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Summary In contrast to Russell, who claimed that sentences of the form "The F is G" are false if there is no F, Strawson (prefigured to some extent by Frege) claimed that the lack of an F would result in sentences of this form being either indeterminate or truth-valueless, not false.  Strawson's basic idea is that a sentence of this form doesn't assert that there is an F; rather, it presupposes it.  Without the existence of an F, it is highly unclear what the sentence says.  While many have found this analysis plausible for certain sentences, such as "The King of France is bald," it is decidedly less plausible for others, such as "The King of France is sitting in that chair."  In fact, judgments regarding sentences like these seem to be highly context-sensitive, leaving us without an easy answer regarding how we ought best understand this set of phenomena.
Key works Strawson 1950 serves to introduce the presuppositional account as a serious alternative to Russell's analysis of definite descriptions (predecessors to these ideas can be found in Frege 1948 and Frege 1956, however).  Von Fintel 2004 and Yablo 2006 delve into the range of subtle cases that can be generated in this domain, and how even minor changes can shift truth-value judgments.  Schoubye 2009 has subsequently pushed against von Fintel and Yablo's positive suggestions and offered a variant of the Strawsonian analysis in their place.  Finally, Elbourne 2010 defends the Strawsonian account by appeal, in particular, to how descriptions embed under attitude verbs.
Introductions Ludlow 2008
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  1. Barbara Abbott, Issues in the Semantics and Pragmatics of Definite Descriptions in English.
  2. Barbara Abbott (2008). Issues in the Semantics and Pragmatics of Definite Descriptions in English. In Nancy Hedberg & Jeanette Gundel (eds.), Reference: Interdisciplinary Perspectives. Oxford University Press. 61-72.
  3. Barbara Abbott (2006). Definite and Indefinite. In Keith Brown (ed.), Encyclopedia of Language and Linguistics. Elsevier. 3--392.
  4. Simon Blackburn (1972). Searle on Descriptions. Mind 81 (323):409-414.
  5. Oswaldo Chateaubriand (2002). Descriptions: Frege and Russell Combined. Synthese 130 (2):213 - 226.
  6. Romane Clark (1956). Presuppositions, Names, and Descriptions. Philosophical Quarterly 6 (23):145-154.
  7. Ariel Cohen (2000). The King of France Is, In Fact, Bald. Natural Language Semantics 8 (4):291-295.
    According to current theories, sentences with definite descriptions that fail to refer are either false or lack a truth value; but they cannot be true. However, I present examples where such sentences are, in fact, judged true. I propose that a definite description may be accommodated as a conditional, and that, in such cases, it is precisely the failure to refer that makes the sentence true.
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  8. Charles B. Daniels (1990). Definite Descriptions. Studia Logica 49 (1):87 - 104.
    Three views on definite descriptions are summarized and discussed, including that of P. F. Strawson in which reference failure results in lack of truth value. When reference failure is allowed, a problem arises concerning Universal Instantiation. Van Fraassen solves the problem by the use of supervaluations, preserving as well such theorems as a=a, and Fa or ~Fa, even when the term a fails to refer. In the present paper a form of relevant, quasi-analytic implication is set out which allows reference (...)
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  9. Friederike Moltmann (2006). Presuppositions and Quantifier Domains. Synthese 149 (1):179 - 224.
    In this paper, I will argue for a new account of presuppositions which is based on double indexing as well as minimal representational contexts providing antecedent material for anaphoric presuppositions, rather than notions of context defined in terms of the interlocutors’ pragmatic presuppositions or the information accumulated from the preceding discourse. This account applies in particular to new phenomena concerning the presupposition of quantifier domains. But it is also intended to be an account of presuppositions in general. The account differs (...)
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  10. Daniel Rothschild (2007). Presuppositions and Scope. Journal of Philosophy 104 (2):71-106.
    This paper discusses the apparent scope ambiguities between definite descriptions and modal operators. I argue that we need the theory of presupposition to explain why these ambiguities are not always present, and that once that theory is in hand, Kripke’s modal argument loses much of its force.
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  11. Anders J. Schoubye (2009). Descriptions, Truth Value Intuitions, and Questions. Linguistics and Philosophy 32 (6):583-617.
    Since the famous debate between Russell (Mind 14: 479–493, 1905, Mind 66: 385–389, 1957) and Strawson (Mind 59: 320–344, 1950; Introduction to logical theory, 1952; Theoria, 30: 96–118, 1964) linguistic intuitions about truth values have been considered notoriously unreliable as a guide to the semantics of definite descriptions. As a result, most existing semantic analyses of definites leave a large number of intuitions unexplained. In this paper, I explore the nature of the relationship between truth value intuitions and non-referring definites. (...)
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  12. Anders Johan Schoubye (2013). Ghosts, Murderers, and the Semantics of Descriptions. Noûs 47 (3):496-533.
    It is widely agreed that sentences containing a non-denoting description embedded in the scope of a propositional attitude verb have true de dicto interpretations, and Russell's (1905) analysis of definite descriptions is often praised for its simple analysis of such cases, cf. e.g. Neale (1990). However, several people, incl. Elbourne (2005, 2009), Heim (1991), and Kripke (2005), have contested this by arguing that Russell's analysis yields incorrect predictions in non-doxastic attitude contexts. Heim and Elbourne have subsequently argued that once certain (...)
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