Download or read book Description of a Notation for the Logic of Relatives Resulting from an Amplification of the Conceptions of Boole s Calculus of Logic written by Charles Sanders Peirce and published by . This book was released on 1870 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Memoirs of the American Academy of Arts and Sciences written by American Academy of Arts and Sciences and published by . This book was released on 1867 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 An Introduction to Substructural Logics written by Greg Restall and published by Routledge. This book was released on 2002-09-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.
Download or read book Clifford Algebras and their Applications in Mathematical Physics written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.
Download or read book Clifford Algebras and their Applications in Mathematical Physics written by Rafał Abłamowicz and published by Springer Science & Business Media. This book was released on 2000 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.
Download or read book Diagrammatic Representation and Inference written by Peter Chapman and published by Springer. This book was released on 2018-06-07 with total page 835 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018, held in Edinburgh, UK, in June 2018. The 26 revised full papers and 28 short papers presented together with 32 posters were carefully reviewed and selected from 124 submissions. The papers are organized in the following topical sections: generating and drawing Euler diagrams; diagrams in mathematics; diagram design, principles and classification; reasoning with diagrams; Euler and Venn diagrams; empirical studies and cognition; Peirce and existential graphs; and logic and diagrams.
Download or read book Logics in AI written by Jan van Eijck and published by Springer Science & Business Media. This book was released on 1991-02-26 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European Workshop on Logics in Artificial Intelligence was held at the Centre for Mathematics and Computer Science in Amsterdam, September 10-14, 1990. This volume includes the 29 papers selected and presented at the workshop together with 7 invited papers. The main themes are: - Logic programming and automated theorem proving, - Computational semantics for natural language, - Applications of non-classical logics, - Partial and dynamic logics.
Download or read book The Rise of Modern Logic from Leibniz to Frege written by Dov M. Gabbay and published by Elsevier. This book was released on 2004-03-08 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Boole s Logic and Probability written by T. Hailperin and published by Elsevier. This book was released on 1986-10-01 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition in 1976, there has been a notable increase of interest in the development of logic. This is evidenced by the several conferences on the history of logic, by a journal devoted to the subject, and by an accumulation of new results. This increased activity and the new results - the chief one being that Boole's work in probability is best viewed as a probability logic - were influential circumstances conducive to a new edition.Chapter 1, presenting Boole's ideas on a mathematical treatment of logic, from their emergence in his early 1847 work on through to his immediate successors, has been considerably enlarged. Chapter 2 includes additional discussion of the ``uninterpretable'' notion, both semantically and syntactically. Chapter 3 now includes a revival of Boole's abandoned propositional logic and, also, a discussion of his hitherto unnoticed brush with ancient formal logic. Chapter 5 has an improved explanation of why Boole's probability method works. Chapter 6, Applications and Probability Logic, is a new addition. Changes from the first edition have brought about a three-fold increase in the bibliography.
Download or read book The Oxford Handbook of British Philosophy in the Nineteenth Century written by W. J. Mander and published by OUP Oxford. This book was released on 2014-02-06 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains thirty new essays by leading experts on British philosophy in the nineteenth century, and provides a comprehensive and unrivalled resource for advanced students and scholars. As well as the most celebrated figures, such as Mill, Spencer, Sidgwick, and Bradley, the Handbook discusses many other less well-known names and debates from the period, such as Whewell, Shadworth Hodgson, and Martineau. The Handbook contains six parts: Part I examines logic and scientific method from Whately through to the advent of modern formal logic; Part II discusses some of the century's most famous metaphysical systems such as those of the Scottish Common Sense school, J. F. Ferrier and F. H. Bradley; Part III covers science and philosophy, paying particular attention to positivism and the impact of Darwin's evolutionary theory; Part IV explores ethical, social, and political thought, including the lesser known themes of feminism and British Socialism; Part V concerns religious philosophy; and Part VI examines the changes which took place in the practice of philosophy itself during the nineteenth-century. Prefaced by an introductory article which contextualises and relates the various themes and controversies of the century, each chapter provides an overview of the topic under consideration and surveys of the state of current research, while at the same time offering new ideas and suggestions for future interpretation.
Download or read book The Development of Modern Logic written by Leila Haaparanta and published by OUP USA. This book was released on 2009-06-18 with total page 1005 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains newly-commissioned articles covering the development of modern logic from the late medieval period (fourteenth century) through the end of the twentieth-century. It is the first volume to discuss the field with this breadth of coverage and depth. It will appeal to scholars and students of philosophical logic and the philosophy of logic.
Download or read book Peirce written by Albert Atkin and published by Routledge. This book was released on 2015-06-26 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Charles Sanders Peirce (1839-1914) is generally regarded as the founder of pragmatism, and one of the greatest ever American philosophers. Peirce is also widely known for his work on truth, his foundational work in mathematical logic, and an influential theory of signs, or semiotics. Albert Atkin introduces the full spectrum of Peirce’s thought for those coming to his work for the first time. The book begins with an overview of Peirce’s life and work, considering his early and long-standing interest in logic and science, and highlighting important views on the structure of philosophical thought. Atkin then explains Peirce’s accounts of pragmatism and truth examining important later developments to these theories. He then introduces Peirce’s full accounts of semiotics, examines his foundational work on formal and graphical logic, and introduces Peirce’s account of metaphysics, the least understood aspect of his philosophy. The final chapter considers Peirce’s legacy and influence on the thought of philosophers such as John Dewey and Richard Rorty, as well as highlighting areas where Peirce’s ideas could still provide important insights for contemporary philosophers. Including chapter summaries, suggestions for further reading and a glossary, this invaluable introduction and guide to Peirce’s philosophy is essential reading for those new to his work.
Download or read book The Adventure of Reason written by Paolo Mancosu and published by OUP Oxford. This book was released on 2014-01-09 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.
Download or read book The Continuity of Peirce s Thought written by Kelly A. Parker and published by Vanderbilt University Press. This book was released on 1998 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: In The Continuity of Peirce's Thought, Kelly Parker shows how the principle of continuity functions in phenomenology and semeiotic, the two most novel and important of Peirce's philosophical sciences, which mediate between mathematics and metaphysics. Parker argues that Peirce's concept of continuity is the central organizing theme of the entire Peircean philosophical corpus. He explains how Peirce's unique conception of the mathematical continuum shapes the broad sweep of his thought, extending from mathematics to metaphysics and in religion. This new book should appeal to all who seek a fuller, unified understanding of the career and overarching contributions of Peirce, one of the key figures in the American philosophical tradition.
Download or read book C S Peirce and the Nested Continua Model of Religious Interpretation written by Gary Slater and published by Oxford University Press. This book was released on 2015-11-26 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study develops resources in the work of Charles S. Peirce (1839-1914) for the purposes of contemporary philosophy. It contextualizes Peirce's prevailing influences and provides greater context in relation to the currents of nineteenth-century thought. Dr Gary Slater articulates 'a nested continua model' for theological interpretation, which is indebted to Peirce's creation of 'Existential Graphs', a system of diagrams designed to provide visual representation of the process of human reasoning. He investigates how the model can be applied by looking at recent debates in historiography. He deals respectively with Peter Ochs and Robert C. Neville as contemporary manifestations of Peircean philosophical theology. This work concludes with an assessment of the model's theological implications.
