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Oneindigheid --- Infini
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Les essais réunis dans ce livre traitent de notions de tout temps centrales dans la réflexion des philosophes, logiciens et mathématiciens : l’infini, le nombre, la vérité, la conséquence logique, l’explication, la pureté des méthodes, le nominalisme, le platonisme. La première partie montre les perspectives philosophiques nouvelles ouvertes d’une part par des théories non cantoriennes de calcul de l’infini et, d’autre part, par la mise en question du prétendu statut analytique du principe de Hume, duquel sont dérivables les axiomes de l’arithmétique du second ordre. Dans la deuxième partie l’auteur exploite des ressources d’archives inédites pour montrer la richesse des débats philosophiques que Tarski a entretenus notamment avec Carnap, Neurath et Quine lors de l’élaboration de ses concepts logiques. La troisième partie est consacrée à la « philosophie de la pratique mathématique ». Des études de cas puisés dans la géométrie projective et dans la géométrie algébrique réelle sont l’occasion d’une étude analytique des notions d’«explication mathématique» et de «pureté des méthodes». Ces contributions à l’histoire et la philosophie de la logique et des mathématiques illustrent la manière très originale dont Paolo Mancosu parvient à marier les perspectives historique, logico-mathématique et analytique de la philosophie.
Logique mathématique --- Infini. --- Mathématiques --- Philosophie. --- Infini --- Logique
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We are all captivated and puzzled by the infinite, in its many varied guises; by the endlessness of space and time; by the thought that between any two points in space, however close, there is always another; by the fact that numbers go on forever; and by the idea of an all-knowing, all-powerful God. In this acclaimed introduction to the infinite, A. W. Moore takes us on a journey back to early Greek thought about the infinite, from its inception to Aristotle. He then examines medieval and early modern conceptions of the infinite, including a brief history of the calculus, before turning to Kant and post-Kantian ideas. He also gives an account of Cantor's remarkable discovery that some infinities are bigger than others. In the second part of the book, Moore develops his own views, drawing on technical advances in the mathematics of the infinite, including the celebrated theorems of Skolem and Goedel, and deriving inspiration from Wittgenstein. He concludes this part with a discussion of death and human finitude. For this third edition Moore has added a new part, `Infinity superseded', which contains two new chapters refining his own ideas through a re-examination of the ideas of Spinoza, Hegel, and Nietzsche. This new part is heavily influenced by the work of Deleuze. Also new for the third edition are: a technical appendix on still unresolved questions about different infinite sizes; an expanded glossary; and updated references and further reading. The Infinite, Third Edition is ideal reading for anyone interested in an engaging and historically informed account of this fascinating topic, whether from a philosophical point of view, a mathematical point of view, or a religious point of view.
Metaphysics --- Infinite. --- Infini. --- Infinite
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Infini. --- Infinite. --- Philosophy. --- Science.
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