Artículos con la etiqueta ‘topos’

Alain Badiou’s Mistake — Two Postulates of Dialectic Materialism

Por • 8 ene, 2013 • Category: Filosofía

To accompany recent openings in category theory and philosophy, I discuss how Alain Badiou attempts to rephrase his dialectic philosophy in topos-theoretic terms. Topos theory bridges the problems emerging in set-theoretic language by a categorical approach that reinscribes set-theoretic language in a categorical framework. Badiou’s own topos-theoretic formalism, however, turns out to be confined only to a limited, set-theoretically bounded branch of locales. This results with his reduced mathematical understanding of the ‘postulate of materialism’ constitutive to his account. Badiou falsely assumes this postulate to be singular whereas topos theory reveals its two-sided nature whose synthesis emerges only as a result of a (quasi-)split structure of truth. Badiou thus struggles with his own mathematical argument. I accomplish a correct version of his proof the sets defined over such a ‘transcendental algebra’ T form a (local) topos. Finally, I discuss the philosophical implications Badiou’s mathematical inadequacies entail.

The unification of Mathematics via Topos Theory

Por • 18 abr, 2011 • Category: Filosofía

We present a set of principles and methodologies which may serve as foundations of a unifying theory of Mathematics. These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as `bridges’ for transferring information, ideas and results between distinct mathematical theories.