Diagrammes et Catégories

Abstract : Some results of mathematics or physical sciences, more particularly from the second half of the XXe century, lead to a new approach of the philosophical concept of diagram, which is the heart of the mathematical theory of categories, topos and sketches. On the basis of the report that diagrams and categories force with ontological options, their relationship is studied by following four fundamental concepts which form the epistemic square (virtuality, fonctoriality, universality and duality). Virtuality is necessary because a table does not exist in the same manner as the blue of the sky which does not have material reality. The fonctoriality and Yoneda's lemma involve to reconsider the statute of object. Diaconescu's theorem shows the idea that the internal logic of a topos is determined by its topology, and sometimes logical investigations are more important than it should be. Universality and duality move the concept of truth. The truth is not a simple valuation, but a "truth-lightning", a "truth-event" which works by adequacy and topological resonance of large sides of knowledge, not any more by logical inference. Diagrams are the place of this truth which goes through gesture. Consequently, it becomes possible to cross ontology and topology in an onto-(po)-logy (or a toposic ontology) which is not in contraction with French theory. Univocity of the concept of being is not opposed to the categorial approach. More : dual forms encourages to think the assumption that the concept of one is the dual of the concept of being
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Submitted on : Monday, December 3, 2007 - 11:28:53 AM
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Franck Jedrzejewski. Diagrammes et Catégories. Philosophie. Université Paris-Diderot - Paris VII, 2007. Français. ⟨tel-00193292⟩

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