The Rise Of Modern Logic From Leibniz To Frege

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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.

Aristotle S Organon In Old And New Logic

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Author : Colin Guthrie King
language : en
Publisher: Bloomsbury Publishing
Release Date : 2025-01-23

Aristotle S Organon In Old And New Logic written by Colin Guthrie King and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-23 with Philosophy categories.

Aristotle's Organon in Old and New Logic 1800–1950 explores the reception and interpretation of Aristotle's logic over the last two centuries. The volume covers seminal works during this period by logicians, historians of logic, and historians of philosophy, including John Lloyd Akrill, Francesco Barone, Günther Patzig, Enrico Berti, and Mario Mignucci. Contributors consider the reception of the Organon in old logic and chart the appearance of formal approaches to logic beginning with Boole. This in-depth study of Aristotelianism also covers logic in Kant and Hegel, alongside the problems and projects of interpreting Aristotle in the new logic after Boole and Frege. The background of modern debates concerning induction and abduction provides further insight into Aristotelian logic during the period. By filling gaps in our understanding of Aristotelian logic, this book provides a fundamental missing link in 21st century studies of the history of Aristotelianism. It brings together scholars of both ancient and modern logic to understand the interpretation of ancient logic before and after the development of the modern, algebraic approach to logic.

The Oxford Handbook Of German Philosophy In The Nineteenth Century

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Author : Michael N. Forster
language : en
Publisher: OUP Oxford
Release Date : 2015-02-05

The Oxford Handbook Of German Philosophy In The Nineteenth Century written by Michael N. Forster and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-05 with Philosophy categories.

The Oxford Handbook of German Philosophy in the Nineteenth Century is the first collective critical study of this important period in intellectual history. The volume is divided into four parts. The first part explores individual philosophers, including Fichte, Hegel, Schopenhauer, Marx, and Nietzsche, amongst other great thinkers of the period. The second addresses key philosophical movements: Idealism, Romanticism, Neo-Kantianism, and Existentialism. The essays in the third part engage with different areas of philosophy that received particular attention at this time, including philosophy of nature, philosophy of mind, philosophy of language, philosophy of history, and hermeneutics. Finally, the contributors turn to discuss central philosophical topics, from skepticism to mat-erialism, from dialectics to ideas of historical and cultural Otherness, and from the reception of antiquity to atheism. Written by a team of leading experts, this Handbook will be an essential resource for anyone working in the area and will lead the direction of future research.

From Frege To G Del

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

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 Mathematics categories.

Gathered together here 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, which concludes with papers by Herbrand and by Gödel.

John Venn

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Author : Lukas M. Verburgt
language : en
Publisher: University of Chicago Press
Release Date : 2022-04-08

John Venn written by Lukas M. Verburgt and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-08 with Biography & Autobiography categories.

The first comprehensive history of John Venn’s life and work. John Venn (1834–1923) is remembered today as the inventor of the famous Venn diagram. The postmortem fame of the diagram has until now eclipsed Venn’s own status as one of the most accomplished logicians of his day. Praised by John Stuart Mill as a “highly successful thinker” with much “power of original thought,” Venn had a profound influence on nineteenth-century scientists and philosophers, ranging from Mill and Francis Galton to Lewis Carroll and Charles Sanders Peirce. Venn was heir to a clerical Evangelical dynasty, but religious doubts led him to resign Holy Orders and instead focus on an academic career. He wrote influential textbooks on probability theory and logic, became a fellow of the Royal Society, and advocated alongside Henry Sidgwick for educational reform, including that of women’s higher education. Moreover, through his students, a direct line can be traced from Venn to the early analytic philosophy of G. E. Moore and Bertrand Russell, and family ties connect him to the famous Bloomsbury group. This essential book takes readers on Venn’s journey from Evangelical son to Cambridge don to explore his life and work in context. Drawing on Venn’s key writings and correspondence, published and unpublished, Lukas M. Verburgt unearths the legacy of the logician’s wide-ranging thinking while offering perspective on broader themes in religion, science, and the university in Victorian Britain. The rich picture that emerges of Venn, the person, is of a man with many sympathies—sometimes mutually reinforcing and at other times outwardly and inwardly contradictory.

Probability Logics

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Author : Zoran Ognjanović
language : en
Publisher: Springer
Release Date : 2016-10-24

Probability Logics written by Zoran Ognjanović and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-24 with Mathematics categories.

The aim of this book is to provide an introduction to probability logic-based formalization of uncertain reasoning. The authors' primary interest is mathematical techniques for infinitary probability logics used to obtain results about proof-theoretical and model-theoretical issues such as axiomatizations, completeness, compactness, and decidability, including solutions of some problems from the literature. An extensive bibliography is provided to point to related work, and this book may serve as a basis for further research projects, as a reference for researchers using probability logic, and also as a textbook for graduate courses in logic.

