MATHEMATICS AS THEORY OF STRUCTURES

In the twentieth century, it was stipulated that the analysis of the conditions of possibility of scientific knowledge was one of the central objectives of the general philosophy of science. And certainly, philosophy of mathematics is part of philosophy of science, so that we should be able to analyze the conditions of possibility of mathematical knowledge according to the dominant approaches in areas such as natural science. But, contrary to what happens with natural-scientific knowledge, where the reality of the phenomena known is given, in mathematics there is no consensus on what is the reality it is dealing with. One of the fundamental problems facing today's philosophy of mathematics is, then, that to undertake a discussion about the possibility of mathematical knowledge we should already have an ontology of mathematics, in order to determine what we want to know in such a theoretical domain. In this paper, we present an approach that tries to satisfy simultaneously an adequate ontological explanation of mathematics and a plausible account of epistemological difficulties from the point of view of mathematics understood as a science of purely formal structures.