Russell, Idealism, and the Emergence of Analytic Philosophy

By Peter Hylton | Go to book overview

6 'On Denoting'

In the previous chapter we briefly examined the notion of denoting as it appears in The Principles of Mathematics. The point of that notion, as we saw, is to allow a proposition to be about an object which it does not contain. The theory is that there are certain entities, called 'denoting concepts', which have the following property: if a proposition contains a denoting concept then it is not about that concept but is rather about an object to which the concept stands in a special relation, called 'denoting'. In such a case the object which the proposition is about, 'the denotation' or 'the denoted object', as we might call it, may be either a single term (as is that denoted by the denoting concept The First President of the USA) or a complicated sort of collection of terms (as is that denoted by Any Republican); there may even be denoting concepts which do not in fact denote anything. Our understanding of the issues surrounding the theory of denoting concepts, as I shall call it, is impeded by a complexity which we have already discussed. Russell often seems to assume that this theory suffices to explain generality—in particular, that we can understand unrestricted variables by means of the denoting concept any term, and that this is all that is needed. At other moments, however, Russell explicitly—and convincingly—argues that the theory of denoting concepts will not explain multiple generality. At such moments it appears that the crucial step in the explanation of generality is the postulation of propositional functions as indefinable entities standing in a particular relation to the propositions which are their values. The theory of denoting concepts is more or less irrelevant to this explanation. We shall return to this complexity. For the moment the relevant point is that Russell rejects the theory of denoting concepts in 'On Denoting'. 1 The aim of this chapter is to examine the nature of this change in Russell's views, and other changes which took place around the same time. Our discussion will draw on as yet unpublished manuscripts written by Russell between 1903 and 1905. 2

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