GARY OSTERTAG A SCOREKEEPING ERROR (Received in final form 14 May 1997) In its naive formulation, Russell’s Theory of Descriptions claims that a sentence exemplifying the F is G is true just in case exactly one thing is F, and all Fs are Gs. Yet, as is well known,this formu- lation fails to account for many of our truth-conditional intuitions concerning sentences exemplifying the relevant surface grammar. The current paper proposes an implementation of Russell’s theory within a framework that accommodates these intuitions. The general framework adopted is one according to which quantifiers, including definite descriptions, are to be interpreted relative to a contextually- determined domain of individuals. I am thus assuming a claim that some may find controversial – namely, that descriptions, according to Russell’s theory, are quantifiers. While I cannot do that issue justice here, I think the assumption is correct. However, those who part company with me with respect to my fidelity to Russell may nonetheless find something of interest in what follows, since the problem I will be discussing, as well as the solution proposed, is applicable to a ubiquitous linguistic phenomenon – incom- plete quantification. Gaining an understanding of this phenomenon will help to illuminate the relation between the uses we make of sentences and the meanings these uses carry. Before discussing the approach I favor, however, I will describe an alternative approach and indicate why we should avoid it. In section 1 this approach is developed and criticized. Section 2 provides increasingly refined characterizations of the general approach I endorse; these are developed in response to a counter- example due to David Lewis. I show that the final formulation is immune to Lewis’s counterexample. Finally, I present possible objections that this account faces, and indicates some lines of response. 1 Philosophical Studies 96: 123–146, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands.