Philosophy of Mathematics seminar

Martin Fischer, LMU München

Predicativity, Potentiality and Partiality

In his ``Reflecting on incompleteness" (1991) Feferman presented a version of predicativism based on the notion of the reflective closure of a schematic theory. In my talk I present a potentialist interpretation of Feferman's predicativism `given the natural numbers'. This reading is supposed to clarify issues concerning the coherence of Feferman's presentation in 1991 but also the connection to Feferman's conceptual structuralism. The notion of definiteness plays a crucial role in this form of structuralism. Feferman suggests a use of intuitionistic logic for non definite parts of mathematics. I will consider the alternative of using an internal, partial notion of truth based on a logic called HYPE, which would be closer to the 1991 presentation.