Oggetti ideali, dimostrazioni e pratica matematica

In the present philosophy of mathematics, we can distinguish three different styles of philosophical analysis: the normal or standard style, logically and foundationally oriented; the analytical style considering the philosophy of mathematics as a branch of analytic philosophy, primarily focused on philosophical issues about ontology and epistemology; and, more recently, a mixed style, trying to capture the many facets of mathematics as a cultural system and anchored to the so-called mathematical practice. After a start focusing on the traditional ontological questions, we deal with the interaction between logical analysis, foundational themes and mathematical practice, and we conclude by suggesting an interpretation of foundational research.