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Axiomatization, Formalization and Completeness, Paris, Collège de France, October 10th & 20th [more]
Ideals of Proof
An interdisciplinary project supported by the Agence Nationale de la Recherche, and hosted by:
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Université Nancy 2 / LHSP - Archives Henri Poincaré (UMR CNRS 7117)
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Université Paris Diderot - Paris 7 / Département d'Histoire et Philosophie des Sciences / RESHEIS (UMR CNRS 7596)
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Collège de France / Chaire de philosophie du langage et de la connaissance (Jacques Bouveresse)
- University of Notre Dame
The term 'ideals' in the title is used in two senses. The first concerns the aims and virtues of proof considered as justificative norms for mathematical practice generally. The second concerns the use of so-called "ideal" elements or methods as means of pursuing these aims.
Ideals in the first sense include not only such traditional standards as rigor, certainty, apriority, purity and explanatory gain, but also such systematic virtues as (various types of) completeness, closure, efficiency and freedom. Generally speaking, we want to improve our understanding of why such conditions and constraints as have figured as ideals of proof in the history of mathematics have so figured and whether they are truly deserving of such regard.
Ideals in the second sense include such things as the introduction of "infinites" (both large and small), imaginary and complex numbers in algebra and analysis, the use of Kummer ideals in number theory and the use of points, lines and planes at infinity in projective geometry.
