O Departamento de Filosofia da UFRN, através da Base de Pesquisa "Lógica, Conhecimento e Ética", dá continuidade a sua programação anual dos Seminários de Lógica e Filosofia Formal, juntamente com o Grupo de Lógica, Linguagem, Informação, Teoria e Aplicações LoLITA, com a palestra:
Genetic Proofs, Reductions and Rational Reconstruction Proofs. Profa. Dra. Michelle Friend Department of Philosophy/Columbian College of Arts & Sciences Washington University Data:22 /06 / 2012, às 16h. Local: UFRN, Setor II, sala I5 Abstract: Some theorems in mathematics have several proofs. Why? It is clear that proofs are not meant to only convince us of the truth of the theorem being proved. Rather, they give us explanations. I explore the philosophical implications of three conceptions of proof: the genetic conception, reductions and the rational reconstruction conception. The genetic conception traces a theorem back to the setting in which the mathematician thought of the proof and the theorem. We learn the historical origin of the theorem. The reduction traces the theorem back to some more primitive conceptions. The primitive conceptions are associated with a foundational project, such as constructivism, realism or logicism. With such a proof, we learn the conceptual justification for the theorem. The rational reconstruction conception of proof is one where we demonstrate that it is possible to understand a theorem in a novel setting, for example, we might give a proof in Topos theory of a theorem in geometry. We learn the spread of the theorem: in what other theories it is provable. The lessons become more interesting when the novel setting is inconsistent with the original setting. As an example, I shall focus on Lobachevskys solution to the problem of indefinite integrals. I shall compare Lobachevsky, Beltrami and Rodins constructions and re-constructions, and offer one of my own, pointing out the lessons in each case. Lobachevsky give the genetic proof, Beltrami reduces the proof to Euclidean geometry, which was thought to be more obvious, or primitive. Rodin reconstructs the proof in topos theory to give a neutral proof, which is closer to Lobachevskys purpose. I give a reconstruction using techniques developed in the paraconsistency literature, in order to justify using what might look like contradictory methods. Each type of proof teaches us different lessons. _______________________________________________ Logica-l mailing list [email protected] http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l
