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Author : Dirk Dalen
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (992 download)
Download or read book Mystic, Geometer, and Intuitionist: Hope and disillusion written by Dirk Dalen and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dirk van Dalen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (263 download)
Download or read book Mystic, Geometer, and Intuitionist written by Dirk van Dalen and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (873 download)
Download or read book Mystic, Geometer, and Intuitionist written by and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : van Dalen (Dirk)
Publisher :
ISBN 13 : 9780198502975
Total Pages : pages
Book Rating : 4.5/5 (29 download)
Download or read book Mystic, Geometer, and Intuitionist written by van Dalen (Dirk) and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dirk Dalen
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (55 download)
Download or read book Mystic, Geometer, and Intuitionist written by Dirk Dalen and published by . This book was released on 2005 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the development of mathematics and in wider Dutch history. A mathematical genius with strong mystical and philosophical leanings, he advocated the intuitionist view of mathematics and science as a constructive mental activity. This drew him into a discussion with David Hilbert, the leading advocate of the formalist school, about the nature of mathematics, a debate which made Brouwer a legend during his lifetime. He also contributed significantly to research in topology, and was a member of the socio- linguistic Signific Circle. As well as his diverse mathematical interests he had a great impact in wider Dutch society. His keen sense of justice made him a party in many conflicts, both scientific and political. He would often be involved in controversial issues, such as the campaign to undo the boycott of German scientists, and this made him a figure both of admiration and embarrassment in his native Holland.; Although his abilities won him offers from prestigious universities such as Berlin and Gottingen, he preferred to stay in Amsterdam, so that he could pursue a life of quiet unconventionality in the artist community at Laren. This book, the second in a two volume set, provides a sophisticated analysis of this crucial era of mathematical research, but also gives an important insight into the wider life of one of the most fascinating characters involved.
Author : Dirk van Dalen
Publisher :
ISBN 13 : 9781280759307
Total Pages : 517 pages
Book Rating : 4.7/5 (593 download)
Download or read book Mystic, Geometer, and Intuitionist written by Dirk van Dalen and published by . This book was released on 2005 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the development of mathematics and in broader Dutch history. This sophisticated analysis of this crucial era of mathematical research gives an insight into his life.
Author : Carl J. Posy
Publisher : Cambridge University Press
ISBN 13 : 1108593259
Total Pages : 116 pages
Book Rating : 4.1/5 (85 download)
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.
Author : Dirk van Dalen
Publisher : Springer Science & Business Media
ISBN 13 : 1447146166
Total Pages : 877 pages
Book Rating : 4.4/5 (471 download)
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.
Author : Sasho Kalajdzievski
Publisher : CRC Press
ISBN 13 : 1000985954
Total Pages : 233 pages
Book Rating : 4.0/5 (9 download)
Download or read book Miracles, Mystics, Mathematicians written by Sasho Kalajdzievski and published by CRC Press. This book was released on 2023-11-30 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Miracles, Mystics, Mathematicians: Searching for Deep Reality focuses on the lives and writings of some of history’s most influential mathematicians and the impact that their mystical beliefs had on their lives and on their mathematical work. Modern biographers often cleanse the lives of renowned scientists of any hint of mysticism or occultism. Such threads are sometimes regarded as relics of the superstitious past; flaws that need to be hushed up, marginalized, or reinterpreted. This book represents a minor attempt to push back against this tendency and to examine these aspects of the history of mathematics with seriousness and intellectual curiosity. Features A breadth of scope covering many centuries Suitable for anyone interested in mathematics, history, philosophy, paranormal phenomena, psi-research, mysticism, or in any combination of the above An almost unique account of known histories, examined from a new vantage point Sasho Kalajdzievski is a Senior Scholar in the Department of Mathematics at the University of Manitoba.
