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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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This title examines the Pythagorean idea that number is the key to understanding reality, describing first the Pythagorean interests of Platonists in the second and third centuries and then Iamblichus's programme to Pythagoreanize Platonism in the fourth century in his work 'On Pythagoreanism'.

Pythagoras and Pythagorean school. --- Mathematics --- Philosophy --- History. --- -Pythagoras and Pythagorean school --- Math --- -History --- Pythagoras and Pythagorean school --- Philosophy, Ancient --- Science --- Philosophy&delete& --- History --- Pythagorisme --- Mathématiques --- Philosophie --- Histoire --- Mathematics - Philosophy - History.

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Amid the unrest, dislocation, and uncertainty of seventeenth-century Europe, readers seeking consolation and assurance turned to philosophical and scientific books that offered ways of conquering fears and training the mind& guidance for living a good life. 'The Good Life in the Scientific Revolution' presents a triptych showing how three key early modern scientists, Rene; Descartes, Blaise Pascal, and Gottfried Leibniz, envisioned their new work as useful for cultivating virtue and for pursuing a good life. Their scientific and philosophical innovations stemmed in part from their understanding of mathematics and science as cognitive and spiritual exercises that could create a truer mental and spiritual nobility. In portraying the rich contexts surrounding Descartes' geometry, Pascal's arithmetical triangle, and Leibniz's calculus, Matthew L. Jones argues that this drive for moral therapeutics guided important developments of early modern philosophy and the Scientific Revolution.

Mathematics --- Science --- Philosophy --- History --- Moral and ethical aspects. --- Descartes, Rene. --- Descartes, René. --- Leibniz, Gottfried Wilhelm. --- Mathematics. --- Mathematics - Philosophy - History - 17th century. --- Pascal, Blaise. --- Science - History - 17th century. --- Science - Moral and ethical aspects. --- Science. --- Physical Sciences & Mathematics --- Sciences - General --- Moral and ethical aspects --- Descartes, René, --- Pascal, Blaise, --- Leibniz, Gottfried Wilhelm,

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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