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Brouwer meets Husserl
Can a line be analysed mathematically such a way that it does not fall apart into a set of discrete points? Are there objects of pure mathematics that can change through time? L. E. J. Brouwer argued that the two questions are related and that the answer to both is "yes", introducing the concept of choice sequences. This book subjects Brouwer's choice sequences to a phenomenological critique in the style of Husserl.
Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer
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...
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...
All Things in Common
All Things in Common explores the history of a Canadian utopian community, highlighting the roles of family, faith, and business pragmatism in its cohesion and longevity.
A Study Guide for Joel Brouwer's "Last Request (Exactly What Happened)"
A Study Guide for Joel Brouwer's "Last Request (Exactly What Happened)," excerpted from Gale's acclaimed Poetry for Students. This concise study guide includes plot summary; character analysis; author biography; study questions; historical context; suggestions for further reading; and much more. For any literature project, trust Poetry for Students for all of your research needs.
On Brouwer
This book offers a concise, yet comprehensive, introduction to this philosopher's most important ideas.
Augustine’s Cyprian
Augustine’s Cyprian retraces the demise of Donatist Christianity in ancient North Africa. Set during the Roman Empire’s collapse, this work accounts how Augustine of Hippo initiated one of the most prolific re-appropriations of authority in ancient Christianity: Cyprian of Carthage.
A Companion to Philosophical Logic
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.
Brouwer Degree
This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The authors define the degree using an analytical approach proposed by Heinz in 1959 and further developed by Mawhin in 2004, linking it to the Kronecker index and employing the language of differential forms. The chapters are organized so that they can be approached in various ways depending on the interests of the reader. Unifying this structure is the central role the Brouwer degree plays in nonlinear analysis, which is illustrated with existence, surjectivity, and fixed point theorems for nonlinear mappings. Special attention is paid to the computation of the degree, as well as to the wide array of applications, such as linking, differential and partial differential equations, difference equations, variational and hemivariational inequalities, game theory, and mechanics. Each chapter features bibliographic and historical notes, and the final chapter examines the full history. Brouwer Degree will serve as an authoritative reference on the topic and will be of interest to professional mathematicians, researchers, and graduate students.
