Arithmetization of Metamathematics
My PhD project investigates the phenomenon of intensionality in metamathematics and, more specifically, in Gödel's second incompleteness theorem.
It aims first to critically evaluate the different sources of intentionality due to the arithmetization of the syntax, and to defend a criterion of admissibility of numbering as well as general conditions under which an arithmetical formula can express a syntactic property.
Second, it explores the philosophical interpretations of Gödel's second incompleteness theorem and its consequences on Hilbert's program. Through the different provability predicates, it seeks to answer the question 'What is a consistency statement?'.
Arbitrary Objects
In my master's thesis, I defended a new interpretation of the principle of generic attribution for arbitrary objects and sketched some potential applications in the philosophy of mathematics. I continue working on these topics.
