Brouwer S Intuitionism
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Brouwer S Intuitionism
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Author : Walter P. van Stigt
language : en
Publisher: North Holland
Release Date : 1990-01-01
Brouwer S Intuitionism written by Walter P. van Stigt and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
Dutch Mathematician Luitzen Egbertus Jan Brouwer (1881-1966) was a rebel. His doctoral thesis... was the manifesto of an angry young man taking on the mathematical establishment on all fronts. In a short time he established a world-wide reputation for himself; his genius and originality were acknowledged by the great mathematicians of his time... The Intuitionist-Formalist debate became a personal feud between the mathematical giants Brouwer and Hilbert, and ended in 1928 with the expulsion of Brouwer from the editorial board of the Mathematische Annalen by dictat of Hilbert. Forsaken, humiliated and disillusioned Brouwer abandoned his Intuitionist Programme and withdrew into silence just about the time when the Formalist Programme appeared to be fundamentally flawed and major opposition collapsed... This book attempts to follow the `genetic' development of Brouwer's ideas, linking the man Brouwer, his Weltanschauung, his philosophy of mathematics and his reconstruction of mathematics. Brouwer's own writings, his publications as well as his unpublished papers, are its immediate and main source of reference. It is the second volume in the new series Studies in the History and Philosophy of Mathematics, and is written for the specialist as well as for the general reader interested in mathematics and the interpretation of its status and function.
Brouwer S Cambridge Lectures On Intuitionism
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Author : Luitzen Egbertus Jan Brouwer
language : en
Publisher: Cambridge University Press
Release Date : 1981
Brouwer S Cambridge Lectures On Intuitionism written by Luitzen Egbertus Jan Brouwer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
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.
L E J Brouwer Topologist Intuitionist Philosopher
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Author : Dirk van Dalen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-04
L E J Brouwer Topologist Intuitionist Philosopher written by Dirk van Dalen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-04 with Mathematics categories.
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.
Intuitionism
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Author : Arend Heyting
language : en
Publisher: Elsevier
Release Date : 1966
Intuitionism written by Arend Heyting and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Electronic books categories.
Gnomes In The Fog
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Author : Dennis E. Hesseling
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Gnomes In The Fog written by Dennis E. Hesseling and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The significance of foundational debate in mathematics that took place in the 1920s seems to have been recognized only in circles of mathematicians and philosophers. A period in the history of mathematics when mathematics and philosophy, usually so far away from each other, seemed to meet. The foundational debate is presented with all its brilliant contributions and its shortcomings, its new ideas and its misunderstandings.
Mathematical Intuitionism And Intersubjectivity
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Author : Tomasz Placek
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Mathematical Intuitionism And Intersubjectivity written by Tomasz Placek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
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.
Ideas And Explorations
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Author : Johannes John Carel Kuiper
language : en
Publisher:
Release Date : 2004
Ideas And Explorations written by Johannes John Carel Kuiper and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Gnomes In The Fog
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Author : Dennis E. Hesseling
language : en
Publisher: Birkhauser
Release Date : 2003
Gnomes In The Fog written by Dennis E. Hesseling and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Fiction categories.
"The book includes the precursors to and the development of intuitionism, as well as the foundational debate itself. After a general overview of the debate, the analysis centers on two main issues: the question of mathematical existence and the status of logic. Finally, the cultural context of the debate is taken into account."--Jacket.
Essays On G Del S Reception Of Leibniz Husserl And Brouwer
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Author : Mark van Atten
language : en
Publisher: Springer
Release Date : 2014-11-21
Essays On G Del S Reception Of Leibniz Husserl And Brouwer written by Mark van Atten and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-21 with Philosophy categories.
This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage. The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism. The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his publishe d writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not. The remaining essays provide further context. The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.
Logicism Intuitionism And Formalism
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Author : Sten Lindström
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-25
Logicism Intuitionism And Formalism written by Sten Lindström and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-25 with Mathematics categories.
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.