DIEGO MANTOANELLI SILVA

Since the systematization of geometry proposed by Euclid, two questions have emerged and attempted to be answered throughout history: "How do you reach the primitive terms of a geometric theory?" and "How can a geometry be applicable to the concrete world of sensible experiences?" Based on these questions, the aim is to offer an analysis of the relation between the foundations of geometry and knowledge of empirical reality through the description of two movements: one ascending, starting from what is concrete (or non-linguistic) to what is abstract (linguistic), and the other, descending, interpreting parts of reality with the abstract terms of a theory to create models that describe empirical reality. To outline these movements, an effort is made to expose the structure of geometric thinking, to question the distinction between synthetic and analytic in the context of geometries, to evaluate the possibilities of the applicability of geometries as coincidence and convenience and to propose the intersubjective interpretation of theoretical terms as the most likely path for applying a geometry to empirical reality