The Evolution of Logic
The Evolution of Logic

Author: W. D. Hart

Publisher: Cambridge University Press

Published: 2010-08-23

Total Pages:

ISBN-13: 1139491202

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Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post's problem, and Morley's theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.

Studies on the History of Logic
Studies on the History of Logic

Author: Ignacio Angelelli

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-03-09

Total Pages: 436

ISBN-13: 3110903822

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Studies in the History of Logic
Studies in the History of Logic

Author: Nicholas Rescher

Publisher: Walter de Gruyter

Published: 2013-05-02

Total Pages: 197

ISBN-13: 3110326442

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It must be acknowledged that the essays presented here do not constitute a systematic account of any sort but represent occasional forays. Some deal with matters that happened to evoke Rescher’s interest, others grew out of a chance encounter with a text he deemed to be of particular value. Throughout, challenges of the work itself more than compensated the author’s efforts. Logic has always been of crucially important concern to philosophers. Rescher’s own involvement with the history of logic goes back to his work on Leibniz in the 1950’s (represented by Chapter 8 of the present book). Thereafter, during the 1960’s he devoted considerable effort to the contributions of the medieval logicians of the Arabic-using world (here represented in Chapters 2-6). Moreover, Rescher have from time to time returned to the area to look at some aspects of the more recent scene, as Chapters 8-9 illustrate. In some instances the present essays have been overtaken by subsequent events-events which in fact helped to promote. This is true in particular in chapter 6’s work on Arabic work regarding temporal modalities, which was instrumental in evoking the important contributions of Tony Street of Cambridge University.

Essays in the Philosophy and History of Logic and Mathematics
Essays in the Philosophy and History of Logic and Mathematics

Author: Roman Murawski

Publisher: BRILL

Published: 2015-06-29

Total Pages: 327

ISBN-13: 9042030917

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The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields.

Studies in Logic and Probability
Studies in Logic and Probability

Author: George Boole

Publisher: Courier Corporation

Published: 2012-01-01

Total Pages: 514

ISBN-13: 0486488268

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Authoritative account of the development of Boole's ideas in logic and probability theory ranges from The Mathematical Analysis of Logic to the end of his career. The Laws of Thought formed the most systematic statement of Boole's theories; this volume contains incomplete studies intended for a follow-up volume. 1952 edition.

The Evolution of Reason
The Evolution of Reason

Author: William S. Cooper

Publisher: Cambridge University Press

Published: 2001

Total Pages: 242

ISBN-13: 9780521540254

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The formal systems of logic have ordinarily been regarded as independent of biology, but recent developments in evolutionary theory suggest that biology and logic may be intimately interrelated. In this book, William Cooper outlines a theory of rationality in which logical law emerges as an intrinsic aspect of evolutionary biology. This biological perspective on logic, though at present unorthodox, could change traditional ideas about the reasoning process. Cooper examines the connections between logic and evolutionary biology and illustrates how logical rules are derived directly from evolutionary principles, and therefore have no independent status of their own. Laws of decision theory, utility theory, induction, and deduction are reinterpreted as natural consequences of evolutionary processes. Cooper's connection of logical law to evolutionary theory ultimately results in a unified foundation for an evolutionary science of reason. It will be of interest to professionals and students of philosophy of science, logic, evolutionary theory, and cognitive science.

Language, Logic, and Mathematics in Schopenhauer
Language, Logic, and Mathematics in Schopenhauer

Author: Jens Lemanski

Publisher: Springer Nature

Published: 2020-06-08

Total Pages: 318

ISBN-13: 3030330907

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The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study.

Leibniz and the Structure of Sciences
Leibniz and the Structure of Sciences

Author: Vincenzo De Risi

Publisher: Springer Nature

Published: 2020-01-01

Total Pages: 304

ISBN-13: 3030255727

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The book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern mathematical tools, and compare Leibniz’s results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz’s work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz’s researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.

The Development of Logic
The Development of Logic

Author: William Calvert Kneale

Publisher:

Published: 1978

Total Pages: 783

ISBN-13:

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This book traces the development of formal logic from its origins in ancient Greece to the present day. The authors first discuss the work of logicians from Aristotle to Frege, showing how they were influenced by the philosophical or mathematical ideas of their time.