Some Remarks about Russellian Incomplete Symbols

Abstract

Russellian incomplete symbols are usually conceived as an analytical residue—as what remains of the would-be entities when properly analyzed. This article aims to reverse the approach in raising another question: what, if any, does the incomplete symbol contribute to the completely analyzed language? I will first show that, from a technical point of view, there is no difference between the way Russell defines his denoting phrases in “On Denoting” and the way Frege defines his second-order concepts. But I will secondly support that the two notions have two widely different conceptual meanings: the same logical procedures which are used by Frege to increase the deductive power of his system allow Russell to logically relate quantificational notation to ordinary language. Focusing on Russell’s treatment of OD’s puzzles, I will thirdly argue that this shift constitutes the source of a deep transformation in the way logic and language are related.