Philosophy of Mathematics seminar

Carolin Antos, Konstanz

Defective concepts and pluralism in mathematics  

Concept defectiveness and its effects on science are at the centre of discussions in the philosophy of science and conceptional engineering. In this talk, I will transfer this discussion to the formal sciences such as mathematics and logic. I will provide an account of defectiveness for formal concepts and discuss how they occur in the formal sciences. Of particular relevance will be the continual occurrence of defectiveness, meaning that there are concepts that while being recognised as defective are still being used without changing or discarding them. As a main example I will discuss the case of choiceless large cardinals and how this might provide an argument for pluralism in set theory.