the rise of modern logic from leibniz to frege handbook of the history of logic

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

Author : Dov M. Gabbay
ISBN : 0444516115
Genre : Induction (Logic)
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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 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.

The Rise Of Modern Logic From Leibniz To Frege

Author : Dov M. Gabbay
ISBN : 008053287X
Genre : Technology & Engineering
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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.

Greek Indian And Arabic Logic

Author : Dov M. Gabbay
ISBN : 0080532861
Genre : Mathematics
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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 A History Of Its Central Concepts

Author : Dov M. Gabbay
ISBN : 9780080931708
Genre : Mathematics
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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

Handbook Of Philosophical Logic

Author : D.M. Gabbay
ISBN : 9781402035210
Genre : Philosophy
File Size : 80. 98 MB
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The ninth volume of the Second Edition contains major contributions on Rewriting Logic as a Logical and Semantic Framework, Logical Frameworks, Proof Theory and Meaning, Goal Directed Deductions, Negations, Completeness and Consistency as well as Logic as General Rationality. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

Approaches To Legal Rationality

Author : Dov M. Gabbay
ISBN : 9048195888
Genre : Law
File Size : 89. 13 MB
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Legal theory, political sciences, sociology, philosophy, logic, artificial intelligence: there are many approaches to legal argumentation. Each of them provides specific insights into highly complex phenomena. Different disciplines, but also different traditions in disciplines (e.g. analytical and continental traditions in philosophy) find here a rare occasion to meet. The present book contains contributions, both historical and thematic, from leading researchers in several of the most important approaches to legal rationality. One of the main issues is the relation between logic and law: the way logic is actually used in law, but also the way logic can make law explicit. An outstanding group of philosophers, logicians and jurists try to meet this issue. The book is more than a collection of papers. However different their respective conceptual tools may be, the authors share a common conception: legal argumentation is a specific argumentation context.

A Practical Logic Of Cognitive Systems

Author : Dov M. Gabbay
ISBN : 9780080460925
Genre : Mathematics
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The present work is a continuation of the authors' acclaimed multi-volume A Practical Logic of Cognitive Systems. After having investigated the notion of relevance in their previous volume, Gabbay and Woods now turn to abduction. In this highly original approach, abduction is construed as ignorance-preserving inference, in which conjecture plays a pivotal role. Abduction is a response to a cognitive target that cannot be hit on the basis of what the agent currently knows. The abducer selects a hypothesis which were it true would enable the reasoner to attain his target. He concludes from this fact that the hypothesis may be conjectured. In allowing conjecture to stand in for the knowledge he fails to have, the abducer reveals himself to be a satisficer, since an abductive solution is not a solution from knowledge. Key to the authors' analysis is the requirement that a conjectured proposition is not just what a reasoner might allow himself to assume, but a proposition he must defeasibly release as a premiss for further inferences in the domain of enquiry in which the original abduction problem has arisen. The coverage of the book is extensive, from the philosophy of science to computer science and AI, from diagnostics to the law, from historical explanation to linguistic interpretation. One of the volume's strongest contributions is its exploration of the abductive character of criminal trials, with special attention given to the standard of proof beyond a reasonable doubt. Underlying their analysis of abductive reasoning is the authors' conception of practical agency. In this approach, practical agency is dominantly a matter of the comparative modesty of an agent's cognitive agendas, together with comparatively scant resources available for their advancement. Seen in these ways, abduction has a significantly practical character, precisely because it is a form of inference that satisfices rather than maximizes its response to the agent's cognitive target. The Reach of Abduction will be necessary reading for researchers, graduate students and senior undergraduates in logic, computer science, AI, belief dynamics, argumentation theory, cognitive psychology and neuroscience, linguistics, forensic science, legal reasoning and related areas. Key features: - Reach of Abduction is fully integrated with a background logic of cognitive systems. - The most extensive coverage compared to competitive works. - Demonstrates not only that abduction is a form of ignorance preserving inference but that it is a mode of inference that is wholly rational. - Demonstrates the satisficing rather than maximizing character of abduction. - The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticated conceptual analysis and extensive logical modelling. · Reach of Abduction is fully integrated with a background logic of cognitive systems. · The most extensive coverage compared to competitive works · Demonstrates not only that abduction is a form of ignorance preserving inference but that it is a mode of inference that is wholly rational. · Demonstrates the satisficing rather than maximizing character of abduction. · The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticated conceptual analysis and extensive logical modelling.

The Logic Of Hegel S Logic

Author : John W. Burbidge
ISBN : 9781551116334
Genre : Philosophy
File Size : 75. 36 MB
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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.

Logische Untersuchungen

Author : Gottlob Frege
ISBN : 3525340311
Genre : History
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Principia Mathematica

Author : Alfred North Whitehead
ISBN : STANFORD:36105039675058
Genre : Logic, Symbolic and mathematical
File Size : 67. 36 MB
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