Prof. Jouko Väänänen (University of Helsinki) on categoricity arguments and their philosophical use 

On April 4, 2023, at the Faculty of Philosophy of the University of Warsaw prof. Jouko Väänänen from the University of Helsinki delivered a lecture “Categoricity Arguments and Their Philosophical Uses.”

Prof. Jouko Väänänen is a Finnish mathematician, logician and philosopher known for his contributions to the foundations of mathematics, logic and model theory. He is currently a professor at the University of Helsinki and the University of Amsterdam. We publish an abstract of his paper below.

Abstract: I will discuss arguments that have been given for the categoricity of second-order foundational theories such as arithmetic and set theory. I will present the concept of internal categoricity which lowers the meta-theoretic assumptions behind the categoricity theorems. Finally, I show that internal categoricity is a phenomenon that exists for first-order arithmetic and set theory, too.