Abstract

In the present philosophy of mathematics, we can distinguish three different styles of philosophical analysis: the normal or standard style, which is logically and foundationally oriented; the analytical style considering philosophy of mathematics as a branch of analytic philosophy, i.e. primarily focused on philosophical issues about ontology and epistemology; a fairly recent mixed style, trying to capture the many facets of mathematics as a cultural system and anchored to the so-called mathematical practice. After 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.