Download or read book From Frege to G del written by Jean van Heijenoort and published by Harvard University Press. This book was released on 2002-01-15 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time. Modern logic, heralded by Leibniz, may be said to have been initiated by Boole, De Morgan, and Jevons, but it was the publication in 1879 of Gottlob Frege’s Begriffsschrift that opened a great epoch in the history of logic by presenting, in full-fledged form, the propositional calculus and quantification theory. Frege’s book, translated in its entirety, begins the present volume. The emergence of two new fields, set theory and foundations of mathematics, on the borders of logic, mathematics, and philosophy, is depicted by the texts that follow. Peano and Dedekind illustrate the trend that led to Principia Mathematica. Burali-Forti, Cantor, Russell, Richard, and König mark the appearance of the modern paradoxes. Hilbert, Russell, and Zermelo show various ways of overcoming these paradoxes and initiate, respectively, proof theory, the theory of types, and axiomatic set theory. Skolem generalizes Löwenheim’s theorem, and he and Fraenkel amend Zermelo’s axiomatization of set theory, while von Neumann offers a somewhat different system. The controversy between Hubert and Brouwer during the twenties is presented in papers of theirs and in others by Weyl, Bernays, Ackermann, and Kolmogorov. The volume concludes with papers by Herbrand and by Gödel, including the latter’s famous incompleteness paper. Of the forty-five contributions here collected all but five are presented in extenso. Those not originally written in English have been translated with exemplary care and exactness; the translators are themselves mathematical logicians as well as skilled interpreters of sometimes obscure texts. Each paper is introduced by a note that sets it in perspective, explains its importance, and points out difficulties in interpretation. Editorial comments and footnotes are interpolated where needed, and an extensive bibliography is included.
Download or read book Frege on Language Logic and Psychology written by Eva Picardi and published by Oxford University Press. This book was released on 2022-06-30 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eva Picardi (1948-2017) was one of the most influential Italian analytic philosophers of her generation. She taught for forty years at the University of Bologna, raising three generations of students. This volume presents a selection of Picardi's essays on Frege's philosophy of logic, language, and psychology. Together, these papers provide a close look at the milieu within which Frege operated, and serve to highlight the relevance of his work for contemporary debates, particularly in the philosophy of language. One strand in Picardi's work on Frege concerns understanding and contextualizing Frege's anti-psychologism. Picardi contends that Frege was motivated by semantic considerations, much more so than by adherence to Kantian transcendentalism. Furthermore, Picardi draws on her deep knowledge of German, and the fact that she was a native speaker of Italian, to reconstruct the intricacies of Frege's relationship with other logicians of his time-both in Germany, like Kerry and Sigwart, and in Italy, like Peano and his school. Picardi's work shows how the historical and the theoretical (typically treated as separate in contemporary analytic philosophy, even in competition), complement and enrich one another.
Download or read book Methods of Geometry written by James T. Smith and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical, accessible introduction to advanced geometryExceptionally well-written and filled with historical andbibliographic notes, Methods of Geometry presents a practical andproof-oriented approach. The author develops a wide range ofsubject areas at an intermediate level and explains how theoriesthat underlie many fields of advanced mathematics ultimately leadto applications in science and engineering. Foundations, basicEuclidean geometry, and transformations are discussed in detail andapplied to study advanced plane geometry, polyhedra, isometries,similarities, and symmetry. An excellent introduction to advancedconcepts as well as a reference to techniques for use inindependent study and research, Methods of Geometry alsofeatures: Ample exercises designed to promote effective problem-solvingstrategies Insight into novel uses of Euclidean geometry More than 300 figures accompanying definitions and proofs A comprehensive and annotated bibliography Appendices reviewing vector and matrix algebra, least upperbound principle, and equivalence relations An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.
