Logical Approaches to Computational Barriers

Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006, Proceedings
Author: Arnold Beckmann,Ulrich Berger,Benedikt Lwe,John V. Tucker
Publisher: Springer Science & Business Media
ISBN: 3540354662
Category: Computers
Page: 608
View: 6586

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This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, in June/July 2006. The 31 revised full papers presented together with 30 invited papers were carefully reviewed and selected from about 80 submissions. Among them are papers corresponding to 8 plenary talks and papers of 6 special sessions entitled proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and G??del centenary: G??del's legacy for computability.

Logic, Mathematics, Philosophy, Vintage Enthusiasms

Essays in Honour of John L. Bell
Author: David DeVidi,Michael Hallett,Peter Clark
Publisher: Springer Science & Business Media
ISBN: 9789400702141
Category: Philosophy
Page: 486
View: 2982

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The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.

Constructivism in Mathematics


Author: A.S. Troelstra,D. van Dalen
Publisher: Elsevier
ISBN: 0080570887
Category: Mathematics
Page: 355
View: 8081

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These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature.

Kurt Gödel

Wahrheit & Beweisbarkeit
Author: Kurt Gödel,Eckehart Köhler,Bernd Buldt
Publisher: N.A
ISBN: 9783209038340
Category: Logicians
Page: 448
View: 7664

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Computable Foundations for Economics


Author: K. Vela Velupillai
Publisher: Routledge
ISBN: 1134253370
Category: Business & Economics
Page: 512
View: 321

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Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode completely non-algorithmic, which means it is numerically meaningless. The book provides a systematic attempt to dissect and expose the non-algorithmic content of orthodox mathematical economics and game theory and suggests a reformalization on the basis of a strictly rigorous algorithmic mathematics. This removes the current schizophrenia in mathematical economics and game theory, where theory is entirely divorced from algorithmic applicability – for experimental and computational exercises. The chapters demonstrate the uncomputability and non-constructivity of core areas of general equilibrium theory, game theory and recursive macroeconomics. The book also provides a fresh look at the kind of behavioural economics that lies behind Herbert Simon’s work, and resurrects a role for the noble classical traditions of induction and verification, viewed and formalised, now, algorithmically. It will therefore be of particular interest to postgraduate students and researchers in algorithmic economics, game theory and classical behavioural economics.

In Defense of Intuitions

A New Rationalist Manifesto
Author: A. Chapman,A. Ellis,R. Hanna,T. Hildebrand,H. Pickford
Publisher: Springer
ISBN: 1137347953
Category: Philosophy
Page: 427
View: 2657

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A reply to contemporary skepticism about intuitions and a priori knowledge, and a defense of neo-rationalism from a contemporary Kantian standpoint, focusing on the theory of rational intuitions and on solving the two core problems of justifying and explaining them.

The Adventure of Reason

Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940
Author: Paolo Mancosu
Publisher: OUP Oxford
ISBN: 0191021997
Category: Philosophy
Page: 632
View: 2408

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Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.

Internal Logic

Foundations of Mathematics from Kronecker to Hilbert
Author: Y. Gauthier
Publisher: Springer Science & Business Media
ISBN: 9401700834
Category: Mathematics
Page: 251
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Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer. The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.

Foundation of Software Science and Computation Structures

Third International Conference, FOSSACS 2000 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2000 Berlin, Germany, March 25 - April 2, 2000 Proceedings
Author: Jerzy Tiuryn
Publisher: Springer
ISBN: N.A
Category: Computer software
Page: 391
View: 4324

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This volume constitutes the refereed proceedings of the Third International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2000, held as part of ETAPS 2000 in Berlin, Germany in March/April 2000. The 25 revised full papers presented were carefully reviewed and selected from a total of 68 submissions. Among the topics covered are rewriting, pi-calculus, lambda-calculus, formal languages, proof systems, type theory, mobile processes, automata theory, predicate logic, etc.

Encyclopedia of Philosophy: Cabanis - Destutt de Tracy


Author: Donald M. Borchert
Publisher: Thomson Gale/MacMillan Reference USA
ISBN: 9780028657820
Category: Philosophy
Page: 10
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Containing material from hundreds of highly distinguished contributors representing the world's top universities and institutions, the second edition has a truly global perspective. It contains more than 2,100 entries -- including more than 450 new articles. Among the many topics covered are African, Islamic, Jewish, Russian, Chinese, and Buddhist philosophies; bioethics and biomedical ethics; art and aesthetics; epistemology; metaphysics; peace and war; social and political philosophy; the Holocaust; feminist thought; and much more. Additionally, the second edition also features 1,000 biographical entries on major figures in philosophical thought throughout history.

Die Grundlagen der Mathematik


Author: David Hilbert
Publisher: Springer-Verlag
ISBN: 3663161021
Category: Mathematics
Page: 29
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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

The Convolution Transform


Author: Isidore Isaac Hirschman,David V. Widder
Publisher: Courier Corporation
ISBN: 0486154564
Category: Mathematics
Page: 288
View: 8946

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The relation between differential operators and integral transforms is the theme of this work. Discusses finite and non-finite kernels, variation diminishing transforms, asymptotic behavior of kernels, real inversion theory, representation theory, the Weierstrass transform, more.

From Logic to Practice

Italian Studies in the Philosophy of Mathematics
Author: Gabriele Lolli,Marco Panza,Giorgio Venturi
Publisher: Springer
ISBN: 3319104349
Category: Philosophy
Page: 336
View: 4053

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This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.