In the Light of Logic

Author: Solomon Feferman

Publisher: Oxford University Press on Demand

ISBN: 0195080300

Category: Philosophy

Page: 340

View: 3017


Solomon Feferman is one of the leading figures in logic and the foundations of mathematics. This volume brings together a selection of his most important essays dealing with the light which results in modern logic cast on significant problems in the foundations of mathematics. It is essential reading for anyone interested in these subjects. Feferman presents key issues in the work of Cantor, Hilbert, Weyl, and Godel among others, and explains how they are dealtwith by proof theory and other parts of logic. A number of the papers appeared originally in obscure places and are not well-known, and others are published here for the first time. All of the material has been revised and annotated to bring it up to date.

The Provenance of Pure Reason

Essays in the Philosophy of Mathematics and Its History

Author: William W. Tait,William Tait

Publisher: Oxford University Press, USA

ISBN: 9780195141924

Category: Mathematics

Page: 332

View: 9375


William Tait is one of the most distinguished philosophers of mathematics of the last fifty years. This volume collects his most important published philosophical papers from the 1980's to the present. The articles cover a wide range of issues in the foundations and philosophy of mathematics, including some on historical figures ranging from Plato to Gödel. Tait's main contributions were initially in proof theory and constructive mathematics, later moving on to more philosophical subjects including finitism and skepticism about mathematics. This collection, presented as a whole, reveals the underlying unity of Tait's work. The volume includes an introduction in which Tait reflects more generally on the evolution of his point of view, as well as an appendix and added endnotes in which he gives some interesting background to the original essays. This is an important collection of the work of one of the most eminent philosophers of mathematics in this generation.

Philosophy of Probability

Author: Jacques Dubucs

Publisher: Springer Science & Business Media

ISBN: 9780792323853

Category: Philosophy

Page: 296

View: 2019


Philosophy of Probability provides a comprehensive introduction to theoretical issues that occupy a central position in disciplines ranging from philosophy of mind and epistemology to cognitive science, decision theory and artificial intelligence. Some contributions shed new light on the standard conceptions of probability (Bayesianism, logical and computational theories); others offer detailed analyses of two important topics in the field of cognitive science: the meaning and the representation of (partial) belief, and the management of uncertainty. The authors of this well-balanced account are philosophers as well as computer scientists (among them, L.J. Cohen, D. Miller, P. Gärdenfors, J. Vickers, D. Dubois and H. Prade). This multidisciplinary approach to probability is designed to illuminate the intricacies of the problems in the domain of cognitive inquiry. No one interested in epistemology or aritificial intelligence will want to miss it.

Logic, Epistemology, and the Unity of Science

Author: Shahid Rahman,John Symons,Dov M. Gabbay,jean paul van bendegem

Publisher: Springer Science & Business Media

ISBN: 1402028083

Category: Philosophy

Page: 626

View: 1454


The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.

Der Wiener Kreis in Ungarn

The Vienna Circle in Hungary

Author: András Máté,Miklós Rédei,Friedrich Stadler

Publisher: Springer-Verlag

ISBN: 3709101778

Category: Philosophy

Page: 304

View: 2402


Der Einfluss des Wiener Kreises zeigt sich bis heute auf allen Gebieten der Philosophie. Mit der erzwungenen Emigration der meisten Mitglieder wurde diese logisch-empiristische Tradition in Mitteleuropa jedoch vorerst unterbrochen. Erst als der logische Empirismus nach dem 2. Weltkrieg in der angelsächsischen Welt zu einer wichtigen Denkrichtung geworden war, wirkte er von dort zurück nach Mitteleuropa. In den Beiträgen analysieren und bewerten namhafte Experten die Auswirkungen des Logischen Empirismus auf die Entwicklung der Philosophie in Ungarn.

Information and Computation

Essays on Scientific and Philosophical Understanding of Foundations of Information and Computation

Author: Gordana Dodig Crnkovic,Mark Burgin

Publisher: World Scientific

ISBN: 9814295477

Category: Computers

Page: 496

View: 8482


This volume provides a cutting-edge view of the world's leading authorities in fields where information and computation play a central role.

Introduction to Formal Philosophy

Author: Sven Ove Hansson,Vincent F. Hendricks

Publisher: Springer

ISBN: 9783319774336

Category: Philosophy

Page: 733

View: 8188


This Undergraduate Textbook introduces key methods and examines the major areas of philosophy in which formal methods play pivotal roles. Coverage begins with a thorough introduction to formalization and to the advantages and pitfalls of formal methods in philosophy. The ensuing chapters show how to use formal methods in a wide range of areas. Throughout, the contributors clarify the relationships and interdependencies between formal and informal notions and constructions. Their main focus is to show how formal treatments of philosophical problems may help us understand them better. Formal methods can be used to solve problems but also to express new philosophical problems that would never have seen the light of day without the expressive power of the formal apparatus. ​Formal philosophy merges work in different areas of philosophy as well as logic, mathematics, computer science, linguistics, physics, psychology, biology, economics, political theory, and sociology. This title offers an accessible introduction to this new interdisciplinary research area to a wide academic audience.


