Abstract

It is often assumed that concepts from the formal sciences, such as mathematics and logic, have to be treated differently from concepts from non-formal sciences. This is especially relevant in cases of concept defectiveness, as in the empirical sciences defectiveness is an essential component of lager disruptive or transformative processes such as concept change or concept fragmentation. However, it is still unclear what role defectiveness plays for concepts in the formal sciences. On the one hand, a common view sees formal concepts to be protected against defects because of their precise and stable nature. On the other, studies going back as far as Lakatos (1963) showcase the changeability of such concepts. In this paper, I will investigate if and how defectiveness based on the occurrence of inconsistencies can appear with formal concepts. To make the case as strong as possible, I employ a strict notion of formal concept that assumes the concept to have a fixed and definite extension. I will show that there are indeed certain types of defectiveness that cannot occur with such concepts; but that there are other types of defectiveness that do occur. This means that while formal concepts have to be treated differently than non-formal concepts, questions about defectiveness---as raised in the conceptual engineering debate and philosophy of science---can still be applied to them. I will highlight this point by showing how formal sciences have special strategies available to them that allow them to resolve defectiveness of their concepts in a flexible and informative manner.