Experts in: Foundations of mathematics
My research in formal logic and philosophy of science essentially focuses on the foundations of mathematics and the foundations of physics from technical, critical, historical and philosophical points of view. From a strictly philosophical viewpoint, I support a radical constructivist thesis that consists of showing that arithmetic or number theory and its internal logic are the building blocks of mathematical theories.
In philosophy of physics, my antirealist viewpoint emphasizes the internal logic of physical theories and of mathematical physics in the same constructivist spirit.
Lastly, I have also carried out parallel research into Hegel's dialectical logic and have been able to show that it is a traditional syllogistic logic coupled with the dynamic process of sublation or sursumption (Aufhebung) with the help of a double negation operation.
My research mainly concerns questions of logic, the foundations of mathematics and the philosophy of mathematics. It can be divided roughly into 3 overlapping fields: the philosophical scope and applications of categorical logic, the foundations of mathematics deriving from category theory and, lastly, the epistemology and ontology of contemporary mathematics.