Author : Rudolf Taschner
Publisher : Springer Science & Business Media
ISBN 13 : 332282036X
Total Pages : 143 pages
Book Rating : 4.3/5 (228 download)
Download or read book The Continuum written by Rudolf Taschner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this small text the basic theory of the continuum, including the elements of metric space theory and continuity is developed within the system of intuitionistic mathematics in the sense of L.E.J. Brouwer and H. Weyl. The main features are proofs of the famous theorems of Brouwer concerning the continuity of all functions that are defined on "whole" intervals, the uniform continuity of all functions that are defined on compact intervals, and the uniform convergence of all pointwise converging sequences of functions defined on compact intervals. The constructive approach is interesting both in itself and as a contrast to, for example, the formal axiomatic one.
Author : Dale Jacquette
Publisher : John Wiley & Sons
ISBN 13 : 1405149949
Total Pages : 832 pages
Book Rating : 4.4/5 (51 download)
Download or read book A Companion to Philosophical Logic written by Dale Jacquette and published by John Wiley & Sons. This book was released on 2008-04-15 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of newly comissioned essays by international contributors offers a representative overview of the most important developments in contemporary philosophical logic. Presents controversies in philosophical implications and applications of formal symbolic logic. Surveys major trends and offers original insights.
Author : Mark van Atten
Publisher : Springer Science & Business Media
ISBN 13 : 3764386533
Total Pages : 432 pages
Book Rating : 4.7/5 (643 download)
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.
Author : Dirk Dalen
Publisher : Oxford University Press
ISBN 13 :
Total Pages : 464 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mystic, Geometer, and Intuitionist: The dawning revolution written by Dirk Dalen and published by Oxford University Press. This book was released on 1999 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the development of mathematics and in wider Dutch history. A mathematical genius with strong mystical and philosophical leanings, he advocated a constructivistic, more human view of mathematics and science. A sophisticated analysis of a crucial era of mathematical research, this book is an important insight into the life of one of its most fascinating characters.
Author : Eckart Menzler-Trott
Publisher : American Mathematical Soc.
ISBN 13 : 1470428121
Total Pages : 466 pages
Book Rating : 4.4/5 (74 download)
Download or read book Logic's Lost Genius written by Eckart Menzler-Trott and published by American Mathematical Soc.. This book was released on 2016-05-05 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gerhard Gentzen (1909–1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called “proof theory” but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for “German logic”, and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smoryński on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Gödel; and its development up to the present day. Smoryński explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program. This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers.
Author : José Ferreirós
Publisher : Princeton University Press
ISBN 13 : 1400874009
Total Pages : 358 pages
Book Rating : 4.4/5 (8 download)
Download or read book Mathematical Knowledge and the Interplay of Practices written by José Ferreirós and published by Princeton University Press. This book was released on 2015-12-22 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, José Ferreirós uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, Ferreirós shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. He argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. Ferreirós demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, Mathematical Knowledge and the Interplay of Practices challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.
Author : Cristoforo Sergio Bertuglia
Publisher : OUP Oxford
ISBN 13 : 0191524441
Total Pages : 402 pages
Book Rating : 4.1/5 (915 download)
Download or read book Nonlinearity, Chaos, and Complexity written by Cristoforo Sergio Bertuglia and published by OUP Oxford. This book was released on 2005-05-12 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique text in the midst of many current books on chaos and complexity. Part 1 deals with the mathematical model as an instrument of investigation. The general meaning of modelling and, more specifically, questions concerning linear modelling are discussed. Part 2 deals with the theme of chaos and the origin of chaotic dynamics. Part 3 deals with the theme of complexity: a property of the systems and of their models which is intermediate between stability and chaos. Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.
Author : Charles Parsons
Publisher : Harvard University Press
ISBN 13 : 0674419499
Total Pages : 365 pages
Book Rating : 4.6/5 (744 download)
Download or read book Philosophy of Mathematics in the Twentieth Century written by Charles Parsons and published by Harvard University Press. This book was released on 2014-03-10 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.
