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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.

Begriffsschrift


Author : Gottlob Frege
language : en
Publisher: Cambridge, Mass. : Harvard University Press
Release Date : 1967

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This volume, a shortened edition of Mr. van Heijenoort's internationally acclaimed From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 (HUP 1967), makes available in English the two most important works in the growth of modern mathematical logic. Heralded by Leibniz, modern logic had its beginnings in the work of Boole, DeMorgan, and Jevons, but the 1879 publication of Gottlob Frege's Begriffsschrift opened a great epoch in the history of logic with the full-form presentation of the propositional calculus and quantification theory. Frege and Gödel: Two Fundamental Texts in Mathematical Logic begins with this short book, which ushered in the classical age of mathematical logic by outlining the construction of a system of logical symbolism. The volume concludes with Gödel's famous incompleteness paper of 1931, which changed the development of logic and the foundations of mathematics by revealing the intrinsic limitations of formal systems, and brought to an end the classical phase. Mr. van Heijenoort has provided a new introduction which sets the Frege and Gödel pieces in perspective in the development of modern logic and points out difficulties in interpretation. Editorial comments, footnotes, and bibliographic information offer additional explanatory material.

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.

From Frege To G Del


Author : Jean Van Heijenoort
language : en
Publisher: Harvard University Press
Release Date : 1967

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Download From Frege To G Del written by Jean Van Heijenoort and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Philosophy categories.


Gathered together in this book are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege's "Begriffsschrift"--which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory--begins the volume. The texts that follow depict the emergence of set theory and foundations of mathematics, two new fields on the borders of logic, mathematics, and philosophy. Essays trace the trends that led to "Principia mathematica," the appearance of modern paradoxes, and topics including proof theory, the theory of types, axiomatic set theory, and Lowenheim's theorem. The volume concludes with papers by Herbrand and by Godel, including the latter's famous incompleteness paper."

Principia Mathematica To 56


Author : Alfred North Whitehead
language : en
Publisher: Cambridge University Press
Release Date : 1997-09-11

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The great three-volume Principia Mathematica (CUP 1927) is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part I (in which the logical properties of propositions, propositional functions, classes and relations are established); section A of Part II (dealing with unit classes and couples); and Appendices A and C (which give further developments of the argument on the theory of deduction and truth functions).

The Development Of Modern Logic


Author : Leila Haaparanta
language : en
Publisher: OUP USA
Release Date : 2009-06-18

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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.