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Mathématiques philosophiques et abduction by Saeb Elamami

Mathématiques philosophiques et abduction

by Saeb Elamami
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Book cover type: Paperback
  • ISBN13: 9786209276712
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Editions Universitaires Europeennes
  • Publisher Imprint: Editions Universitaires Europeennes
  • Publication Date:
  • Pages: 276
  • Original Price: GBP 79.95
  • Language: French
  • Edition: N/A
  • Item Weight: 372 grams
  • BISAC Subject(s): General

L'hypoth�se de ce travail consiste � dire qu'il y a des "math�matiques philosophiques". L'id�e qui sera d�fendue est que certaines pratiques des math�matiques fondamentales (comme le forcing, la recherche d'axiomes pour r�soudre CH, les math�matiques inverses) et non fondamentales (alg�bre, analyse, topologie et th�orie des nombres) incorporent une dimension philosophique � travers l'usage de m�thodes abductives, structur�es par trois perspectives h�rit�es de l'histoire de la philosophie: socratique (questionnement), aristot�licienne (recherche des principes premiers) et kantienne (exigence de sens). L'exemple central de ces m�thodes reste le forcing, o� la construction du mod�le M[G] satisfaisant �CH s'appuie sur un raisonnement abductif pr�alable (recherche des hypoth�ses � injecter) qui rel�ve des trois perspectives philosophiques cit�es. Mais, outre l'exemple technique du forcing comme cas paradigmatique o� la triade philosophique est op�rante, la r�flexion sera �tendue au-del� des math�matiques formelles (des fondements) vers les math�matiques habituelles, montrant ainsi l'universalit� de cette recherche.

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