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The Rise Of Modern Logic From Leibniz To Frege


Author : Dov M. Gabbay
language : en
Publisher: Elsevier
Release Date : 2004-03-08

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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.

Handbook Of The History Of Logic The Rise Of Modern Logic From Leibniz To Frege


Author : Dov M. Gabbay
language : en
Publisher:
Release Date : 2004

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Download Handbook Of The History Of Logic The Rise Of Modern Logic From Leibniz To Frege written by Dov M. Gabbay and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Induction (Logic) 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 Hegel make clear. Of the two, Hegel'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.

Greek Indian And Arabic Logic


Author : Dov M. Gabbay
language : en
Publisher: Elsevier
Release Date : 2004-02-06

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Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and Renaissance Logic and Logic: A History of its Central. In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality. Logic is an indispensably important pivot of the Western intellectual tradition. But, as the chapters on Indian and Arabic logic make clear, logic's parentage extends more widely than any direct line from the Greek city states. It is hardly surprising, therefore, that for centuries logic has been an unfetteredly international enterprise, whose research programmes reach to every corner of the learned world. Like its companion volumes, Greek, Indian and Arabic Logic is the result of a design that gives to its distinguished authors as much space as would be needed to produce highly authoritative chapters, rich in detail and interpretative reach. The aim of the Editors is to have placed before the relevant intellectual communities a research tool of indispensable value. Together with the other volumes, Greek, Indian and Arabic Logic, will be essential reading for everyone with a curiosity about logic's long development, especially researchers, graduate and senior undergraduate students in logic in all its forms, argumentation theory, AI and computer science, cognitive psychology and neuroscience, linguistics, forensics, philosophy and the history of philosophy, and the history of ideas.

Logic And Its Applications


Author : Mohua Banerjee
language : en
Publisher: Springer
Release Date : 2010-12-10

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Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 4th Indian Conference on Logic and Its Applications, ICLA 2011, held in Delhi, India, in January 2011. The 14 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 34 submissions. The papers present current research in all aspects of formal logic ranging from pure and applied logic to history of logic.

The Oxford Handbook Of German Philosophy In The Nineteenth Century


Author : Michael N. Forster
language : en
Publisher: Oxford University Press, USA
Release Date : 2015

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No period of history has been richer in philosophical discoveries than Germany during the eighteenth and nineteenth centuries. And while it was the eighteenth century that saw Germany attain maturity in the discipline (above all in the works of Immanuel Kant), it was arguably the nineteenth century that bore the greatest philosophical fruits. he Oxford Handbook of German Philosophy in the Nineteenth Century is the first collective critical study of thisgreat period in intellectual history. A team of leading experts explore individual philosophers working in the period, including Fichte, Hegel, Kierkegaard, and Nietzsche; key philosophical movements associatedwith it, Idealism and Romanticism amongst them; different areas of philosophy that received particular attention at this time; and the central philosophical topics under debate. An essential resource for anyone working in the area, the Handbook will lead the direction of future research in this vital period of philosophy.

Inductive Logic


Author : Dov M. Gabbay
language : en
Publisher: Elsevier
Release Date : 2011-05-27

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This volume is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. • Chapter on the Port Royal contributions to probability theory and decision theory • Serves as a singular contribution to the intellectual history of the 20th century • Contains the latest scholarly discoveries and interpretative insights

The Logic Of Hegel S Logic


Author : John W. Burbidge
language : en
Publisher: Broadview Press
Release Date : 2006-03-28

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George Wilhelm Friedrich Hegel has seldom been considered a major figure in the history of logic. His two texts on logic, both called The Science of Logic, both written in Hegel’s characteristically dense and obscure language, are often considered more as works of metaphysics than logic. But in this highly readable book, John Burbidge sets out to reclaim Hegel’s Science of Logic as logic and to get right at the heart of Hegel’s thought. Burbidge examines the way Hegel moves from concept to concept through every chapter of his work, and traces the origins of Hegel’s effort to “think through the way thought thinks” to Plato, Kant, and Fichte. Having established the framework of Hegel’s logical thought, Burbidge demonstrates how Hegel organized the rest of his system, including the Philosophy of Nature, Philosophy of Spirit and his Lectures on World History, Art, Religion and Philosophy. A final section discusses English-language interpretations of Hegel’s logic from the nineteenth through twentieth centuries. Burbidge’s The Logic of Hegel’s ‘Logic’ is written with an eye to the reader of general interests, avoiding as much as possible the use of Hegel’s technical vocabulary. It is an excellent introduction to an otherwise very difficult text, and has recently appeared in an Iranian translation.