Matthias Schirn

University of Munich, Munich Center for Mathematical Philosophy,

Second-Order Abstraction before and After Russells Paradox

Abstract In this talk, I analyze several aspects of Frege’s paradigms of second-order abstraction: Hume’s Principle and Axiom V. The issues dealt with include self-evidence and epistemic value with special emphasis on Axiom V, Frege’s attitude towards Axiom V before and after Russell’s discovery of the contradiction, as well as the possible role and the status of Hume’s Principle in the wake of Russell’s Paradox. In the central part, I pursue a twofold aim: (a) to shed new light on the connection between Frege’s way of introducing the primitive function-names of his logical system and the requisite self-evidence of his axioms in whose expression such a function-name occurs; and (b) to examine the conflict between the requirements of self-evidence and real epistemic value arising inevitably and invariably from Fregean abstraction principles, if they are singled out as axioms of a theory T.