The mathematization of nature and the philosophical foundations of mechanical theory

The aim is approaching the problem of the mathematization, as knowledge philosophy, and representation of the natural phenomena according to the synthetic method of mechanical theory. This method reduces physical theory to building up mechanical models. The criticism to this approach, by construction of bizarre models, is followed by the development of the analytic mechanics and its interpretation as a language and its extension to other domains of physics. The conflict between both interpretations defines the background for the debate between Duhem and Poincare on the cognitive value of science the source of Duhem's structural and convergent realism.