On The Formal Elements Of The Absolute Algebra

Author : Ernst Schröder
Publisher : LED Edizioni Universitarie
Page : 153 pages
File Size : 52,6 Mb
Release : 2012-05-23T00:00:00+02:00
Category : Mathematics
ISBN : 9788879165877

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On the Formal Elements of the Absolute Algebra by Ernst Schröder Pdf

TABLE OF CONTENTS: ALGEBRA, WHAT ELSE?: 1. The Birth of a Masterwork - 2. Commutativity and Left- and Right-Division - 3. Algorithms, Algorithms, Algorithms - 4. Formalism - 5. A Fateful Choice - 6. Overview - 7. A Strange Document - 8. Acknowledgements - 9. Tools - Notes — ON THE FORMAL ELEMENTS OF THE ABSOLUTE ALGEBRA: §. 1. Character des zu behandelnden Problems. Character of the Problem in Issue - §. 2. Einschränkungen der Aufgabe. Restrictions of our Scope - §. 3. Die Fundamentalgleichungen für nur zwei Zahlen. Algorithmen. The Fundamental Equations for only Two Numbers. Algorithms - §. 4. Vertauschungsprincipien. Principles of Permutation - §. 5. Die Fundamentalgleichungen für drei Zahlen. Elementarcyklen und Gruppen. The Fundamental Equations for Three Numbers. Elementary Cycles and Groups - §. 6. Consequenzen der Algorithmen C1; C2; C3 für drei Zahlen. Consequences of the Algorithms C1; C2; C3 for Three Numbers - §. 7. Consequenzen von C0. Consequences of C0 - §. 8. Combination der Ci. Combination of the Ci - §. 9. Das Formelsystem O1 der ordinäre Algebra. The Formal System O1 of the Usual Algebra - §. 10. Untergeordnete Algorithmen von O1: Weitere ermittelte Tragweitezahlen. Subordinate Algorithms of O1: Further Sizes — FIGURES - Notes — APPENDIX - Notes — ILLUSTRATIONS - Bibliography - Index of the Main Concepts - Index of the Illustrations.

Author : Ernst Schröder
Publisher : Unknown
Page : 109 pages
File Size : 47,7 Mb
Release : 2012
Category : Mathematics
ISBN : 887916516X

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On the formal elements of the absolute algebra by Ernst Schröder Pdf

Author : Jordi Cat,Adam Tamas Tuboly
Publisher : Springer
Page : 706 pages
File Size : 45,5 Mb
Release : 2019-02-12
Category : Science
ISBN : 9783030021283

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Neurath Reconsidered by Jordi Cat,Adam Tamas Tuboly Pdf

This highly readable book is a collection of critical papers on Otto Neurath (1882-1945). It comprehensively re-examines Neurath’s scientific, philosophical and educational contributions from a range of standpoints including historical, sociological and problem-oriented perspectives. Leading Neurath scholars disentangle and connect Neurath’s works, ideas and ideals and evaluate them both in their original socio-historical context and in contemporary philosophical debates. Readers will discover a new critical understanding. Drawing on archive materials, essays discuss not only Neurath’s better-known works from lesser-known perspectives, but also his lesser-known works from the better-known perspective of their place in his overall philosophical oeuvre. Reflecting the full range of Neurath's work, this volume has a broad appeal. Besides scholars and researchers interested in Neurath, Carnap, the Vienna Circle, work on logical empiricism and the history and philosophy of science, this book will also appeal to graduate students in philosophy, sociology, history and education. Readers will find Neurath’s thoughts described and evaluated in an accessible manner, making it a good read for those beyond the academic world such as social leaders and activists. The book includes the edited 1940-45 Neurath-Carnap correspondence and the English translation of Neurath's logic papers.

Author : Leila Haaparanta
Publisher : Oxford University Press
Page : 1008 pages
File Size : 47,6 Mb
Release : 2009-06-18
Category : Philosophy
ISBN : 0199722722

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The Development of Modern Logic by Leila Haaparanta Pdf

