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Brouwer's Cambridge Lectures on Intuitionism
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
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 prot...
Brouwer's Intuitionism
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 ab...
Mystic, Geometer, and Intuitionist
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.
Intuitionistic Proof Versus Classical Truth
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.
The German Way of War
How the German Army combined opposing characteristics, such as drill and creativity, authority and independent thinking, into a potent mix of fighting power. The German Army lost two consecutive wars and the conclusion is often drawn that it simply wasn’t able to cope with its opponents. This image is constantly reinforced in literature and in the media, where seemingly brainless operating German units led by fanatical officers predominate. Nothing was as far from the truth. The records show that the Germans consistently outfought the far more numerous Allied armies that eventually defeated them: their relative battlefield performance was at least 1.5 and in most cases 3 times as high as t...
Mystic, Geometer, and Intuitionist
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 sens...
On Brouwer
This book offers a concise, yet comprehensive, introduction to this philosopher's most important ideas.
Gnomes in the Fog
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.
The German Way of War on the Eastern Front, 1941-1943
On 22 June 1941, at 0410hrs, Operation Barbarossa began. More than 3 million German soldiers crossed the border with the Soviet Union and moved east, where 4.7 million Soviet soldiers were waiting for them. Hitler expected his troops would be on the Volga before the end of the year and that important cities such as Moscow and Leningrad would have been captured. But the reality was very different; the Germans made impressive territorial gains, but their offensive eventually came to a halt at Stalingrad in December 1942, which proved to be a turning point in the war. This titanic battle is illustrated here using eyewitness accounts from generals, soldiers and civilians. Attention is not only paid to the course of the battle, but also to the tactics and organizational dimensions of the armies involved, the challenges of the vastness of the country, the dilemmas for people in the conquered areas, and the way the Germans tried to conquer their hearts while at the same time fighting a fierce guerrilla war. The role of the Reichsbahn in the field of logistics is also examined, as is the importance of the innovation and production capacity of both armies.
