Download or read book Logic s Lost Genius written by Eckart Menzler-Trott and published by American Mathematical Soc.. This book was released on 2016-05-05 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gerhard Gentzen (1909–1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called “proof theory” but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for “German logic”, and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smoryński on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Gödel; and its development up to the present day. Smoryński explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program. This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers.
Download or read book Hiroakira Ono on Substructural Logics written by Nikolaos Galatos and published by Springer Nature. This book was released on 2021-12-13 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Hiroakira Ono life’s work on substructural logics. Chapters, written by well-established academics, cover topics related to universal algebra, algebraic logic and the Full Lambek calculus; the book includes a short biography about Hiroakira Ono. The book starts with detailed surveys on universal algebra, abstract algebraic logic, topological dualities, and connections to computer science. It further contains specialised contributions on connections to formal languages (recognizability in residuated lattices and connections to the finite embedding property), covering systems for modal substructural logics, results on the existence and disjunction properties and finally a study of conservativity of expansions. This book will be primarily of interest to researchers working in algebraic and non-classical logic.
Download or read book Elements of Logical Reasoning written by Jan von Plato and published by Cambridge University Press. This book was released on 2014-01-23 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics and computer science.
Download or read book The Great Formal Machinery Works written by Jan von Plato and published by Princeton University Press. This book was released on 2017-08-02 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, The Great Formal Machinery Works is essential reading for students and researchers in logic, mathematics, and computer science.
Download or read book How the World Computes written by Barry S. Cooper and published by Springer. This book was released on 2012-05-28 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Turing Centenary Conference and the 8th Conference on Computability in Europe, CiE 2012, held in Cambridge, UK, in June 2012. The 53 revised papers presented together with 6 invited lectures were carefully reviewed and selected with an acceptance rate of under 29,8%. The CiE 2012 Turing Centenary Conference will be remembered as a historic event in the continuing development of the powerful explanatory role of computability across a wide spectrum of research areas. The papers presented at CiE 2012 represent the best of current research in the area, and forms a fitting tribute to the short but brilliant trajectory of Alan Mathison Turing. Both the conference series and the association promote the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences such as physics and biology, and also including the promotion of related non-scientific fields such as philosophy and history of computing.
Download or read book Gentzen s Centenary written by Reinhard Kahle and published by Springer. This book was released on 2015-11-02 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory.
Download or read book Paul Lorenzen Mathematician and Logician written by Gerhard Heinzmann and published by Springer Nature. This book was released on 2021-08-17 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.
Download or read book The Victorian Cult of Shakespeare written by Charles LaPorte and published by Cambridge University Press. This book was released on 2020-11-05 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Victorian era, William Shakespeare's work was often celebrated as a sacred text: a sort of secular English Bible. Even today, Shakespeare remains a uniquely important literary figure. Yet Victorian criticism took on religious dimensions that now seem outlandish in retrospect. Ministers wrote sermons based upon Shakespearean texts and delivered them from pulpits in Christian churches. Some scholars crafted devotional volumes to compare his texts directly with the Bible's. Still others created Shakespearean societies in the faith that his inspiration was not like that of other playwrights. Charles LaPorte uses such examples from the Victorian cult of Shakespeare to illustrate the complex relationship between religion, literature and secularization. His work helps to illuminate a curious but crucial chapter in the history of modern literary studies in the West, as well as its connections with Biblical scholarship and textual criticism.
Download or read book Elements of Logics written by Richard Whately and published by . This book was released on 1866 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Unifying Field in Logics Neutrosophic Logic Neutrosophy Neutrosophic Set Neutrosophic Probability fourth edition written by Florentin Smarandache and published by Infinite Study. This book was released on 2005 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: N-Norm and N-conorm are extended in Neutrosophic Logic/Set.
Download or read book Riding the Windhorse written by Robert S. Corrington and published by Rowman & Littlefield. This book was released on 2003 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: That creativity and the quest for wholeness can support the erratic flight of the windhorse of manic-depression."--BOOK JACKET.
Download or read book Saturday Review written by and published by . This book was released on 1861 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Saturday Review of Politics Literature Science Art and Finance written by and published by . This book was released on 1861 with total page 948 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Saturday Review of Politics Literature Science and Art written by and published by . This book was released on 1861 with total page 948 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Western Democratic Review written by and published by . This book was released on 1854 with total page 1102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Girl Logic written by Iliza Shlesinger and published by Hachette Books. This book was released on 2017-11-07 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: From breakout stand-up comedian Iliza Shlesinger comes a subversively funny collection of essays and observations on the secret genius of irrational behavior. Have you ever been pissed because you're not pretty enough, and then gotten even more pissed that someone didn't find you as pretty as you think you are? Have you ever obsessed over the size of your thighs while eating dessert, all the while saying you'll work out extra tomorrow? Or spent endless hours wondering why you have to bear the brunt of other people's insecurities? I mean, after all, I'm pretty great. Why cope with insecurities I don't already have? That last one's just me? All right, then. But if the rest sounds familiar, you are experiencing Girl Logic: a characteristically female way of thinking that appears contradictory and circuitous but is actually a complicated and highly evolved way of looking at the world. You end up considering every repercussion of every choice (about dating, career, clothes, lunch) before making a move toward what you really want. And why do we attempt these mental hurdles? Well, that's what this book is all about. The fact is, whether you're obsessing over his last text or the most important meeting of your career, your Girl Logic serves a purpose: It helps push you, question what you want, and clarify what will make you a happier, better person. Girl Logic can be every confident woman's secret weapon, and this book shows you how to wield it.
Download or read book Creativity in Science written by Dean Keith Simonton and published by Cambridge University Press. This book was released on 2004-05-03 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Psychologists, sociologists, philosophers, historians - and even scientists themselves - have often tried to decipher the basis for creativity in science. Some have attributed creativity to a special logic, the so-called scientific method, whereas others have pointed to the inspirations of genius or to the inevitable workings of the zeitgeist. Finally, some have viewed scientific breakthroughs as the product of chance, as witnessed in the numerous episodes of serendipity. Too often these four alternative interpretations are seen as mutually exclusive. Yet the central thesis of this book is that the chance, logic, genius, and zeitgeist perspectives can be integrated into a single coherent theory of creativity in science. But for this integration to succeed, change must be elevated to the status of primary cause. Logic, genius and the zeitgeist still have significant roles to play but mainly operate insofar as they enhance, or constrain the operation of a chance combinatorial process.
