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Excerpt from A Letter to Augustus De Morgan, Esq. Of Trinity College, Cambridge, Professor of Mathematics in University College, London, on His Claim to an Independent Re-Discovery of a New Principle in the Theory of Syllogism On looking at a proposition so called, I find it is in truth several propositions; that is, there are several distinct assertions, each of which is a contradiction of the proposition. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
AUTHORITATIVE AND ACCESSIBLE, THIS LANDMARK WORK IS THE FIRST SINGLE-VOLUME HISTORY OF PHILOSOPHY SHARED FOR DECADES 'A cerebrally enjoyable survey, written with great clarity and touches of wit' Sunday Times The story of philosophy is an epic tale: an exploration of the ideas, views and teachings of some of the most creative minds known to humanity. But there has been no comprehensive history of this great intellectual journey since 1945. Intelligible for students and eye-opening for philosophy readers, A. C. Grayling covers with characteristic clarity and elegance subjects like epistemology, metaphysics, ethics, logic, and the philosophy of mind, as well as the history of debates in these areas, through the ideas of celebrated philosophers as well as less well-known influential thinkers. The History of Philosophy takes the reader on a journey from the age of the Buddha, Confucius and Socrates. Through Christianity's dominance of the European mind to the Renaissance and Enlightenment. On to Mill, Nietzsche, Sartre, then the philosophical traditions of India, China and the Persian-Arabic world. And finally, into philosophy today.
A number of years ago, Harriet Sheridan, then Dean of Brown University, organized a series oflectures in which individual faculty members described how it came about that they entered their various fields. I was invited to participate in this series and found in the invitation an opportunity to recall events going back to my early teens. The lecture was well received and its reception encouraged me to work up an expanded version. My manuscript lay dormant all these years. In the meanwhile, sufficiently many other mathematical experiences and encounters accumulated to make this little book. My 1981 lecture is the basis of the first piece: "Napoleon's Theorem. " Although there is a connection between the first piece and the second, the four pieces here are essentially independent. The sec ond piece, "Carpenter and the Napoleon Ascription," has as its object a full description of a certain type of scholar-storyteller (of whom I have known and admired several). It is a pastiche, contain ing a salad bar selection blended together by my own imagination. This piece purports, as a secondary goal, to present a solution to a certain unsolved historical problem raised in the first piece. The third piece, "The Man Who Began His Lectures with 'Namely'," is a short reminiscence of Stefan Bergman, one of my teachers of graduate mathematics. Bergman, a remarkable person ality, was born in Poland and came to the United States in 1939.
In the twenty-first century there are two ways to study logic. The more recent approach is symbolic logic. The history of teaching logic since World War II, however, casts doubt on the idea that symbolic logic is best for a first logic course. Logic as a Liberal Art is designed as part of a minority approach, teaching logic in the "verbal" way, in the student's "natural" language, the approach invented by Aristotle. On utilitarian grounds alone, this "verbal" approach is superior for a first course in logic, for the whole range of students. For millennia, this "verbal" approach to logic was taught in conjunction with grammar and rhetoric, christened the trivium. The decline in teaching grammar and rhetoric in American secondary schools has led Dr. Rollen Edward Houser to develop this book. The first part treats grammar, rhetoric, and the essential nature of logic. Those teachers who look down upon rhetoric are free, of course, to skip those lessons. The treatment of logic itself follows Aristotle's division of the three acts of the mind (Prior Analytics 1.1). Formal logic is then taken up in Aristotle's order, with Parts on the logic of Terms, Propositions, and Arguments. The emphasis in Logic as a Liberal Art is on learning logic through doing problems. Consequently, there are more problems in each lesson than would be found, for example, in many textbooks. In addition, a special effort has been made to have easy, medium, and difficult problems in each Problem Set. In this way the problem sets are designed to offer a challenge to all students, from those most in need of a logic course to the very best students.
This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation. * Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects* Includes chapter summaries of important vocabulary, formulas, and properties, plus the chapter review exercises* Features interesting anecdotes and biographies of 60 mathematicians and computer scientists* Instructor's Manual available for adopters* Student Solutions Manual available separately for purchase (ISBN: 0124211828)
This gorgeous 150th anniversary edition of Alice's Adventures in Wonderland is also a revelatory work of scholarship. Alice's Adventures in Wonderland--published 150 years ago in 1865--is a book many of us love and feel we know well. But it turns out we have only scratched the surface. Scholar David Day has spent many years down the rabbit hole of this children's classic and has emerged with a revelatory new view of its contents. What we have here, he brilliantly and persuasively argues, is a complete classical education in coded form--Carroll's gift to his "wonder child" Alice Liddell. In two continuous commentaries, woven around the complete text of the novel for ease of cross-reference on every page, David Day reveals the many layers of teaching, concealed by manipulation of language, that are carried so lightly in the beguiling form of a fairy tale. These layers relate directly to Carroll's interest in philosophy, history, mathematics, classics, poetry, spiritualism and even to his love of music--both sacred and profane. His novel is a memory palace, given to Alice as the great gift of an education. It was delivered in coded form because in that age, it was a gift no girl would be permitted to receive in any other way. Day also shows how a large number of the characters in the book are based on real Victorians. Wonderland, he shows, is a veritable "Who's Who" of Oxford at the height of its power and influence in the Victorian Age. There is so much to be found behind the imaginary characters and creatures that inhabit the pages of Alice's Adventures in Wonderland. David Day's warm, witty and brilliantly insightful guide--beautifully designed and stunningly illustrated throughout in full colour--will make you marvel at the book as never before.