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Constructive mathematics --- Intuitionistic mathematics --- Mathématiques constructives --- Mathématiques intuitionnistes --- Congresses --- Congrès --- Brouwer, L. E. J. --- Brouwer, L E J --- -Intuitionistic mathematics --- -Constructive mathematics --- Mathematics --- Mathematics, Constructive --- Logic, Symbolic and mathematical --- Congresses. --- -Congresses --- Brouwer, Luitzen Egbertus Jan --- -Mathematics, Constructive --- Physical Sciences & Mathematics --- Mathematical Theory --- Brouwer, Luitzen Egbertus Jan, --- Brouwer, Bertus, --- Constructive mathematics - Congresses --- Intuitionistic mathematics - Congresses --- Brouwer, L E J - (Luitzen Egbertus Jan), - 1881-1966

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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, Luitzen Egbertus Jan --- Brouwer, L. E. J. (Luitzen Egbertus Jan), 1881-1966. --- Intuitionistic mathematics. --- Mathematicians -- Netherlands -- Biography. --- Mathematics -- Philosophy. --- Mathematicians --- Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- Brouwer, L. E. J. --- Brouwer, Luitzen Egbertus Jan, --- Mathematics. --- History. --- Mathematical logic. --- Topology. --- Popular works. --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Popular Science, general. --- Logic, Symbolic and mathematical. --- Science (General). --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Algebras, Linear --- Annals --- Auxiliary sciences of history --- Math --- Science --- Mathematicians. --- Symbolisk logik. --- Brouwer, Luitzen E. J., --- Netherlands. --- Brouwer, Bertus,

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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? The 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. "It is almost as if one could hear the two rebels arguing their case in a European café or on a terrace, and coming to a common understanding, with both men taking their hat off to the other, in admiration and gratitude. Dr. van Atten has convincingly applied Husserl's method to Brouwer's program, and has equally convincingly applied Brouwer's intuition to Husserl's program. Both programs have come out the better." Piet Hut, professor of Interdisciplinary Studies, Institute for Advanced Study, Princeton, U.S.A.

Phenomenology. --- Sequences (Mathematics) --- Intuitionistic mathematics. --- Brouwer, L. E. J. --- Husserl, Edmund, --- Philosophy, Modern --- Constructive mathematics --- Mathematics --- Mathematical sequences --- Numerical sequences --- Algebra --- Husserl, Edmund --- Husserl, Edmond --- Brouwer, Luitzen Egbertus Jan, --- Logic, Symbolic and mathematical. --- Phenomenology . --- Ontology. --- Metaphysics. --- Mathematical Logic and Foundations. --- God --- Ontology --- Philosophy --- Philosophy of mind --- Being --- Metaphysics --- Necessity (Philosophy) --- Substance (Philosophy) --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Mathematical logic. --- Brouwer, Bertus,

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History --- Art --- biographies [documents] --- Laer, van, Pieter --- Dou, Gerard --- Rembrandt --- Witte, de, Emanuel --- Painters --- Flinck, Govaert --- Weenix, Jan Baptist --- Hondecoeter, d', Melchior --- Brouwer, Adriaen --- Berchem, Nicolaes --- Houbraken, Arnold --- Seghers, Hercules --- Potter, Paulus --- Schurman, van, Anna Maria --- Wouwerman, Philips --- Steen, Jan --- Artists --- Painting, Dutch --- Portraits --- Early works to 1800. --- Biography --- Biography. --- -Painting, Dutch --- Early works to 1800 --- biographies [literary works] --- Hollandse school --- kunstenaars --- biografieën --- van Mander, Karel I --- 15de eeuw --- 16de eeuw --- 17de eeuw --- Nederlanden --- kunstenaars. --- biografieën. --- van Mander, Karel I. --- 15de eeuw. --- 16de eeuw. --- 17de eeuw. --- Nederlanden. --- van de Venne, Adriaen Pietersz.

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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.

Lògica --- Argumentació --- Dialèctica (Lògica) --- Lògica deductiva --- Filosofia --- Intel·ligència --- Psicologia --- Abstracció --- Alteritat (Filosofia) --- Categories (Filosofia) --- Certesa --- Condicionals (Lògica) --- Definició (Lògica) --- Dilema --- Evidència --- Hipòtesi --- Inconsistència (Lògica) --- Inducció (Lògica) --- Intenció (Lògica) --- Judici lògic --- Lògica deòntica --- Metodologia --- Modalitat (Lògica) --- Nominalisme --- Positivisme lògic --- Probabilitats --- Raó suficient --- Sil·logisme --- Sofismes --- Teoria del coneixement --- Universals (Filosofia) --- Metodologia de la ciència --- Pensament --- Raonament --- Karl R. Popper --- Deductive Logic --- Logical Constants --- Proof-theoretic Semantics --- Classical Logic --- Non-classical Logic --- Inferential Definitions --- Mathematical Logic --- Negation --- Modalities --- History of Logic --- L.E.J. Brouwer --- Paul Bernays --- Rudolf Carnap --- Alonzo Church --- Kalman Joseph Cohen --- Henry George Forder --- Harold Jeffreys --- Stephen Cole Kleene --- Logic. --- Mathematical logic. --- Language and languages --- Mathematical Logic and Foundations. --- Stylistics. --- Style. --- Linguostylistics --- Stylistics --- Literary style --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Methodology