Apenas pequenas correções: os nomes corretos da nossa convidada e de sua instituição são "Michèle Friend" e "George Washington University" http://departments.columbian.gwu.edu/philosophy/people/131
Agradecido pela atenção, Joao Marcos LoLITA On Thu, Jun 7, 2012 at 11:15 AM, <[email protected]> wrote: > 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 Lobachevsky’s solution to the > problem of indefinite integrals. I shall compare Lobachevsky, Beltrami and > Rodin’s 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 Lobachevsky’s 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 -- http://sequiturquodlibet.googlepages.com/ _______________________________________________ Logica-l mailing list [email protected] http://www.dimap.ufrn.br/cgi-bin/mailman/listinfo/logica-l