Download or read book Chapters from G del s Unfinished Book on Foundational Research in Mathematics written by Jan von Plato and published by Springer Nature. This book was released on 2022-05-06 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains English translations of Gödel's chapters on logicism and the antinomies and on the calculi of pure logic, as well as outlines for a chapter on metamathematics. It also comprises most of his reading notes. This book is a testimony to Gödel's understanding of the situation of foundational research in mathematics after his great discovery, the incompleteness theorem of 1931. It is also a source for his views on his logical predecessors, from Leibniz, Frege, and Russell to his own times. Gödel's "own book on foundations," as he called it, is essential reading for logicians and philosophers interested in foundations. Furthermore, it opens a new chapter to the life and achievement of one of the icons of 20th century science and philosophy.
Download or read book Guide to Deep Learning Basics written by Sandro Skansi and published by Springer Nature. This book was released on 2020-01-23 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This stimulating text/reference presents a philosophical exploration of the conceptual foundations of deep learning, presenting enlightening perspectives that encompass such diverse disciplines as computer science, mathematics, logic, psychology, and cognitive science. The text also highlights select topics from the fascinating history of this exciting field, including the pioneering work of Rudolf Carnap, Warren McCulloch, Walter Pitts, Bulcsú László, and Geoffrey Hinton. Topics and features: Provides a brief history of mathematical logic, and discusses the critical role of philosophy, psychology, and neuroscience in the history of AI Presents a philosophical case for the use of fuzzy logic approaches in AI Investigates the similarities and differences between the Word2vec word embedding algorithm, and the ideas of Wittgenstein and Firth on linguistics Examines how developments in machine learning provide insights into the philosophical challenge of justifying inductive inferences Debates, with reference to philosophical anthropology, whether an advanced general artificial intelligence might be considered as a living being Investigates the issue of computational complexity through deep-learning strategies for understanding AI-complete problems and developing strong AI Explores philosophical questions at the intersection of AI and transhumanism This inspirational volume will rekindle a passion for deep learning in those already experienced in coding and studying this discipline, and provide a philosophical big-picture perspective for those new to the field.
Download or read book The Nineteenth Century written by C.L. Ten and published by Routledge. This book was released on 2016-07-10 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers many of the most important philosophers and movements of the nineteenth century, including utilitarianism, positivism and pragmatism.
Download or read book Piaget s Logic written by Muriel Seltman and published by Routledge. This book was released on 2013-01-11 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The literature relating to the work of Piaget is large and still growing. Some of it is Piagetian; some of it is critical. Most of this has been directed towards his experimental methodology and the conclusions drawn from it. The justification for the present contribution lies in what the authors believe to be the special embodiment in Piagetian thought of a central theme of our time. This theme is that the only possibility of truth lies in measurability and that knowledge is not recognisable unless it satisfies this criterion. This work is concentrated in the first instance on Piaget's claims that mental structures are exclusively logical mathematical in form, especially since this part of his work has received least attention. This book was first published in 1985.
Download or read book Mathematics and Philosophy written by Daniel Parrochia and published by John Wiley & Sons. This book was released on 2018-05-24 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which studies the links between mathematics and philosophy, highlights a reversal. Initially, the (Greek) philosophers were also mathematicians (geometers). Their vision of the world stemmed from their research in this field (rational and irrational numbers, problem of duplicating the cube, trisection of the angle...). Subsequently, mathematicians freed themselves from philosophy (with Analysis, differential Calculus, Algebra, Topology, etc.), but their researches continued to inspire philosophers (Descartes, Leibniz, Hegel, Husserl, etc.). However, from a certain level of complexity, the mathematicians themselves became philosophers (a movement that begins with Wronsky and Clifford, and continues until Grothendieck).