This edited volume presents a comprehensive history of modern logic from the Middle Ages through the end of the twentieth century. In addition to a history of symbolic logic, the contributors also examine developments in the philosophy of logic and philosophical logic in modern times. The book begins with chapters on late medieval developments and logic and philosophy of logic from Humanism to Kant. The following chapters focus on the emergence of symbolic logic with special emphasis on the relations between logic and mathematics, on the one hand, and on logic and philosophy, on the other. This discussion is completed by a chapter on the themes of judgment and inference from 1837-1936. The volume contains a section on the development of mathematical logic from 1900-1935, followed by a section on main trends in mathematical logic after the 1930s. The volume goes on to discuss modal logic from Kant till the late twentieth century, and logic and semantics in the twentieth century; the philosophy of alternative logics; the philosophical aspects of inductive logic; the relations between logic and linguistics in the twentieth century; the relationship between logic and artificial intelligence; and ends with a presentation of the main schools of Indian logic. The Development of Modern Logic includes many prominent philosophers from around the world who work in the philosophy and history of mathematics and logic, who not only survey developments in a given period or area but also seek to make new contributions to contemporary research in the field. It is the first volume to discuss the field with this breadth of coverage and depth, and will appeal to scholars and students of logic and its philosophy.

Author : Jeffrey M. Binder
Publisher : University of Chicago Press
Page : 328 pages
File Size : 45,5 Mb
Release : 2022-12-06
Category : Technology & Engineering
ISBN : 9780226822549

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Language and the Rise of the Algorithm by Jeffrey M. Binder Pdf

A wide-ranging history of the algorithm. Bringing together the histories of mathematics, computer science, and linguistic thought, Language and the Rise of the Algorithm reveals how recent developments in artificial intelligence are reopening an issue that troubled mathematicians well before the computer age: How do you draw the line between computational rules and the complexities of making systems comprehensible to people? By attending to this question, we come to see that the modern idea of the algorithm is implicated in a long history of attempts to maintain a disciplinary boundary separating technical knowledge from the languages people speak day to day. Here Jeffrey M. Binder offers a compelling tour of four visions of universal computation that addressed this issue in very different ways: G. W. Leibniz’s calculus ratiocinator; a universal algebra scheme Nicolas de Condorcet designed during the French Revolution; George Boole’s nineteenth-century logic system; and the early programming language ALGOL, short for algorithmic language. These episodes show that symbolic computation has repeatedly become entangled in debates about the nature of communication. Machine learning, in its increasing dependence on words, erodes the line between technical and everyday language, revealing the urgent stakes underlying this boundary. The idea of the algorithm is a levee holding back the social complexity of language, and it is about to break. This book is about the flood that inspired its construction.

Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 754 pages
File Size : 48,8 Mb
Release : 2007-10-11
Category : Mathematics
ISBN : 9780817646134

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Advanced Algebra by Anthony W. Knapp Pdf

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.

Author : Thomas W. Hungerford,Richard Mercer
Publisher : Elsevier
Page : 520 pages
File Size : 50,6 Mb
Release : 1982
Category : Mathematics
ISBN : 0030595215

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College Algebra by Thomas W. Hungerford,Richard Mercer Pdf

Author : Dov M. Gabbay,John Woods
Publisher : Elsevier
Page : 781 pages
File Size : 42,5 Mb
Release : 2004-03-08
Category : Mathematics
ISBN : 9780080532875

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The Rise of Modern Logic: from Leibniz to Frege by Dov M. Gabbay,John Woods Pdf

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.

Author : Anonim
Publisher : Academic Press
Page : 370 pages
File Size : 46,8 Mb
Release : 1982-10-07
Category : Mathematics
ISBN : 0080874231

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Rings That are Nearly Associative by Anonim Pdf

Rings That are Nearly Associative

Author : Dennis Dieks,Wenceslao J. Gonzalez,Stephan Hartmann,Michael Stöltzner,Marcel Weber
Publisher : Springer Science & Business Media
Page : 505 pages
File Size : 45,5 Mb
Release : 2012-02-02
Category : Science
ISBN : 9789400730304

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Probabilities, Laws, and Structures by Dennis Dieks,Wenceslao J. Gonzalez,Stephan Hartmann,Michael Stöltzner,Marcel Weber Pdf

This volume, the third in this Springer series, contains selected papers from the four workshops organized by the ESF Research Networking Programme "The Philosophy of Science in a European Perspective" (PSE) in 2010: Pluralism in the Foundations of Statistics Points of Contact between the Philosophy of Physics and the Philosophy of Biology The Debate on Mathematical Modeling in the Social Sciences Historical Debates about Logic, Probability and Statistics The volume is accordingly divided in four sections, each of them containing papers coming from the workshop focussing on one of these themes. While the programme's core topic for the year 2010 was probability and statistics, the organizers of the workshops embraced the opportunity of building bridges to more or less closely connected issues in general philosophy of science, philosophy of physics and philosophy of the special sciences. However, papers that analyze the concept of probability for various philosophical purposes are clearly a major theme in this volume, as it was in the previous volumes of the same series. This reflects the impressive productivity of probabilistic approaches in the philosophy of science, which form an important part of what has become known as formal epistemology - although, of course, there are non-probabilistic approaches in formal epistemology as well. It is probably fair to say that Europe has been particularly strong in this area of philosophy in recent years.​

