The De Mathematisation Of Logic
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The De Mathematisation Of Logic
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Author : Barry Hartley Slater
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2007
The De Mathematisation Of Logic written by Barry Hartley Slater and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The Rise Of Modern Logic From Leibniz To Frege
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Author : Dov M. Gabbay
language : en
Publisher: Elsevier
Release Date : 2004-03-08
The Rise Of Modern Logic From Leibniz To Frege written by Dov M. Gabbay and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Mathematics categories.
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.
Aristotle S Syllogism And The Creation Of Modern Logic
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Author : Lukas M. Verburgt
language : en
Publisher: Bloomsbury Publishing
Release Date : 2023-01-26
Aristotle S Syllogism And The Creation Of Modern Logic written by Lukas M. Verburgt and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-26 with Philosophy categories.
Offering a bold new vision on the history of modern logic, Lukas M. Verburgt and Matteo Cosci focus on the lasting impact of Aristotle's syllogism between the 1820s and 1930s. For over two millennia, deductive logic was the syllogism and syllogism was the yardstick of sound human reasoning. During the 19th century, this hegemony fell apart and logicians, including Boole, Frege and Peirce, took deductive logic far beyond its Aristotelian borders. However, contrary to common wisdom, reflections on syllogism were also instrumental to the creation of new logical developments, such as first-order logic and early set theory. This volume presents the period under discussion as one of both tradition and innovation, both continuity and discontinuity. Modern logic broke away from the syllogistic tradition, but without Aristotle's syllogism, modern logic would not have been born. A vital follow up to The Aftermath of Syllogism, this book traces the longue durée history of syllogism from Richard Whately's revival of formal logic in the 1820s through the work of David Hilbert and the Göttingen school up to the 1930s. Bringing together a group of major international experts, it sheds crucial new light on the emergence of modern logic and the roots of analytic philosophy in the 19th and early 20th centuries.
British Logic In The Nineteenth Century
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Author : Dov M. Gabbay
language : en
Publisher: Elsevier
Release Date : 2008-03-10
British Logic In The Nineteenth Century written by Dov M. Gabbay and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-10 with Mathematics categories.
The present volume of the Handbook of the History of Logic is designed to establish 19th century Britain as a substantial force in logic, developing new ideas, some of which would be overtaken by, and other that would anticipate, the century's later capitulation to the mathematization of logic. British Logic in the Nineteenth Century is indispensable reading and a definitive research resource for anyone with an interest in the history of logic.- Detailed and comprehensive chapters covering the entire range of modal logic - Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic
Logic A History Of Its Central Concepts
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Author : Dov M. Gabbay
language : en
Publisher: Newnes
Release Date : 2012-12-31
Logic A History Of Its Central Concepts written by Dov M. Gabbay and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Mathematics categories.
The Handbook of the History of Logic is a multi-volume research instrument that brings to the development of logic the best in modern techniques of historical and interpretative scholarship. It is the first work in English in which the history of logic is presented so extensively. The volumes are numerous and large. Authors have been given considerable latitude to produce chapters of a length, and a level of detail, that would lay fair claim on the ambitions of the project to be a definitive research work. Authors have been carefully selected with this aim in mind. They and the Editors join in the conviction that a knowledge of the history of logic is nothing but beneficial to the subject's present-day research programmes. One of the attractions of the Handbook's several volumes is the emphasis they give to the enduring relevance of developments in logic throughout the ages, including some of the earliest manifestations of the subject. - Covers in depth the notion of logical consequence - Discusses the central concept in logic of modality - Includes the use of diagrams in logical reasoning
Truth And Assertibility
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Author : Nik Weaver
language : en
Publisher: World Scientific
Release Date : 2015-04-22
Truth And Assertibility written by Nik Weaver and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-22 with Mathematics categories.
The book is a research monograph on the notions of truth and assertibility as they relate to the foundations of mathematics. It is aimed at a general mathematical and philosophical audience. The central novelty is an axiomatic treatment of the concept of assertibility. This provides us with a device that can be used to handle difficulties that have plagued philosophical logic for over a century. Two examples relate to Frege's formulation of second-order logic and Tarski's characterization of truth predicates for formal languages. Both are widely recognized as fundamental advances, but both are also seen as being seriously flawed: Frege's system, as Russell showed, is inconsistent, and Tarski's definition fails to capture the compositionality of truth. A formal assertibility predicate can be used to repair both problems. The repairs are technically interesting and conceptually compelling. The approach in this book will be of interest not only for the uses the author has put it to, but also as a flexible tool that may have many more applications in logic and the foundations of mathematics.
A Boole Anthology
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Author : James Gasser
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
A Boole Anthology written by James Gasser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Philosophy categories.
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.
Routledge Encyclopedia Of Philosophy
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Author : Edward Craig
language : en
Publisher:
Release Date : 1998
Routledge Encyclopedia Of Philosophy written by Edward Craig and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Philosophy categories.
Volume five of a ten volume set which provides full and detailed coverage of all aspects of philosophy, including information on how philosophy is practiced in different countries, who the most influential philosophers were, and what the basic concepts are.
The Priority Of Propositions A Pragmatist Philosophy Of Logic
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Author : María José Frápolli
language : en
Publisher: Springer Nature
Release Date : 2023-02-22
The Priority Of Propositions A Pragmatist Philosophy Of Logic written by María José Frápolli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-22 with Philosophy categories.
This monograph is a defence of the Fregean take on logic. The author argues that Frege ́s projects, in logic and philosophy of language, are essentially connected and that the formalist shift produced by the work of Peano, Boole and Schroeder and continued by Hilbert and Tarski is completely alien to Frege's approach in the Begriffsschrift. A central thesis of the book is that judgeable contents, i.e. propositions, are the primary bearers of logical properties, which makes logic embedded in our conceptual system. This approach allows coherent and correct definitions of logical constants, logical consequence, and truth and connects their use to the practices of rational agents in science and everyday life.
The Oxford Handbook Of British Philosophy In The Nineteenth Century
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Author : W. J. Mander
language : en
Publisher: OUP Oxford
Release Date : 2014-02-06
The Oxford Handbook Of British Philosophy In The Nineteenth Century written by W. J. Mander and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-06 with Philosophy categories.
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.