Download or read book Logic Colloquium 76 Proceedings of a conference written by Lev D. Beklemishev and published by Elsevier. This book was released on 2009-06-15 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic Colloquium 76, Proceedings of a conference
Download or read book Frege Synthesized written by L. Haaparanta and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: cake, even though it is typically given the pride of place in expositions in Frege's semantics. As a part of this attempted reversal of emphasis, Jaakko Hintikka has also called attention to the role Frege played in convincing almost everyone that verbs for being had to be treated as multiply ambiguous between the "is" of identity, the "is" of predication, the "is" of existence, and the "is" of class-inclusion - a view that had been embraced by few major figures (if any) before Frege, with the exception of John Stuart Mill and Augustus De Morgan. Hintikka has gone on to challenge this ambiguity thesis. At the same time, Frege's role in the genesis of another major twentieth-century philosophical movement, the phenomenological one, has become an important issue. Even the translation of Frege's key term "Bedeutung" as "reference" has become controversial. The interpretation of Frege is thus thrown largely back in the melting pot. In editing this volume, we have not tried to publish the last word on Frege. Even though we may harbor such ambitions ourselves, they are not what has led to the present editorial enterprise. What we have tried to do is to bring together some of the best ongoing work on Frege. Even though the ultimate judgment on our success lies with out readers, we want to register our satisfaction with all the contributions.
Download or read book Mathematics and Logic in History and in Contemporary Thought written by Ettore Carruccio and published by Routledge. This book was released on 2017-09-29 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is not a conventional history of mathematics as such, a museum of documents and scientific curiosities. Instead, it identifies this vital science with the thought of those who constructed it and in its relation to the changing cultural context in which it evolved. Particular emphasis is placed on the philosophic and logical systems, from Aristotle onward, that provide the basis for the fusion of mathematics and logic in contemporary thought.
Download or read book B Systematic philosophy C Logic D Aesthetics E Philosophy of religion F Ethics G Psychology written by and published by . This book was released on 1905 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Giuseppe Peano between Mathematics and Logic written by Fulvia Skof and published by Springer Science & Business Media. This book was released on 2011-04-30 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the papers developing out the presentations given at the International Conference organized by the Torino Academy of Sciences and the Department of Mathematics Giuseppe Peano of the Torino University to celebrate the 150th anniversary of G. Peano's birth - one of the greatest figures in modern mathematics and logic and the most important mathematical logician in Italy - a century after the publication of Formulario Mathematico, a great attempt to systematise Mathematics in symbolic form.
Download or read book Truth in Perspective written by Concha Martínez and published by Routledge. This book was released on 2019-05-23 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1998, this volume has its origin in a meeting that was held in Santiago de Compostela University, Santiago de Compostela (Spain) in January 1996. The meeting was organized by the Department of Logic and Philosophy of Science in cooperation with the Association for Logic, Methodology and Philosophy of Science in Spain. Within analytical philosophy issues such as the definability of truth, its semantic relevance, its role in the distinction between formal and natural languages, the status of truth-bearers or in its case of truth-makers, have become a crossroads in the studies of logic, philosophy of science, philosophy of language, philosophy of mind, epistemology and ontology. Thus, in spite of what the title Truth in Perspective may suggest to the reader at first, the present volume is not only - though it is also a presentation of different theories or conceptions of truth. Most of the book presents a vision of different groups of philosophical questions in which the issue of truth appears embedded together with other related themes, from different points of view.
Download or read book Bibliography of Philosophy Psychology and Cognate Subjects written by and published by . This book was released on 1905 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Atti del convegno internazionale di storia della logica written by and published by . This book was released on 1989 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Boole Anthology written by James Gasser and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern mathematical logic would not exist without the analytical tools first developed by George Boole in The Mathematical Analysis of Logic and The Laws of Thought. The influence of the Boolean school on the development of logic, always recognised but long underestimated, has recently become a major research topic. This collection is the first anthology of works on Boole. It contains two works published in 1865, the year of Boole's death, but never reprinted, as well as several classic studies of recent decades and ten original contributions appearing here for the first time. From the programme of the English Algebraic School to Boole's use of operator methods, from the problem of interpretability to that of psychologism, a full range of issues is covered. The Boole Anthology is indispensable to Boole studies and will remain so for years to come.
