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Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 0080954731
Category : Computers
Languages : en
Pages : 525
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Book Description
Intuitionism and Proof Theory: Proceedings of the Summer Conference at Buffalo N.Y. 1968
Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 0080954731
Category : Computers
Languages : en
Pages : 525
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Book Description
Intuitionism and Proof Theory: Proceedings of the Summer Conference at Buffalo N.Y. 1968
Author: Jacques Dubucs
Publisher: Springer
ISBN: 9401792178
Category : Philosophy
Languages : en
Pages : 223
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Book Description
Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. The authors argue that even though constructivists have largely shed Brouwer’s solipsistic attitude to logic, there remain points of disagreement to this day. Focusing on the growing pains computability experienced as it was forced to address the demands of rapidly expanding applications, the content maps the developments following Turing’s ground-breaking linkage of computation and the machine, the resulting birth of complexity theory, the innovations of Kolmogorov complexity and resolving the dissonances between proof theoretical semantics and canonical proof feasibility. Finally, it explores one of the most fundamental questions concerning the interface between constructivity and computability: whether the theory of recursive functions is needed for a rigorous development of constructive mathematics. This volume contributes to the unity of science by overcoming disunities rather than offering an overarching framework. It posits that computability’s adoption of a classical, ontological point of view kept these imperatives separated. In studying the relationship between the two, it is a vital step forward in overcoming the disagreements and misunderstandings which stand in the way of a unifying view of logic.
Author: Joseph M. Scandura
Publisher: Routledge
ISBN: 1351839403
Category : Psychology
Languages : en
Pages : 340
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Book Description
Originally published in 1976, this title is an edited volume and reflects the major approaches being taken in structural learning at the time. Chapter 1 deals with the basic question of whether competence (knowledge) should be characterized in terms of rules (automata), on the one hand, or associations on the other. The bulk of Chapter 2 is devoted to a series of earlier experiments on rule learning by the editor and his associates. The two contributions in Chapter 3 deal with graph theoretical models. Piagetian models constitute the subject of Chapter 4. Chapter 5 deals with attempts to stimulate human behaviour with a computer. Chapter 6 ranges over a wide variety of competence models, with particular reference to logic and mathematics. In Chapter 7 the editor proposes a new theory of structural learning, together with some empirical results.
Author: S. Barry Cooper
Publisher: Cambridge University Press
ISBN: 0521635500
Category : Computers
Languages : en
Pages : 433
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Book Description
Second of two volumes providing a comprehensive guide to the current state of mathematical logic.
Author: Wolfgang Bibel
Publisher: Springer Science & Business Media
ISBN: 9783540100096
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Author: Ajit Sinha
Publisher: Springer Nature
ISBN: 303047206X
Category : Business & Economics
Languages : en
Pages : 611
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Book Description
This book presents a substantial collection of essays from a wide range of well respected scholars addressing several aspects of Piero Sraffa’s economics in light of continuing controversies over the interpretation that should be placed on his work. It moves beyond extant scholarship with an added emphasis on the philosophical dimension of Sraffa’s seminal work, Production of Commodities by Means of Commodities. Contributors probe new ways of thinking about the political economy of Sraffa and in doing so, alongside the comments to each contribution by other scholars, provide a cutting edge debate and discussion on non-mainstream economic theory. This book will be of interest to academics and advanced graduate students in economics, with additional interest from scholars in philosophy and the methodology of science.
Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 0080954944
Category : Computers
Languages : en
Pages : 383
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Book Description
Sets and Classes on The Work by Paul Bernays
Author: Neil Jones
Publisher: Springer Science & Business Media
ISBN: 9783540579359
Category : Mathematics
Languages : en
Pages : 292
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Book Description
This volume contains 15 papers from research areas where Japanese theoretical computer science is particularly strong. Many are about logic, and its realization and applications to computer science; others concern synthesis, transformation and implementation of programming languages, and complexity and coding theory. Not coincidentally, all the authors are either former students or close colleagues of Satoru Takasu, professor and director at the Research Institute of Mathematical Sciences at the University of Kyoto. The purpose of this volume is to celebrate Professor Takasu's influence on theoretical computer science in Japan and worldwide by his research, his philosophy, and his advising of students. The breadth, depth and quality of the papers are characteristic of his interests and activities.
Author:
Publisher: Elsevier
ISBN: 008046663X
Category : Mathematics
Languages : en
Pages : 1219
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Book Description
The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter
Author: Wilfried Sieg
Publisher: Oxford University Press
ISBN: 0199707154
Category : Philosophy
Languages : en
Pages : 452
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Book Description
Hilbert's Programs & Beyond presents the foundational work of David Hilbert in a sequence of thematically organized essays. They first trace the roots of Hilbert's work to the radical transformation of mathematics in the 19th century and bring out his pivotal role in creating mathematical logic and proof theory. They then analyze techniques and results of "classical" proof theory as well as their dramatic expansion in modern proof theory. This intellectual experience finally opens horizons for reflection on the nature of mathematics in the 21st century: Sieg articulates his position of reductive structuralism and explores mathematical capacities via computational models.
