Mathematical Intuitionism and Intersubjectivity

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Publisher : Springer Science & Business Media
ISBN 13 : 9401593159
Total Pages : 229 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Mathematical Intuitionism and Intersubjectivity by : Tomasz Placek

Download or read book Mathematical Intuitionism and Intersubjectivity written by Tomasz Placek and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1907 Luitzen Egbertus Jan Brouwer defended his doctoral dissertation on the foundations of mathematics and with this event the modem version of mathematical intuitionism came into being. Brouwer attacked the main currents of the philosophy of mathematics: the formalists and the Platonists. In tum, both these schools began viewing intuitionism as the most harmful party among all known philosophies of mathematics. That was the origin of the now-90-year-old debate over intuitionism. As both sides have appealed in their arguments to philosophical propositions, the discussions have attracted the attention of philosophers as well. One might ask here what role a philosopher can play in controversies over mathematical intuitionism. Can he reasonably enter into disputes among mathematicians? I believe that these disputes call for intervention by a philo sopher. The three best-known arguments for intuitionism, those of Brouwer, Heyting and Dummett, are based on ontological and epistemological claims, or appeal to theses that properly belong to a theory of meaning. Those lines of argument should be investigated in order to find what their assumptions are, whether intuitionistic consequences really follow from those assumptions, and finally, whether the premises are sound and not absurd. The intention of this book is thus to consider seriously the arguments of mathematicians, even if philosophy was not their main field of interest. There is little sense in disputing whether what mathematicians said about the objectivity and reality of mathematical facts belongs to philosophy, or not.

Mathematical Intuitionism

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Publisher : Cambridge University Press
ISBN 13 : 1108593259
Total Pages : 116 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Mathematical Intuitionism by : Carl J. Posy

Download or read book Mathematical Intuitionism written by Carl J. Posy and published by Cambridge University Press. This book was released on 2020-11-12 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism – from elementary number theory through to Brouwer's uniform continuity theorem – and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth.

Elements of Intuitionism

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Publisher : Oxford University Press
ISBN 13 : 9780198505242
Total Pages : 350 pages
Book Rating : 4.5/5 (52 download)

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Book Synopsis Elements of Intuitionism by : Michael Dummett

Download or read book Elements of Intuitionism written by Michael Dummett and published by Oxford University Press. This book was released on 2000 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics has been completely revised for this second edition. Brouwer's proof of the Bar Theorem has been reworked, the account of valuation systems simplified, and the treatment of generalized Beth Trees and the completeness of intuitionistic first-order logic rewritten. Readers are assumed to have some knowledge of classical formal logic and a general awareness of the history of intuitionism.

Intuitionism an Introduction

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Publisher :
ISBN 13 :
Total Pages : 145 pages
Book Rating : 4.:/5 (63 download)

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Book Synopsis Intuitionism an Introduction by : Arend Heyting

Download or read book Intuitionism an Introduction written by Arend Heyting and published by . This book was released on 1971 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Intuition

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Publisher : Springer Science & Business Media
ISBN 13 : 9400922930
Total Pages : 223 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Mathematical Intuition by : R.L. Tieszen

Download or read book Mathematical Intuition written by R.L. Tieszen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book.

Intuition in Science and Mathematics

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Publisher : Springer Science & Business Media
ISBN 13 : 0306472376
Total Pages : 234 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Intuition in Science and Mathematics by : Efraim Fischbein

Download or read book Intuition in Science and Mathematics written by Efraim Fischbein and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In writing the present book I have had in mind the following objectives: - To propose a theoretical, comprehensive view of the domain of intuition. - To identify and organize the experimental findings related to intuition scattered in a wide variety of research contexts. - To reveal the educational implications of the idea, developed for science and mathematics education. Most of the existing monographs in the field of intuition are mainly concerned with theoretical debates - definitions, philosophical attitudes, historical considerations. (See, especially the works of Wild (1938), of Bunge (1 962) and of Noddings and Shore (1 984).) A notable exception is the book by Westcott (1968), which combines theoretical analyses with the author’s own experimental studies. But, so far, no attempt has been made to identify systematically those findings, spread throughout the research literature, which could contribute to the deciphering of the mechanisms of intuition. Very often the relevant studies do not refer explicitly to intuition. Even when this term is used it occurs, usually, as a self-evident, common sense term.

Intuitionism

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Publisher : Elsevier
ISBN 13 : 0444534067
Total Pages : 159 pages
Book Rating : 4.4/5 (445 download)

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Book Synopsis Intuitionism by : Arend Heyting

Download or read book Intuitionism written by Arend Heyting and published by Elsevier. This book was released on 1966 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Intuitionistic Proof Versus Classical Truth

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Publisher : Springer
ISBN 13 : 3319743570
Total Pages : 173 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Intuitionistic Proof Versus Classical Truth by : Enrico Martino

Download or read book Intuitionistic Proof Versus Classical Truth written by Enrico Martino and published by Springer. This book was released on 2018-02-23 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers – both new and previously published – it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism. The author explores Brouwer’s idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer’s work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting. This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics.

