Brouwer S Cambridge Lectures On Intuitionism
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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.
Brouwer Meets Husserl
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Author : Mark van Atten
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-08
Brouwer Meets Husserl written by Mark van Atten 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 2006-11-08 with Mathematics categories.
Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? Mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But other mathematicians and philosophers have been voicing objections to choice sequences from the start. This book aims to provide a sound philosophical basis for Brouwer's choice sequences by subjecting them to a phenomenological critique in the style of the later Husserl.
Luitzen Egbertus Jan Brouwer S Cambridge Lectures On Intuitionism
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Author :
language : en
Publisher:
Release Date : 1981
Luitzen Egbertus Jan Brouwer S Cambridge Lectures On Intuitionism written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Intuitionistic Proof Versus Classical Truth
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Author : Enrico Martino
language : en
Publisher: Springer
Release Date : 2018-02-23
Intuitionistic Proof Versus Classical Truth written by Enrico Martino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Mathematics categories.
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.
Oskar Becker On The Logic Of Modalities 1930 Translation Commentary And Analysis
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Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2022-04-11
Oskar Becker On The Logic Of Modalities 1930 Translation Commentary And Analysis written by Stefania Centrone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-11 with Philosophy categories.
This book offers the first-ever English translation of Oskar Becker’s Zur Logik der Modalitäten. This essay, published in 1930, is a pioneering yet often neglected contribution in the context of prewar modal logic research in Europe. Becker’s text is complemented by an extended commentary that explains, analyzes and highlights Becker’s accomplishments and the philosophical background of his investigations. The commentary provides an in-depth analysis of all of Becker's important contributions, both from a philosophical and logical perspective, making it a very useful book for scholars in both philosophy and logic.
The New Yearbook For Phenomenology And Phenomenological Philosophy
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Author : Burt Hopkins
language : en
Publisher: Routledge
Release Date : 2015-03-24
The New Yearbook For Phenomenology And Phenomenological Philosophy written by Burt Hopkins and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-24 with Philosophy categories.
The New Yearbook for Phenomenology and Phenomenological Philosophy provides an annual international forum for phenomenological research in the spirit of Husserl's groundbreaking work and the extension of this work by such figures as Scheler, Heidegger, Sartre, Levinas, Merleau-Ponty and Gadamer.
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.
Cognition Content And The A Priori
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Author : Robert Hanna
language : en
Publisher: OUP Oxford
Release Date : 2015-10-08
Cognition Content And The A Priori written by Robert Hanna and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-08 with Philosophy categories.
In Cognition, Content, and the A Priori, Robert Hanna works out a unified contemporary Kantian theory of rational human cognition and knowledge. Along the way, he provides accounts of (i) intentionality and its contents, including non-conceptual content and conceptual content, (ii) sense perception and perceptual knowledge, including perceptual self-knowledge, (iii) the analytic-synthetic distinction, (iv) the nature of logic, and (v) a priori truth and knowledge in mathematics, logic, and philosophy. This book is specifically intended to reach out to two very different audiences: contemporary analytic philosophers of mind and knowledge on the one hand, and contemporary Kantian philosophers or Kant-scholars on the other. At the same time, it is also riding the crest of a wave of exciting and even revolutionary emerging new trends and new work in the philosophy of mind and epistemology, with a special concentration on the philosophy of perception. What is revolutionary in this new wave are its strong emphases on action, on cognitive phenomenology, on disjunctivist direct realism, on embodiment, and on sense perception as a primitive and proto-rational capacity for cognizing the world. Cognition, Content, and the A Priori makes a fundamental contribution to this philosophical revolution by giving it a specifically contemporary Kantian twist, and by pushing these new lines of investigation radically further.
Handbook Of Philosophical Logic
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Author : Dov M. Gabbay
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Handbook Of Philosophical Logic written by Dov M. Gabbay 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 2013-03-14 with Philosophy categories.
It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good,! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.