Philosophy of Mathematics seminar

Carlo Nicolai, King’s College London

Graph conceptions of properties  

Concerns about the expressive limitations of type-theoretic approaches to properties may lead philosophers to favour type-free options, typically formulated in a first-order language. Given the success of standard set theory and the iterative conception, there have been attempts to formulate theories of properties based on ZFC, justified by an iterative picture. Such approaches, although prima facie type-free, ban any form of self-predication/instantiation, which is in some cases desirable for properties, if not for sets. An obvious alternative is to explore theories of properties based on non-wellfounded set theories and the conceptions on which they are based. In the talk I will discuss and develop this alternative.