L E J Brouwer Topologist Intuitionist Philosopher

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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.

Handbook Of The History And Philosophy Of Mathematical Practice

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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26

Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.

The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques

Critical Philosophy Of Mathematics

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Author : Ole Skovsmose
language : en
Publisher: Springer Nature
Release Date : 2024-09-25

Critical Philosophy Of Mathematics written by Ole Skovsmose and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-25 with Education categories.

This book provides a philosophy of mathematics that resonates with critical mathematics education. It draws attention to the social complexities that characterise the period of Modernity including the extreme exploitation of manual workers and their families, brutal forms of colonisations, trading of slaves, and the formation of racist ideologies. It portrays Modernity as a period of contradictions and highlights that mathematics is a part of these contradictions. The text interprets mathematics as being indefinite, seeing that mathematics is a part of the ongoing human constructions. It outlines a performative interpretation of mathematics, portraying mathematics as intrinsically connected to actions. Any kind of action, including mathematics-based actions, calls for ethical considerations and this leads to any mathematical practice, either in research, application, or education, to face ethical challenges. It illustrates with examples how a critical philosophy of mathematics can come to be an integral part of classroom practices.

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.

Rediscovering L On Brunschvicg S Critical Idealism

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Author : Pietro Terzi
language : en
Publisher: Bloomsbury Publishing
Release Date : 2022-01-13

Rediscovering L On Brunschvicg S Critical Idealism written by Pietro Terzi and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-13 with Mathematics categories.

Léon Brunschvicg's contribution to philosophical thought in fin-de-siècle France receives full explication in the first English-language study on his work. Arguing that Brunschvicg is crucial to understanding the philosophical schools which took root in 20th-century France, Pietro Terzi locates Brunschvicg alongside his contemporary Henri Bergson, as well as the range of thinkers he taught and influenced, including Lévinas, Merleau-Ponty, de Beauvoir, and Sartre. Brunschvicg's deep engagement with debates concerning spiritualism and rationalism, neo-Kantian philosophy, and the role of mathematics in philosophy made him the perfect supervisor for a whole host of nascent philosophical ideas which were forming in the work of his students. Terzi outlines Brunchvicg's defence of neo-Kantian judgement, historical analysis and the inextricability of the natural and humanist sciences to any rigorous system of philosophy, with wide-ranging implications for contemporary scholarship.

Connecting With Computability

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Author : Liesbeth De Mol
language : en
Publisher: Springer Nature
Release Date : 2021-07-01

Connecting With Computability written by Liesbeth De Mol and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-01 with Computers categories.

This book constitutes the proceedings of the 17th Conference on Computability in Europe, CiE 2021, organized by the University of Ghent in July 2021. Due to COVID-19 pandemic the conference was held virtually. The 48 full papers presented in this volume were carefully reviewed and selected from 50 submissions. CiE promotes the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2021 had as its motto Connecting with Computability, a clear acknowledgement of the connecting and interdisciplinary nature of the conference series which is all the more important in a time where people are more than ever disconnected from one another due to the COVID-19 pandemic.

Mathematical Communities In The Reconstruction After The Great War 1918 1928

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Author : Laurent Mazliak
language : en
Publisher: Springer Nature
Release Date : 2021-03-27

Mathematical Communities In The Reconstruction After The Great War 1918 1928 written by Laurent Mazliak and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-27 with Science categories.

This book is a consequence of the international meeting organized in Marseilles in November 2018 devoted to the aftermath of the Great War for mathematical communities. It features selected original research presented at the meeting offering a new perspective on a period, the 1920s, not extensively considered by historiography. After 1918, new countries were created, and borders of several others were modified. Territories were annexed while some countries lost entire regions. These territorial changes bear witness to the massive and varied upheavals with which European societies were confronted in the aftermath of the Great War. The reconfiguration of political Europe was accompanied by new alliances and a redistribution of trade – commercial, intellectual, artistic, military, and so on – which largely shaped international life during the interwar period. These changes also had an enormous impact on scientific life, not only in practice, but also in its organization and communication strategies. The mathematical sciences, which from the late 19th century to the 1920s experienced a deep disciplinary evolution, were thus facing a double movement, internal and external, which led to a sustainable restructuring of research and teaching. Concomitantly, various areas such as topology, functional analysis, abstract algebra, logic or probability, among others, experienced exceptional development. This was accompanied by an explosion of new international or national associations of mathematicians with for instance the founding, in 1918, of the International Mathematical Union and the controversial creation of the International Research Council. Therefore, the central idea for the articulation of the various chapters of the book is to present case studies illustrating how in the aftermath of the war, many mathematicians had to organize their personal trajectories taking into account the evolution of the political, social and scientific environment which had taken place at the end of the conflict.

The Logical Writings Of Karl Popper

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Author : David Binder
language : en
Publisher: Springer Nature
Release Date : 2022-08-07

The Logical Writings Of Karl Popper written by David Binder and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-07 with Philosophy categories.

This open access book is the first ever collection of Karl Popper's writings on deductive logic. Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics. This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.

Structures And Algorithms

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Author : Jens Erik Fenstad
language : en
Publisher: Springer
Release Date : 2018-03-10

Structures And Algorithms written by Jens Erik Fenstad and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-10 with Philosophy categories.

This book explains exactly what human knowledge is. The key concepts in this book are structures and algorithms, i.e., what the readers “see” and how they make use of what they see. Thus in comparison with some other books on the philosophy (or methodology) of science, which employ a syntactic approach, the author’s approach is model theoretic or structural. Properly understood, it extends the current art and science of mathematical modeling to all fields of knowledge. The link between structure and algorithms is mathematics. But viewing “mathematics” as such a link is not exactly what readers most likely learned in school; thus, the task of this book is to explain what “mathematics” should actually mean. Chapter 1, an introductory essay, presents a general analysis of structures, algorithms and how they are to be linked. Several examples from the natural and social sciences, and from the history of knowledge, are provided in Chapters 2–6. In turn, Chapters 7 and 8 extend the analysis to include language and the mind. Structures are what the readers see. And, as abstract cultural objects, they can almost always be seen in many different ways. But certain structures, such as natural numbers and the basic theory of grammar, seem to have an absolute character. Any theory of knowledge grounded in human culture must explain how this is possible. The author’s analysis of this cultural invariance, combining insights from evolutionary theory and neuroscience, is presented in the book’s closing chapter. The book will be of interest to researchers, students and those outside academia who seek a deeper understanding of knowledge in our present-day society.

Advances In Peircean Mathematics

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Author : Fernando Zalamea
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-11-07

Advances In Peircean Mathematics written by Fernando Zalamea and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-07 with Philosophy categories.

The book explores Peirce's non standard thoughts on a synthetic continuum, topological logics, existential graphs, and relational semiotics, offering full mathematical developments on these areas. More precisely, the following new advances are offered: (1) two extensions of Peirce's existential graphs, to intuitionistic logics (a new symbol for implication), and other non-classical logics (new actions on nonplanar surfaces); (2) a complete formalization of Peirce's continuum, capturing all Peirce's original demands (genericity, supermultitudeness, reflexivity, modality), thanks to an inverse ordinally iterated sheaf of real lines; (3) an array of subformalizations and proofs of Peirce's pragmaticist maxim, through methods in category theory, HoTT techniques, and modal logics. The book will be relevant to Peirce scholars, mathematicians, and philosophers alike, thanks to thorough assessments of Peirce's mathematical heritage, compact surveys of the literature, and new perspectives offered through formal and modern mathematizations of the topics studied.