Formas de matematización de la filosofía natural: Galileo y la redefinición sociocognitiva de sus matemáticas

The topic of this paper is the certainty of mathematics during the 16th and 17th centuries. The specific problem it addresses is that mathematics, in this context, does not provide causal explanations and therefore is not considered to be part of natural philosophy. My working-hypothesis is that the epistemological redefinition of mathematics depends on the practices and on sociocognitive factors; I suggest that there is a redefinition of practices and of the treatment of objects, such as the inclined plane, the balance, the lever and the pendulum. In order to develop this idea, I will firstly analyze the question of the hegemony of natural philosophy over mathematics. Secondly, I will present the relationship between mathematics and natural philosophy, based on the conceptual and practical uses of objects in the Galilean context. Finally, I will point out the practical and epistemological redefinition of mathematics as the study of mathematics applied to motion.