Rodrigo Figueiredo

In this article, we seek to analyze some of the methodological assumptions that contribute to the understanding of Foucault’s nominalism, as well as some of the theoretical consequences of this nominalism. With this intent, in the first part, we deal with his “refusal” of universals, emphasizing the distinction, made in the first volume of the History of Sexuality, between sex and sexuality. In a second moment, we underline this option of Foucault’s method based on excerpts from Nietzsche that demarcate the knowledge’s arbitrary and contingent character.

O-minimal geometry generalizes both semialgebraic and subanalytic geometries, and has been very successful in solving special cases of some problems in arithmetic geometry, such as André–Oort conjecture. Among the many tools developed in an o-minimal setting are cohomology theories for abstract-definable continuous manifolds such as singular cohomology, sheaf cohomology and Čech cohomology, which have been used for instance to prove Pillay’s conjecture concerning definably compact groups. In the present thesis we elaborate an o-minimal de Rham cohomology theory for abstract-definable $C^{\infty }$ manifolds in an o-minimal expansion of the real field which admits smooth cell decomposition and defines the exponential function. We can specify the o-minimal cohomology groups and attain some properties such as the existence of Mayer–Vietoris sequence and the invariance under abstract-definable $C^{\infty }$ diffeomorphisms. However, in order to obtain the invariance of our o-minimal cohomology under abstract-definable homotopy we must work in a tame context that defines sufficiently many primitives and assume the validity of a statement related to Bröcker’s question.Abstract prepared by Rodrigo Figueiredo.E-mail: [email protected]: https://doi.org/10.11606/T.45.2019.tde-28042019-181150.

Este artigo tem como objetivo abordar o tratamento dado por Foucault ao tema da produção dos sujeitos e objetos do conhecimento. A partir de conceitos fundamentais de Foucault como saber, poder, prática e discurso, procuro ressaltar a influência que os textos de Nietzsche dedicados ao conhecimento tiveram sobre a abordagem genealógica foucaultiana. Passando por alguns textos de teor metodológico de Foucault, pretendo mostrar como a sua genealogia é marcada por uma crítica do conhecimento em que se questiona, a partir de uma perspectiva nietzschiana, o estatuto da relação entre sujeito e objeto e os modos de constituição da verdade são questionados.