Turing, Gödel, Church, and Beyond

Author: B. Jack Copeland,Carl J. Posy,Oron Shagrir

Publisher: MIT Press

ISBN: 0262018993

Category: Computers

Page: 362

View: 6564


Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments.

Vision and Mind

Selected Readings in the Philosophy of Perception

Author: Alva Noë,Evan Thompson

Publisher: MIT Press

ISBN: 9780262640473

Category: Philosophy

Page: 627

View: 6673


A collection of works, many of them classics, on the orthodox view of visual perception.

Unified Science

The Vienna Circle Monograph Series originally edited by Otto Neurath, now in an English edition

Author: B.F. McGuinness

Publisher: Springer Science & Business Media

ISBN: 9400938659

Category: Science

Page: 306

View: 9621


a priori, and what is more, to a rejection based ultimately on a posteriori findings; in other words, the "pure" science of nature in Kant's sense of the term had proved to be, not only not pure, but even false. As for logic and mathematics, the decisive works of Frege, Russell, and White head suggested two conclusions: first, that it was possible to construct mathematics on the basis of logic (logicism), and secondly, that logical propositions had an irrevocably analytic status. But within the frame work of logicism, the status of logical propositions is passed on to mathematical ones, and mathematical propositions are therefore also conceived of as analytic. All this creates a situation where the existential presupposition contained in the Kantian question about the possibility of judgements that are both synthetic and a priori must, it seems, be rejected as false. But to drop this presupposition is, at the same time, to strike at the very core of Kant's programme of putting the natural sciences on a philosophical foundation. The failure of the modern attempt to do so suggests at the same time a reversal of the relationship between philosophy and the individual sciences: it is not the task of philosophy to meddle with the foundations of the individual sciences; being the less successful discipline, its task is rather to seek guidance from the principles of rationality operative in the individual sciences.


Readings in the Philosophy of Mental Representation

Author: S. Silvers

Publisher: Springer Science & Business Media

ISBN: 9400926499

Category: Philosophy

Page: 417

View: 5657


This collection of papers on issues in the theory of mental representation expresses a diversity of recent reflections on the idea that C. D. Broad so aptly characterized in the title of his book Mind and the World Order. An important impetus in the project of organizing this work were the discussions I had with Keith Lehrer while I was a Visiting Scholar in the department of Philosophy at the University of Arizona. His encouragement and friendship were of great value to me and I wish to express my thanks to him here. A word of thanks too for Mike Harnish who casually suggested the title Rerepresentation. I wish to express my thanks to Hans Schuurmans of the Computer Center at Tilburg University for his patient and cheerful assistance in preparing the manuscript. Professor J. Verster of the University of Groningen kindly provided the plates for the Ames Room figures. Thieu Kuys helped not only with the texts but also relieved me of chores so that I could devote more time to meeting deadlines. Barry Mildner had a major role in the text preparation using his skills and initiative in solving what seemed like endless technical problems. My deepest thanks are reserved for Anti Sax whose contribution to the project amount to a co-editorship of this volume. She participated in every phase of its development with valuable suggestions, prepared the indexes, and worked tirelessly to its completion.

Logical Foundations of Computer Science

International Symposium, LFCS 2009, Deerfield Beach, FL, USA, January 3-6, 2009, Proceedings

Author: Sergei Artemov,Anil Nerode

Publisher: Springer Science & Business Media

ISBN: 3540926860

Category: Computers

Page: 469

View: 5889


The Symposium on Logical Foundations of Computer Science series provides a forum for the fast-growing body of work in the logical foundations of computer science, e.g., those areas of fundamental theoretical logic related to computer science. The LFCS series began with “Logic at Botik,” Pereslavl-Zalessky,1989, which was co-organized by Albert R. Meyer (MIT) and Michael Taitslin (Tver). After that, organization passed to Anil Nerode. Currently LFCS is governed by a Steering Committee consisting of Anil Nerode (General Chair), Stephen Cook, Dirk van Dalen, Yuri Matiyasevich, John McCarthy, J. Alan Robinson, Gerald Sacks, and Dana Scott. The 2009 Symposium on Logical Foundations of Computer Science (LFCS 2009) took place in Howard Johnson Plaza Resort, Deer?eld Beach, Florida, USA, during January 3–6. This volume contains the extended abstracts of talks selected by the Program Committee for presentation at LFCS 2009. The scope of the symposium is broad and contains constructive mathematics and type theory; automata and automatic structures; computability and r- domness; logical foundations of programming; logical aspects of computational complexity; logic programmingand constraints;automated deduction and int- active theorem proving; logical methods in protocol and program veri?cation; logical methods in program speci?cation and extraction; domain theory l- ics; logical foundations of database theory; equational logic and term rewriting; lambda andcombinatorycalculi;categoricallogicandtopologicalsemantics;l- ear logic; epistemic and temporal logics; intelligent and multiple agent system logics; logics of proof and justi?cation; nonmonotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics;


