Talk: Robert May (UC Davis)

Title:

Value-ranges

Abstract:

The introduction of value-ranges of functions is an essential step forward", Frege says in describing the innovations introduced in the logical system of Grundgesetze, and he is forthcoming about the source of this superlative speech: "I define cardinal numbers themselves as extensions of concepts, and extensions of concepts are value-ranges, according to my specifications." Presenting work in collaboration with Rachel Boddy, we explore this fundamental importance Frege places on value-ranges, with focus on the tension that arises between Frege's characterization of value-ranges as objectual correlates representing concepts, essential for definitions, and the logical role they play in defining the concept of number, and how this tension leads to the inconsistency of Frege's system.