Mathematics and Philosophical Reflection. (Ordinario)

Since the very beginnings of Western philosophy, mathematics has been a profound and enduring source of philosophical inquiry. Starting with the question of its conceptual autonomy, mathematics has not only fueled key epistemological and ontological debates, but has also served as a paradigm of rigor and precision for philosophical reflection itself.

The two modules aims to introduce students to several central themes in the philosophy of mathematics, with particular emphasis on issues that are central to contemporary debates and of relevance to philosophy as a whole. Topics addressed include:

• the ontological nature of mathematical objects (Do they exist independently of us? Are they abstract entities or mental constructions?);
• the notion of mathematical truth and the comparison of different conceptions (Platonism, formalism, intuitionism, constructivism);
• the problem of mathematical knowledge (How can we come to know abstract truths? What is the role of intuition, proof, and evidence?);
• the role of logic in the foundations and development of mathematics;
• the applicability of mathematics to the physical world (Why and how do such abstract structures prove to be extraordinarily effective in describing reality?).