Author: Kathleen Akins

Publisher: Oxford University Press

ISBN: 9780195359169

Category: Medical

Page: 352

View: 7202


Vancouver Studies in Cognitive Science is an interdisciplinary series bringing together topics of interest to psychologists, philosophers, cognitive scientists, and linguists. Each volume is based on conferences organized at Simon Fraser University, with chapters added from nonparticipants to ensure balanced and adequate coverage from the topic under study. The fifth volume examines the role of perception in cognitive psychology in light of recent events. Despite the wide scope of the intended topic, however, papers presented at the conference and solicited for this text all focus on fundamental questions about the nature of visual perception, specifically concerning the form and content of visual representations.

Computing and Philosophy

Selected Papers from IACAP 2014

Author: Vincent C. Müller

Publisher: Springer

ISBN: 3319232916

Category: Philosophy

Page: 282

View: 737


This volume offers very selected papers from the 2014 conference of the “International Association for Computing and Philosophy” (IACAP) - a conference tradition of 28 years. The theme of the papers is the two-way relation between computing technologies and philosophical questions: Computing technologies both raise new philosophical questions, and shed light on traditional philosophical problems. The chapters cover: 1) philosophy of computing, 2) philosophy of computer science & discovery, 3) philosophy of cognition & intelligence, 4) computing & society, and 5) ethics of computation.

Descartes' Dream

The World According to Mathematics

Author: Philip J. Davis,Reuben Hersh

Publisher: Courier Corporation

ISBN: 0486442527

Category: Mathematics

Page: 321

View: 9482


These provocative essays take a modern look at the 17th-century thinker's dream, examining the influences of mathematics on society, particularly in light of technological advances. They survey the conditions that elicit the application of mathematic principles; the applications' effectiveness; and how applied mathematics transform perceptions of reality. 1987 edition.

The Cognitive Science of Science

Explanation, Discovery, and Conceptual Change

Author: Paul Thagard

Publisher: MIT Press

ISBN: 0262300974

Category: Science

Page: 384

View: 4451


Many disciplines, including philosophy, history, and sociology, have attempted to make sense of how science works. In this book, Paul Thagard examines scientific development from the interdisciplinary perspective of cognitive science. Cognitive science combines insights from researchers in many fields: philosophers analyze historical cases, psychologists carry out behavioral experiments, neuroscientists perform brain scans, and computer modelers write programs that simulate thought processes. Thagard develops cognitive perspectives on the nature of explanation, mental models, theory choice, and resistance to scientific change, considering disbelief in climate change as a case study. He presents a series of studies that describe the psychological and neural processes that have led to breakthroughs in science, medicine, and technology. He shows how discoveries of new theories and explanations lead to conceptual change, with examples from biology, psychology, and medicine. Finally, he shows how the cognitive science of science can integrate descriptive and normative concerns; and he considers the neural underpinnings of certain scientific concepts.

The Number Systems

Foundations of Algebra and Analysis

Author: Solomon Feferman

Publisher: American Mathematical Soc.

ISBN: 0821829157

Category: Mathematics

Page: 418

View: 4438


The subject of this book is the successive construction and development of the basic number systems of mathematics: positive integers, integers, rational numbers, real numbers, and complex numbers. This second edition expands upon the list of suggestions for further reading in Appendix III. From the Preface: ``The present book basically takes for granted the non-constructive set-theoretical foundation of mathematics, which is tacitly if not explicitly accepted by most working mathematicians but which I have since come to reject. Still, whatever one's foundational views, students must be trained in this approach in order to understand modern mathematics. Moreover, most of the material of the present book can be modified so as to be acceptable under alternative constructive and semi-constructive viewpoints, as has been demonstrated in more advanced texts and research articles.''

Dag Prawitz on Proofs and Meaning

Author: Heinrich Wansing

Publisher: Springer

ISBN: 3319110411

Category: Philosophy

Page: 458

View: 2729


This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.