On russell’s arguments for restricting modes of specification and domains of quantification

Abstract

Russell takes his paper ‘On denoting’ to have achieved the repudiation of the theory of denoting concepts and Frege’s theory of sense, and the invention of the notion of incomplete symbols.This means that Russell attempts to solve the set theoretic and semantic paradoxes without making use of a theory of sense.Instead, his strategy is to revise his logical ontology by arguing that certain symbols should be treated as incomplete.In constructing such arguments Russell, at various points, makes use of epistemological and metaphysical considerations.These arguments do not form themselves into a systemic set of considerations to be used in appraising a logical system.Finally, the vicious circle principle is argued for on the basis of considerations, which are presumed evident, about the nature of propositional functions.The stringency of this principle is a basic problem for the system of Principia mathematica.However, even given the terms of the argument, ‘On denoting’ does not offer a complete repudiation of the notion of sense.This allows the possibility of retaining some of the insights of Principia mathematica whilst rejecting the stringency of the vicious circle principle.The basis of such a system is the theory of sense