The Routledge Handbook Of Metaphysical Grounding

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Author : Michael J. Raven
language : en
Publisher: Routledge
Release Date : 2020-05-04

The Routledge Handbook Of Metaphysical Grounding written by Michael J. Raven and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-04 with Philosophy categories.

Some of philosophy’s biggest questions, both historically and today, are in-virtue-of questions: In virtue of what is an action right or wrong? In virtue of what am I the same person my mother bore? In virtue of what is an artwork beautiful? Philosophers attempt to answer many of these types of in-virtue-of questions, but philosophers are also increasingly focusing on what an in-virtue-of question is in the first place. Many assume, at least as a working hypothesis, that in-virtue-of questions involve a distinctively metaphysical kind of determinative explanation called “ground.” This Handbook surveys the state of the art on ground as well as its connections and applications to other topics. The central issues of ground are discussed in 37 chapters, all written exclusively for this volume by a wide range of leading experts. The chapters are organized into the following sections: I. History II. Explanation and Determination III. Logic and Structure IV. Connections V. Applications Introductions at the start of each section provide an overview of the section’s contents, and a list of Related Topics at the end of each chapter points readers to other germane areas throughout the volume. The resulting volume is accessible enough for advanced students and informative enough for researchers. It is essential reading for anyone hoping to get clearer on what the biggest questions of philosophy are really asking.

Logic In Question

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Author : Jean-Yves Béziau
language : en
Publisher: Springer Nature
Release Date : 2023-01-11

Logic In Question written by Jean-Yves Béziau and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-11 with Mathematics categories.

This contributed volume collects papers related to the Logic in Question workshop, which has taken place annually at Sorbonne University in Paris since 2011. Each year, the workshop brings together historians, philosophers, mathematicians, linguists, and computer scientists to explore questions related to the nature of logic and how it has developed over the years. As a result, chapter authors provide a thorough, interdisciplinary exploration of topics that have been studied in the workshop. Organized into three sections, the first part of the book focuses on historical questions related to logic, the second explores philosophical questions, and the third section is dedicated to mathematical discussions. Specific topics include: • logic and analogy• Chinese logic• nineteenth century British logic (in particular Boole and Lewis Carroll)• logical diagrams • the place and value of logic in Louis Couturat’s philosophical thinking• contributions of logical analysis for mathematics education• the exceptionality of logic• the logical expressive power of natural languages• the unification of mathematics via topos theory Logic in Question will appeal to pure logicians, historians of logic, philosophers, linguists, and other researchers interested in the history of logic, making this volume a unique and valuable contribution to the field.

The Relevance Of Romanticism

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Author : Dalia Nassar
language : en
Publisher: Oxford University Press
Release Date : 2014-03-03

The Relevance Of Romanticism written by Dalia Nassar and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-03 with Philosophy categories.

Since the early 1990s, there has been a resurgence of interest in philosophy between Kant and Hegel, and in early German romanticism in particular. Philosophers have come to recognize that, in spite of significant differences between the contemporary and romantic contexts, romanticism continues to persist, and the questions which the romantics raised remain relevant today. The Relevance of Romanticism: Essays on Early German Romantic Philosophy is the first collection of essays that offers an in-depth analysis of the reasons why philosophers are (and should be) concerned with romanticism. Through historical and systematic reconstructions, the collection offers a deeper understanding and more encompassing picture of romanticism as a philosophical movement than has been presented thus far, and explicates the role that romanticism plays -- or can play -- in contemporary philosophical debates. The volume includes essays by a number of preeminent international scholars and philosophers -- Karl Ameriks, Frederick Beiser, Richard Eldridge, Michael Forster, Manfred Frank, Jane Kneller, and Paul Redding -- who discuss the nature of philosophical romanticism and its potential to address contemporary questions and concerns. Through contributions from established and emerging philosophers, discussing key romantic themes and concerns, the volume highlights the diversity both within romantic thought and its contemporary reception. Part One consists of the first published encounter between Manfred Frank and Frederick Beiser, in which the two major scholars directly discuss their vastly differing interpretations of philosophical romanticism. Part Two draws significant connections between romantic conceptions of history, sociability, hermeneutics and education and explores the ways in which these views can illuminate pressing questions in contemporary social-political philosophy and theories of interpretation. Part Three consists in some of the most innovative takes on romantic aesthetics, which seek to bring romantic thought into dialogue, with, for instance, contemporary Analytic aesthetics and theories of cognition/mind. The final part offers one of the few rigorous engagements with romantic conceptions science, and demonstrates ways in which the romantic views of nature, scientific experimentation and mathematics need not be relegated to historical curiosities.