Philosophy of Mathematics: Ontology and Structures

This lecture delves into the philosophical perspectives on the exact sciences, exploring the existence of mathematical objects, the truth of mathematical propositions, and our knowledge about them. It discusses various theories such as Platonism, Intuitionism, Structuralism, Nominalism, Logicism, and Formalism. The lecture also covers significant concepts like the two constructions of natural numbers, Russell's Paradox, Gödel's Theorem, and the Axiom of Choice, shedding light on the nature of mathematics and its relationship with logic and reality.