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Brouwer's Intuitionism
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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, humilia...
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 Brouwer's own writings, his publications as well as his unpublished papers, are its immediate and main source of reference.It is the second volume in the new series Studies in the History and Philosophy of Mathematics, and is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.
Review quote:
...a fascinating intellectual biography... American Mathematical Monthly This is a fascinating book describing the development of Brouwer's ideas, linking the man, his Weltanschauung, his philosophy and his programme of reconstruction of mathematics on a constructive basis. Revue Roumaine de Mathématiques Pures et Appliquées Walter van Stigt has done a masterly job gathering and interpreting the facts surrounding Brouwer's life and mathematical times... He has done philosophers and historians of mathematics a considerable service by collecting and organising a vast archive of complex material, much of it written originally in Dutch. This material is highly organised with systematic appendices giving translations of many important documents. The Times Higher Education Supplement Anyone interested in Brouwer or Intuitionism in a general way will enjoy reading Chapters II, III and IV and some of the appendices... The later chapters and the appendices should be extremely valuable to anyone who would like a detailed and scholarly account of the basic logical and mathematical concepts, based on the original text. The Journal for Symbolic Logic With its emphasis on Brouwer's person and philosophy, which were instrumental for the development of the mathematics, the book is a welcome complement to the more technical introductions to constructive mathematics that are around. Mathematical Reviews Van Stigt provides an in-depth view of Brouwer, his philosophy and his foundations of mathematics... the decisive text on Brouwer's Intuitionism for many years to come. Modern Logic
Table of contents:
The Brouwer Bibliography. Publications. Unpublished Papers.
Brouwer, Life and Work. Childhood and Student Years. Post-Graduate Study. Life, Art and Mysticism. The Foundations of Mathematics. Towards an Academic Career. Intuitionism and Formalism. The Signific Interlude. The Second Act of Intuitionism. The Turbulent Years. The Brouwer Logic. The Reconstruction of Analysis. The Unfinished Books. The Brouwer-Hilbert Controversy and the Annalen Affair. The Silent Years. Post-War Lectures and Final Years.
Brouwer's Philosophy. Introduction. Character and Early Background. Philosophy, Metaphysics and Ideology. Mysticism. God and the Moral Principle. Kant and the French Intuitionist Tradition. French Mathematical Intuitionism. The Self, Consciousness and Mind. Causal Attention, Will and Cunning Activity. The Phase of Social Acting and Language.
Brouwer's Philosophy of Mathematics. The Primordial Intuition of Time. Intuitive Thinking and Mathematics. The Nature of Mathematics. Reflection on the Nature of Mathematics. Constructiveness and Existence. The Subject and the Intersubjectivity of Mathematics. The Application of Mathematics.
Language and Logic. Society and Communication. The Purpose and Origin of Language. Language and Pure Thought. The Programme of Reform. Brouwerian Semantic Theory. Brouwer's Analysis of Mathematical and Linguistic Activity. Brouwer's Analysis of Logic. Brouwer Negation. The Refutation of the PEM. Logical Negotiation and `Brouwer Logic'. The Crisis in Brouwer's Intuitionism. The Formalization of Mathematics.
Brouwer's Intuitionist Mathematics. Brouwerian Separable Mathematics. The Brouwer Mathematical Continuum.
Appendices.
Bibliography. Index.
Review quote:
...a fascinating intellectual biography... American Mathematical Monthly This is a fascinating book describing the development of Brouwer's ideas, linking the man, his Weltanschauung, his philosophy and his programme of reconstruction of mathematics on a constructive basis. Revue Roumaine de Mathématiques Pures et Appliquées Walter van Stigt has done a masterly job gathering and interpreting the facts surrounding Brouwer's life and mathematical times... He has done philosophers and historians of mathematics a considerable service by collecting and organising a vast archive of complex material, much of it written originally in Dutch. This material is highly organised with systematic appendices giving translations of many important documents. The Times Higher Education Supplement Anyone interested in Brouwer or Intuitionism in a general way will enjoy reading Chapters II, III and IV and some of the appendices... The later chapters and the appendices should be extremely valuable to anyone who would like a detailed and scholarly account of the basic logical and mathematical concepts, based on the original text. The Journal for Symbolic Logic With its emphasis on Brouwer's person and philosophy, which were instrumental for the development of the mathematics, the book is a welcome complement to the more technical introductions to constructive mathematics that are around. Mathematical Reviews Van Stigt provides an in-depth view of Brouwer, his philosophy and his foundations of mathematics... the decisive text on Brouwer's Intuitionism for many years to come. Modern Logic
Table of contents:
The Brouwer Bibliography. Publications. Unpublished Papers.
Brouwer, Life and Work. Childhood and Student Years. Post-Graduate Study. Life, Art and Mysticism. The Foundations of Mathematics. Towards an Academic Career. Intuitionism and Formalism. The Signific Interlude. The Second Act of Intuitionism. The Turbulent Years. The Brouwer Logic. The Reconstruction of Analysis. The Unfinished Books. The Brouwer-Hilbert Controversy and the Annalen Affair. The Silent Years. Post-War Lectures and Final Years.
Brouwer's Philosophy. Introduction. Character and Early Background. Philosophy, Metaphysics and Ideology. Mysticism. God and the Moral Principle. Kant and the French Intuitionist Tradition. French Mathematical Intuitionism. The Self, Consciousness and Mind. Causal Attention, Will and Cunning Activity. The Phase of Social Acting and Language.
Brouwer's Philosophy of Mathematics. The Primordial Intuition of Time. Intuitive Thinking and Mathematics. The Nature of Mathematics. Reflection on the Nature of Mathematics. Constructiveness and Existence. The Subject and the Intersubjectivity of Mathematics. The Application of Mathematics.
Language and Logic. Society and Communication. The Purpose and Origin of Language. Language and Pure Thought. The Programme of Reform. Brouwerian Semantic Theory. Brouwer's Analysis of Mathematical and Linguistic Activity. Brouwer's Analysis of Logic. Brouwer Negation. The Refutation of the PEM. Logical Negotiation and `Brouwer Logic'. The Crisis in Brouwer's Intuitionism. The Formalization of Mathematics.
Brouwer's Intuitionist Mathematics. Brouwerian Separable Mathematics. The Brouwer Mathematical Continuum.
Appendices.
Bibliography. Index.