Este artigo tem como objetivo geral apresentar alguns aspectos básicos da filosofia da matemática de Charles Sanders Peirce, com o intuito de suscitar discussão posterior. Especificamente, são ressaltados: o lugar da matemática na classificação das ciências do autor; a diferença entre matemática e filosofia como cenoscopia; a relação entre as categorias da fenomenologia e matemática; o conceito de experiência e sua formalização possível; a distinção geral entre lógica, como parte da investigação filosófica, e matemática.

Discussions concerning belief revision, theorydevelopment, and ``creativity'' in philosophy andAI, reveal a growing interest in Peirce'sconcept of abduction. Peirce introducedabduction in an attempt to providetheoretical dignity and clarification to thedifficult problem of knowledge generation. Hewrote that ``An Abduction is Originary inrespect to being the only kind of argumentwhich starts a new idea'' (Peirce, CP 2.26).These discussions, however, led to considerabledebates about the precise way in which Peirce'sabduction can be used to explain knowledgegeneration (cf. Magnani, 1999; Hoffmann, 1999).The crucial question is (...) that of understandinghow we can get the new elements capableof enlarging our theories. Under thesecircumstances, it might be helpful to step outof the entanglement and reconsider the basis ofthe problem that originally triggered Peirce'sinterest in abduction. This will lead us toanother Peircean concept, that of ``diagrammaticreasoning,'' which I discuss here in the contextof his ``pragmatism.'' In this way, I hope toreach a better understanding of thecontribution of ``abduction'' to the knowledgegeneration process. (shrink)