to look at them because they understood the significance in your eyes, are people for whom you have not finished the uttered sentence and they are given the solution, there are ...people!




The Modern Era, 1800-1950. The Boole-De Morgan Correspondence, 1842-1864


Book Description

The InteLex Past Masters English Letters database The Modern Era: 1800-1950 contains 40 volumes of letters and correspondence of the most important figures of the Nineteenth and Twentieth Centuries in Britain published by Oxford University Press.




The Logician and the Engineer


Book Description

Third printing. First paperback printing. Original copyright date: 2013.




Extensionalism: The Revolution in Logic


Book Description

a single life-span. Philosophers, then, do not see more or know more, and they do not see less or know less. They aim to see less detail and more of the abstract. Their details, if you like, are abstractions. Walking on God’s earth as a pedestrian, as a farmer working his fields or as a passer-by, one’s picture of one’s surroundings is every bit as intelligent as that of the pilot riding the sky. The views of the field are radically different, however. One sees only a specific field and in all lively detail: the exact pattern of the land, or even the exact outline of a given leaf, grasshopper, grain of sand even. Acquaintance with minute detail is not without its price: details may stand in the way of conjuring the big picture. It may be difficult to compare whichever field one happens to be in with far off fields, with respect to their size or shape or any other quality. One may wish to inquire if far off fields were already planted, harvested, or even if they exist. A pedestrian may find it hard or even impossible to do so. The pedestrian view contains fine points that the pilot’s map never would, but it does not necessarily contain more information, for it lacks the general context. After all, there are only so many items that one can observe and account for at a single glance, a single map, a single book, a single life-span.




Logic in Question


Book Description

This contributed volume collects papers related to the Logic in Question workshop, which has taken place annually at Sorbonne University in Paris since 2011. Each year, the workshop brings together historians, philosophers, mathematicians, linguists, and computer scientists to explore questions related to the nature of logic and how it has developed over the years. As a result, chapter authors provide a thorough, interdisciplinary exploration of topics that have been studied in the workshop. Organized into three sections, the first part of the book focuses on historical questions related to logic, the second explores philosophical questions, and the third section is dedicated to mathematical discussions. Specific topics include: • logic and analogy• Chinese logic• nineteenth century British logic (in particular Boole and Lewis Carroll)• logical diagrams • the place and value of logic in Louis Couturat’s philosophical thinking• contributions of logical analysis for mathematics education• the exceptionality of logic• the logical expressive power of natural languages• the unification of mathematics via topos theory Logic in Question will appeal to pure logicians, historians of logic, philosophers, linguists, and other researchers interested in the history of logic, making this volume a unique and valuable contribution to the field.




"Visions of the Industrial Age, 1830?914 "


Book Description

Providing a comprehensive interdisciplinary assessment, and with a particular focus on expressions of tension and anxiety about modernity, this collection examines visual culture in nineteenth-century Europe as it attempted to redefine itself in the face of social change and new technologies. Contributing scholars from the fields of history, art, literature and the history of science investigate the role of visual representation and the dominance of the image by looking at changing ideas expressed in representations of science, technology, politics, and culture in advertising, art, periodicals, and novels. They investigate how, during the period, new emphasis was placed on the visual with emerging forms of mass communication?photography, lithography, newspapers, advertising, and cinema?while older forms as varied as poetry, the novel, painting, interior decoration, and architecture became transformed. The volume includes investigations into new innovations and scientific development such as the steam engine, transportation and engineering, the microscope, "spirit photography," and the orrery, as well as how this new technology is reproduced in illustrated periodicals. The essays also look at more traditional forms of creative expression to show that the same concerns and anxieties about science, technology and the changing perceptions of the natural world can be seen in the art of Armand Guillaumin, Auguste Rodin, Gustave Caillebotte, and Camille Pissarro, in colonial nineteenth-century novels, in design manuals, in museums, and in the decorations of domestic interior spaces. Visions of the Industrial Age, 1830-1914 offers a thorough exploration of both the nature of modernity, and the nature of the visual.