Logicism, Intuitionism, and Formalism

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Publisher : Springer Science & Business Media
ISBN 13 : 1402089260
Total Pages : 509 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Logicism, Intuitionism, and Formalism by : Sten Lindström

Download or read book Logicism, Intuitionism, and Formalism written by Sten Lindström and published by Springer Science & Business Media. This book was released on 2008-11-25 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.

Thinking About Equations

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Publisher : John Wiley & Sons
ISBN 13 : 1118210646
Total Pages : 189 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis Thinking About Equations by : Matt A. Bernstein

Download or read book Thinking About Equations written by Matt A. Bernstein and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences. Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including: Approximation and estimation Isolating important variables Generalization and special cases Dimensional analysis and scaling Pictorial methods and graphical solutions Symmetry to simplify equations Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension. Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.

L.E.J. Brouwer – Topologist, Intuitionist, Philosopher

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Publisher : Springer Science & Business Media
ISBN 13 : 1447146166
Total Pages : 877 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis L.E.J. Brouwer – Topologist, Intuitionist, Philosopher by : Dirk van Dalen

Download or read book L.E.J. Brouwer – Topologist, Intuitionist, Philosopher written by Dirk van Dalen and published by Springer Science & Business Media. This book was released on 2012-12-04 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.

One Hundred Years of Intuitionism (1907-2007)

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Publisher : Springer Science & Business Media
ISBN 13 : 3764386533
Total Pages : 432 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis One Hundred Years of Intuitionism (1907-2007) by : Mark van Atten

Download or read book One Hundred Years of Intuitionism (1907-2007) written by Mark van Atten and published by Springer Science & Business Media. This book was released on 2008-11-09 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intuitionism is one of the main foundations for mathematics proposed in the twentieth century and its views on logic have also notably become important with the development of theoretical computer science. This book reviews and completes the historical account of intuitionism. It also presents recent philosophical work on intuitionism and gives examples of new technical advances and applications. It brings together 21 contributions from today's leading authors on intuitionism.

Mathematical Intuitionism

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Publisher : Cambridge University Press
ISBN 13 : 9781108723022
Total Pages : 75 pages
Book Rating : 4.7/5 (23 download)

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Book Synopsis Mathematical Intuitionism by : Carl J. Posy

Download or read book Mathematical Intuitionism written by Carl J. Posy and published by Cambridge University Press. This book was released on 2020-11-12 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism - from elementary number theory through to Brouwer's uniform continuity theorem - and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth.

Brouwer's Cambridge Lectures on Intuitionism

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Publisher : Cambridge University Press
ISBN 13 : 9780521177368
Total Pages : 130 pages
Book Rating : 4.1/5 (773 download)

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Book Synopsis Brouwer's Cambridge Lectures on Intuitionism by : Luitzen Egbertus Jan Brouwer

Download or read book Brouwer's Cambridge Lectures on Intuitionism written by Luitzen Egbertus Jan Brouwer and published by Cambridge University Press. This book was released on 1981 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work.

Provability, Computability and Reflection

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Publisher : Elsevier
ISBN 13 : 0080957595
Total Pages : 215 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Provability, Computability and Reflection by : Lev D. Beklemishev

Download or read book Provability, Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection

Kurt Gödel

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Publisher : Springer Nature
ISBN 13 : 3030872963
Total Pages : 133 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Kurt Gödel by : Maria Hämeen-Anttila

Download or read book Kurt Gödel written by Maria Hämeen-Anttila and published by Springer Nature. This book was released on 2021-12-15 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paris of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Gödel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel's incompleteness theorem. Gödel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of the credit of this seeming faux pas going to Gödel. The second is a problem still wide open. Gödel worked on it for years, with no definitive results; The best he could offer was a start with the arithmetic of the entire numbers. This book, Gödel's lectures at the famous Princeton Institute for Advanced Study in 1941, shows how far he had come with Hilbert's second problem, namely to a theory of computable functionals of finite type and a proof of the consistency of ordinary arithmetic. It offers indispensable reading for logicians, mathematicians, and computer scientists interested in foundational questions. It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers. The book also gives insights into the conceptual and formal work that is needed for the solution of profound scientific questions, by one of the central figures of 20th century science and philosophy.

Provability, Computability and Reflection

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Publisher : Elsevier
ISBN 13 : 0080957617
Total Pages : 159 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Provability, Computability and Reflection by : Lev D. Beklemishev

Download or read book Provability, Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection