Russell's first theory of denoting and quantification
Russell presented his first theory of denoting in his 1903 work, The principles of mathematics. One of the most important applications of that theory is to the analysis of sentences containing denoting phrases; but in spite of its importance this application has been widely misunderstood. Misinterpretation of Russell's theory is largely due to a failure to notice two complications; first, that the finished text contains two different formulations of the theory of denoting - the 'early' and the 'late' formulations - drawn from different drafts of the manuscript. Second, that the early formulation of the theory, on which Russell's analysis of sentences containing denoting phrases is based, itself contains incompatible accounts of denoting and of denoted objects. This paper addresses these complications, and has two objectives: first, to disentangle and examine the different versions of Russell's theory, with special emphasis on the common features by virtue of which each version of the early formulation is supposed to apply to the analysis of sentences containing denoting phrases. Second, to examine the cogency and consistency of the resulting accounts, which for convenience are called the official and unofficial versions. It is argued that both versions are meant to distinguish among denoting phrases by appealing to their quantificational force and their scope in sentences in which they occur. This thesis is defended by a detailed examination of Russell's illustrations of his theory. As interpreted, each version of Russell's theory of denoting can, with some restructuring, be given a logically cogent and rigorous formulation, and one, moreover, which is metaphysically neutral in the sense of requiring no special ontological commitments. The official version's appeal to complex objects can be given a metaphysically neutral explication in terms of the resources of Montague semantics; and the unofficial version's appeal to variable (or arbitrary) objects can be explicated in terms of supervaluations.
scientific article; zbMATH DE number 3950481