Author : Arnold Koslow,Arthur Buchsbaum
Publisher : Springer
Page : 520 pages
File Size : 50,6 Mb
Release : 2014-10-10
Category : Mathematics
ISBN : 9783319101934

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The Road to Universal Logic by Arnold Koslow,Arthur Buchsbaum Pdf

This is the first volume of a collection of papers in honor of the fiftieth birthday of Jean-Yves Béziau. These 25 papers have been written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Arnon Avron, John Corcoran, Wilfrid Hodges, Laurence Horn, Lloyd Humbertsone, Dale Jacquette, David Makinson, Stephen Read, and Jan Woleński. It is a state-of-the-art source of cutting-edge studies in the new interdisciplinary field of universal logic. The papers touch upon a wide range of topics including combination of logic, non-classical logic, square and other geometrical figures of opposition, categorical logic, set theory, foundation of logic, philosophy and history of logic (Aristotle, Avicenna, Buridan, Schröder, MacColl). This book offers new perspectives and challenges in the study of logic and will be of interest to all students and researchers interested the nature and future of logic.

Author : Gert Schubring
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 40,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401587532

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Hermann Günther Graßmann (1809-1877): Visionary Mathematician, Scientist and Neohumanist Scholar by Gert Schubring Pdf

In this volume specialists in mathematics, physics, and linguistics present the first comprehensive analysis of the ideas and influence of Hermann G. Graßmann (1809-1877), the remarkable universalist whose work recast the foundations of these disciplines and shaped the course of their modern development.

Author : Jingjing Ma
Publisher : World Scientific
Page : 260 pages
File Size : 43,6 Mb
Release : 2014-03-14
Category : Mathematics
ISBN : 9789814571449

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Lecture Notes On Algebraic Structure Of Lattice-ordered Rings by Jingjing Ma Pdf

Algebraic Structure of Lattice-Ordered Rings presents an introduction to the theory of lattice-ordered rings and some new developments in this area in the last 10-15 years. It aims to provide the reader with a good foundation in the subject, as well as some new research ideas and topic in the field.This book may be used as a textbook for graduate and advanced undergraduate students who have completed an abstract algebra course including general topics on group, ring, module, and field. It is also suitable for readers with some background in abstract algebra and are interested in lattice-ordered rings to use as a self-study book.The book is largely self-contained, except in a few places, and contains about 200 exercises to assist the reader to better understand the text and practice some ideas.

Author : Pierpaolo Degano,Joshua D. Guttman
Publisher : Springer
Page : 279 pages
File Size : 55,6 Mb
Release : 2010-04-29
Category : Computers
ISBN : 9783642124594

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Formal Aspects in Security and Trust by Pierpaolo Degano,Joshua D. Guttman Pdf

This book constitutes the thoroughly refereed post-workshop proceedings of the 6th International Workshop on Formal Aspects in Security and Trust, FAST 2009, held under the auspices of IFIP WG 1.7 in Eindhoven, The Netherlands, in November 2009 as an event of the Formal Methods Week, FMweek 2009. The 18 revised papers presented together with an abstract of the invited lecture were carefully reviewed and selected from 50 submissions. The papers focus of formal aspects in security and trust policy models, security protocol design and analysis, formal models of trust and reputation, logics for security and trust, distributed trust management systems, trust-based reasoning, digital assets protection, data protection, privacy and id issues, information flow analysis, language-based security, security and trust aspects in ubiquitous computing, validation/analysis tools, Web service security/trust/privacy, grid security, security risk assessment, and case studies.

Author : Miguel Cabrera García,Ángel Rodríguez Palacios
Publisher : Cambridge University Press
Page : 735 pages
File Size : 44,7 Mb
Release : 2014-07-31
Category : Mathematics
ISBN : 9781107043060

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Non-Associative Normed Algebras by Miguel Cabrera García,Ángel Rodríguez Palacios Pdf

The first systematic account of the basic theory of normed algebras, without assuming associativity. Sure to become a central resource.