**Author**: A.S. Troelstra,D. van Dalen

**Publisher:**Elsevier

**ISBN:**0080570887

**Category:**Mathematics

**Page:**355

**View:**1407

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# Search Results for: constructivism-in-mathematics-vol-2-an-introduction-v-2-studies-in-logic-and-the-foundations-of-mathematics

**Author**: A.S. Troelstra,D. van Dalen

**Publisher:** Elsevier

**ISBN:** 0080570887

**Category:** Mathematics

**Page:** 355

**View:** 1407

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.
*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:** 8236

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.
*Proceedings of the 1990 Computational Algebra Seminar at CWI, Amsterdam*

**Author**: Arjeh M. Cohen

**Publisher:** N.A

**ISBN:** N.A

**Category:** Lie groups

**Page:** 142

**View:** 7856

*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:** 5239

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.
*Foundations of Mathematics from Kronecker to Hilbert*

**Author**: Y. Gauthier

**Publisher:** Springer Science & Business Media

**ISBN:** 9401700834

**Category:** Mathematics

**Page:** 251

**View:** 6517

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.
*A New Rationalist Manifesto*

**Author**: A. Chapman,A. Ellis,R. Hanna,T. Hildebrand,H. Pickford

**Publisher:** Springer

**ISBN:** 1137347953

**Category:** Philosophy

**Page:** 427

**View:** 1570

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.
*Wahrheit & Beweisbarkeit*

**Author**: Kurt Gödel,Eckehart Köhler,Bernd Buldt

**Publisher:** N.A

**ISBN:** 9783209038340

**Category:** Logicians

**Page:** 448

**View:** 4376

**Author**: K. Vela Velupillai

**Publisher:** Routledge

**ISBN:** 1134253370

**Category:** Business & Economics

**Page:** 512

**View:** 8035

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.
*Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940*

**Author**: Paolo Mancosu

**Publisher:** OUP Oxford

**ISBN:** 0191021997

**Category:** Philosophy

**Page:** 632

**View:** 6243

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.

**Author**: David Hilbert

**Publisher:** Springer-Verlag

**ISBN:** 3663161021

**Category:** Mathematics

**Page:** 29

**View:** 9876

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.
*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:** 9202

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.
*An International Journal of Mathematics Education*

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Mathematics

**Page:** N.A

**View:** 8605

*Italian Studies in the Philosophy of Mathematics*

**Author**: Gabriele Lolli,Marco Panza,Giorgio Venturi

**Publisher:** Springer

**ISBN:** 3319104349

**Category:** Philosophy

**Page:** 336

**View:** 5847

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.

**Author**: Donald M. Borchert

**Publisher:** Thomson Gale/MacMillan Reference USA

**ISBN:** 9780028657820

**Category:** Philosophy

**Page:** 10

**View:** 6500

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.

**Author**: David Hilbert,Paul Bernays

**Publisher:** Springer-Verlag

**ISBN:** 3642868967

**Category:** Mathematics

**Page:** 568

**View:** 1839

Der vorliegende Band schließt die Darstellung der Beweistheorie ab, die ich vor einigen Jahren zusammen mit P. BERNAYS begann. Auf meinen Wunsch hat P. BERNAYS wieder die Abfassung des Textes über nommen. Ich danke ihm für die Sorgfalt und Treue, mit der er meine Gedanken wiedergegeben hat, an deren Entwicklung er in jahrelanger Zusammenarbeit aufs stärkste beteiligt war. Ohne seine Mithilfe wäre die Vollendung dieses Buches unmöglich gewesen. Den Herren W. ACKERMANN, G. GENTZEN, A. SCHMIDT, H. SCHOLZ danke ich für ihre freundliche Mitwirkung bei den Korrekturen. Göttingen, im März 1939 HILBERT Zur Einführung Das vorliegende Buch soll einer eingehenden Orientierung über den gegenwärtigen Stoff der HILBERTschen Beweistheorie dienen. Wenn gleich das bisher hier Erreichte gemessen an den Zielen der Theorie sehr bescheiden ist, so liegt doch ein reichlicher Stoff an prägnanten Ergebnissen, an Gesichtspunkten und Beweisgedanken vor, die zur Kenntnis zu bringen als lohnend erscheint. Für die inhaltliche Gestaltung dieses zweiten Bandes waren durch den Zweck des Buches zwei Hauptthemata vorgezeichnet. - Es handelte sich einmal darum, die hauptsächlichen, an das e-Symbol sich knüpfenden beweistheoretischen Ansätze HILBERTS und ihre Durchführung zur ein gehenden Darstellung zu bringen.

**Author**: Isidore Isaac Hirschman,David V. Widder

**Publisher:** Courier Corporation

**ISBN:** 0486154564

**Category:** Mathematics

**Page:** 288

**View:** 7602

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.

**Author**: Bowker Editorial Staff,[Anonymus AC01316077]

**Publisher:** N.A

**ISBN:** 9780835235105

**Category:**

**Page:** 3600

**View:** 3521

*An Index to the Publishers' Trade List Annual*

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** American literature

**Page:** N.A

**View:** 3514

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