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Mathematics --- Mathematicians --- Philosophy --- History --- Hilbert, David, --- Influence. --- Mathematics - Philosophy - History - 20th century. --- Mathematics - History - 20th century. --- Mathematicians - Germany - Biography.

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Comment les mathématiques, pure création de l'esprit humain, peuvent-elles s'appliquer au monde réel qui nous entoure ? Comment les géométries non euclidiennes, nées de spéculations abstraites, peuvent-elles décrire l'atome ou l'Univers ? Comment la pure logique du calcul des probabilités peut-elle servir à établir les lois de la physique ou les statistiques des assurances ? Ce sont ces questions qu'affronte dans l'entre-deux guerres l'empirisme logique, ce grand courant du rationalisme européen qui suscite aujourd'hui un intérêt nouveau. Ses grandes figures, Carnap, Schlick. Reichenbach et quelques autres, ont été des penseurs très différents et profondément originaux. La philosophie des sciences contemporaine a encore de nombreuses leçons à tirer de leurs innovations conceptuelles et de leurs débats internes, mais aussi de la réflexion sur les limites de leur démarche et sur les obstacles qu'ils ont rencontrés.

Mathematics --- Logical positivism --- Philosophy --- History --- Mathematics - Philosophy - History - 20th century - Congresses --- Logical positivism - History - 20th century - Congresses --- Philosophie et mathématiques --- Positivisme logique --- Philosophie et sciences --- Logique symbolique et mathématique --- Congrès

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Geschiedenis van de wetenschappen --- Histoire des sciences --- Huldeboeken --- Mélanges --- Rashed, Roshdi --- Science --- Mathematics --- Philosophy --- Mathematics, Arab --- History --- Philosophy. --- Mathematics, Arab. --- History. --- Natural science --- Science of science --- Sciences --- Mental philosophy --- Humanities --- Math --- Arab mathematics --- Mathematics, Arabic --- Philosophy&delete& --- Natural sciences --- Science - Philosophy - History --- Science - History --- Mathematics - Philosophy - History --- Mathematics - History

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La conception qu’Emmanuel Kant se faisait des mathématiques était en parfaite consonance avec l’opinion philosophique la plus courante au XVIIIe siècle à l’égard de cette science. Il conviendrait par conséquent de tenir davantage compte de l’histoire des idées scientifiques, ce qui permettrait de faire remarquer que la pensée kantienne relève d’un paradigme scientifique plus ancien, celui de la géométrie euclidienne (où l’image reste intimement articulée au signe), alors que les critiques ordinairement adressées au Kant mathématicien s’appuient indirectement sur l’héritage de la révolution algébrique par lequel le signe est désormais dissocié de l’image. Il convenait donc d’examiner dans le plus grand détail la manière dont, à travers son œuvre, Kant recevait et discutait les conceptions mathématiques de son temps, et en particulier la tension marquée entre la géométrie et l’arithmétique. Ce faisant, il redevient possible de recontextualiser le concept kantien d’intuition par rapport aux évidences de son temps, qui ne sont plus tout à fait les nôtres. Les réticences de Kant vis-à-vis des concepts les plus problématiques de l’algèbre se laissent ainsi interpréter à nouveaux frais, faisant ressortir la signification de l’architectonique.

Mathematics --- Kant, Immanuel --- Philosophy, German --- Mathématiques --- Philosophie allemande --- Philosophy --- History --- Philosophie --- Histoire --- Kant, Immanuel, --- Knowledge --- Mathematics. --- Mathématiques --- Math --- Science --- Kant, Emmanuel --- Kant, Emanuel --- Kant, Emanuele --- Kant, I. --- Kānt, ʻAmmānūʼīl, --- Kant, Immanouel, --- Kant, Immanuil, --- Kʻantʻŭ, --- Kant, --- Kant, Emmanuel, --- Ḳanṭ, ʻImanuʼel, --- Kant, E., --- Kant, Emanuel, --- Cantơ, I., --- Kant, Emanuele, --- Kant, Im. --- קאנט --- קאנט, א. --- קאנט, עמנואל --- קאנט, עמנואל, --- קאנט, ע. --- קנט --- קנט, עמנואל --- קנט, עמנואל, --- كانت ، ايمانوئل --- كنت، إمانويل، --- カントイマニユエル, --- Kangde, --- 康德, --- Kanṭ, Īmānwīl, --- كانط، إيمانويل --- Kant, Manuel, --- Mathematics - Philosophy - History - 18th century.

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The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating in the famous Hilbert-Brouwer controversy in the 1920s. The purpose of this anthology is to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. What can we say, in retrospect, about the various foundational programmes of the classical period and the disputes that took place between them? To what extent do the classical programmes of logicism, intuitionism and formalism represent options that are still alive today? These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics. The volume will be of interest primarily to researchers and graduate students of philosophy, logic, mathematics and theoretical computer science. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.

Intuitionistic mathematics. --- Mathematics -- Philosophy -- History. --- Mathematics. --- Intuitionistic mathematics --- Mathematics --- Mathematical Theory --- Physical Sciences & Mathematics --- History --- Philosophy --- History. --- Math --- Epistemology. --- Logic. --- Ontology. --- Language and languages --- Mathematical logic. --- Mathematical Logic and Foundations. --- Philosophy of Language. --- History of Mathematical Sciences. --- Philosophy. --- Science --- Constructive mathematics --- Logic, Symbolic and mathematical. --- Linguistics --- Genetic epistemology. --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Psychology --- Reasoning --- Thought and thinking --- 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 --- Developmental psychology --- Knowledge, Theory of --- Methodology --- Language and languages—Philosophy. --- Annals --- Auxiliary sciences of history --- Epistemology --- Theory of knowledge