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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. The Pragmatics of Non-denoting Descriptions.Andrei Moldovan - 2020 - Topoi (2):413-423.
    One challenge that the proponent of the Fregean theory of definite descriptions has to meet is to account for those truth-value intuitions that do not match the predictions of her theory. What needs an explanation is why sentences such as ‘The king of France is sitting in that chair’ [pointing at an empty chair] are intuitively false, while semantically truth-valueless. The existence of such cases was pointed out by Strawson :216–231, 1954) and Russell :385–389, 1957), and much discussed in the (...)
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  2. Presuppositional Anaphora Is The Sobel Truth.Daniel Dohrn - 2017 - In Salvatore Pistoia-Reda & Filippo Domaneschi (eds.), Linguistic and Psycholinguistic Approaches on Implicatures and Presuppositions. Cham: Palgrave Macmillan. pp. 199-238.
    Sobel sequences have had a huge impact on the discussion of counterfactuals. They can be composed of conditionals and mere descriptions. What is especially puzzling about them is that they are often felicitously uttered when their reversal is not. Up to now, there is no unified explanation. I examine two strategies. We might begin with conditionals and proceed to descriptions. Or we might begin with descriptions and proceed to conditionals. I argue for the latter variant and outline a universal theory (...)
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  3. Definiteness and Determinacy.Elizabeth Coppock & David Beaver - 2015 - Linguistics and Philosophy 38 (5):377-435.
    This paper distinguishes between definiteness and determinacy. Definiteness is seen as a morphological category which, in English, marks a uniqueness presupposition, while determinacy consists in denoting an individual. Definite descriptions are argued to be fundamentally predicative, presupposing uniqueness but not existence, and to acquire existential import through general type-shifting operations that apply not only to definites, but also indefinites and possessives. Through these shifts, argumental definite descriptions may become either determinate or indeterminate. The latter option is observed in examples like (...)
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  4. Same but Different.Daniel Hardt & Line Mikkelsen - 2015 - Linguistics and Philosophy 38 (4):289-314.
    In this paper, we argue that same is fundamentally different from different, in that same imposes a discourse condition on eventualities, while different compares individuals. This difference has not been noted in previous literature. Furthermore, in the literature on same, there has been a persistent puzzle about the contribution of the definite article with which same must co-occur. We show that this puzzle is resolved once the contribution of same is adjusted to apply to eventualities: then the definite article can (...)
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  5. Impossible Interpretations, Impossible Demands.Francesco Pupa - 2015 - Linguistics and Philosophy 38 (3):269-287.
    While there has been much ado about the innumerable ways a speaker can alter the reach of her quantifier phrases, little fuss has been made over the fact that some forms of alteration are, as it were, impossible to pull off. These impossible interpretations cast a shadow over both syntactic and free enrichment approaches to the phenomenon of quantifier domain restriction. Indeed, I argue that these impossible interpretations help to undermine the presupposition that domain restriction is amenable to a uniform (...)
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  6. Definite Descriptions.Paul Elbourne - 2013 - Oxford University Press.
    Paul Elbourne defends the Fregean view that definite descriptions ('the table', 'the King of France') refer to individuals, and offers a new and radical account of the semantics of pronouns. He draws on a wide range of work, from Frege, Peano, and Russell to the latest findings in linguistics, philosophy of language, and psycholinguistics.
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  7. Ghosts, Murderers, and the Semantics of Descriptions.Anders Johan Schoubye - 2013 - 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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  8. Descriptions, Truth Value Intuitions, and Questions.Anders J. Schoubye - 2009 - 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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  9. Issues in the Semantics and Pragmatics of Definite Descriptions in English.Barbara Abbott - 2008 - In Nancy Hedberg & Jeanette Gundel (eds.), Reference: Interdisciplinary Perspectives. Oxford University Press. pp. 61-72.
  10. A Presuppositional Analysis of Definite Descriptions in Proof Theory.Koji Mineshima - 2008 - In Satoh (ed.), New Frontiers in Artificial Intelligence. Springer. pp. 214--227.
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  11. Presuppositions and Scope.Daniel Rothschild - 2007 - 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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  12. Definite and Indefinite.Barbara Abbott - 2006 - In Keith Brown (ed.), Encyclopedia of Language and Linguistics. Elsevier. pp. 3--392.
  13. Presuppositions and Quantifier Domains.Friederike Moltmann - 2006 - 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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  14. Descriptions: Frege and Russell Combined.Oswaldo Chateaubriand - 2002 - Synthese 130 (2):213 - 226.
  15. The King of France Is, In Fact, Bald.Ariel Cohen - 2000 - 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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  16. Definite Descriptions.Charles B. Daniels - 1990 - 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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  17. Searle on Descriptions.Simon Blackburn - 1972 - Mind 81 (323):409-414.
  18. Presuppositions, Names, and Descriptions.Romane Clark - 1956 - Philosophical Quarterly 6 (23):145-154.
  19. Issues in the Semantics and Pragmatics of Definite Descriptions in English.Barbara Abbott - manuscript