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Author: Luitzen Egbertus Jan Brouwer
Publisher: Cambridge University Press
ISBN: 9780521177368
Category : Mathematics
Languages : en
Pages : 130
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Book Description
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.
Author: Luitzen Egbertus Jan Brouwer
Publisher: Cambridge University Press
ISBN: 9780521177368
Category : Mathematics
Languages : en
Pages : 130
Get Book Here
Book Description
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.
Author: Walter P. van Stigt
Publisher: North Holland
ISBN: 9780444883841
Category : Mathematics
Languages : en
Pages : 530
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Book Description
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.
Author: Tomasz Placek
Publisher: Springer Science & Business Media
ISBN: 9401593159
Category : Science
Languages : en
Pages : 229
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Book Description
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.
Author: Richard W. Kaye
Publisher: Cambridge University Press
ISBN: 1139467212
Category : Mathematics
Languages : en
Pages : 12
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Book Description
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.
Author: Dirk van Dalen
Publisher: Springer Science & Business Media
ISBN: 1447146166
Category : Mathematics
Languages : en
Pages : 877
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Book Description
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.
Author: A. Heyting
Publisher: Elsevier
ISBN: 1483278158
Category : Mathematics
Languages : de
Pages : 645
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Book Description
L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.
Author: Christopher Norris
Publisher: A&C Black
ISBN: 1441139923
Category : Philosophy
Languages : en
Pages : 209
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Book Description
In this path-breaking study Christopher Norris proposes a transformed understanding of the much-exaggerated differences between analytic and continental philosophy. While keeping the analytic tradition squarely in view his book focuses on the work of Jacques Derrida and Alain Badiou, two of the most original and significant figures in the recent history of ideas. Norris argues that these thinkers have decisively reconfigured the terrain of contemporary philosophy and, between them, pointed a way beyond some of those seemingly intractable issues that have polarised debate on both sides of the notional rift between the analytic and continental traditions. In particular his book sets out to show - against the received analytic wisdom - that continental philosophy has its own analytic resources and is capable of bringing some much-needed fresh insight to bear on problems in philosophy of language, logic and mathematics. Norris provides not only a unique comparative account of Derrida's and Badiou's work but also a remarkably wide-ranging assessment of their joint contribution to philosophy's current - if widely resisted - potential for self-transformation.
Author: Florian Franken Figueiredo
Publisher: Taylor & Francis
ISBN: 1000843122
Category : Philosophy
Languages : en
Pages : 255
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Book Description
The book explores the impact of manuscript remarks during the year 1929 on the development of Wittgenstein’s thought. Although its intention is to put the focus specifically on the manuscripts, the book is not purely exegetical. The contributors generate important new insights for understanding Wittgenstein’s philosophy and his place in the history of analytic philosophy. Wittgenstein’s writings from the years 1929-1930 are valuable, not simply because they marked Wittgenstein’s return to academic philosophy after a seven-year absence, but because these works indicate several changes in his philosophical thinking. The chapters in this volume clarify the significance of Wittgenstein’s return to philosophy in 1929. In Part 1, the contributors address different issues in the philosophy of mathematics, e.g. Wittgenstein's understanding of certain aspects of intuitionism and his commitment to verificationism, as well as his idea of "a new system". Part 2 examines Wittgenstein's philosophical development and his understanding of philosophical method. Here the contributors examine particular problems Wittgenstein dealt with in 1929, e.g. the colour-exclusion problem, and the use of thought experiments as well as his relationship to Frank Ramsey and philosophical pragmatism. Part 3 features essays on phenomenological language. These chapters address the role of spatial analogies and the structure of visual space. Finally, Part 4 includes one chapter on Wittgenstein’s few manuscript remarks about ethics and religion and relates it to his Lecture on Ethics. Wittgenstein’s Philosophy in 1929 will be of great interest to scholars and advanced students working on Wittgenstein and the history of analytic philosophy.
Author: Robert Hanna
Publisher: OUP Oxford
ISBN: 0191025593
Category : Philosophy
Languages : en
Pages : 490
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Book Description
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.
Author: Jadran Mimica
Publisher: Routledge
ISBN: 1000324761
Category : Social Science
Languages : en
Pages : 199
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Book Description
This is a remarkable work which captures the reader's imagination as only few books do. From a description of the counting system of Iqwaye people of Papua New Guinea, the author develops a deeper and broader interpretation of the Iqwaye kinship system and cosmology, culminating in a powerful critique of western assumptions about the development of rational thought.
