Incomplete Symbols and Russell's Proof

Abstract

The primary purpose of this paper is to explain Russell's notion of ‘incomplete symbol’. The paper was provoked by some discussions of a controversial argument, advanced by Russell in several places - as early as Principia Mathematica (1910) and as late as My Philosophical Development (1959) - whose conclusion is that definite descriptive phrases have no meaning. It will be shown how the doctrine of incomplete symbols helps to resolve some of the questions raised about this argument.One virtue of the account given here is that the theory of definite descriptions may be seen to continue the departure from the earlier Principles of Mathematics approach, where it is allowed that “grammar, though not our master, will yet be taken as our guide” (p. 42), to the quite different outlook of “The Philosophy of Logical Atomism” where logical grammar and a logically perfect language are distinguished from natural languages and their (apparent) grammars. It marks a departure from “surface” grammar even more radical than that marked by the Frege-Russell treatment of quantification, but yet is a continuation of that same approach to language.