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Summary According to Russell's classic semantics for definite descriptions, descriptions like "the F" are satisfied only if there is a unique F.  Other accounts of definite descriptions opt to make this uniqueness requirement a presupposition rather than a part of the strict semantic content expressed by the description.  Either way, such a requirement seems at odds with how we commonly use descriptions: to talk about objects that neither are, nor are presupposed to be, uniquely F.  This puts the predictions of many popular theories of definite descriptions at odds with at least one aspect of common usage.  Some theorists have proposed to deal with this "problem of incompleteness" by allowing that the context can effectively supplement the available descriptive material.  Others have proposed to deal with this problem by appealing to a supplemental pragmatic theory.
Key works Strawson 1950 first appealed to incomplete descriptions as an objection to Russell 1905's theory of definite descriptions.  Kripke 1977 allows that the problem of incomplete descriptions might constitute a sufficient reason to accept that there are semantically-significant referential uses of definite descriptions.  Neale 1990 argues, conversely, that this is not so.  More recently, the literature on incomplete descriptions has become bound up in the literature on quantifier-domain restriction.  Since the Russellian analysis has it that definite descriptions are to be treated as a certain sort of quantifier, it stands to reason that solutions to this larger problem should port over to the problem of incomplete descriptions.  This strategy is pursued explicitly in Stanley & Szabó 2000.
Introductions Ludlow 2008
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  1. A Problem for Predicativism Not Solved by Predicativism.Anders J. Schoubye - forthcoming - Semantics and Pragmatics.
    In 'The Reference Book' (2012), Hawthorne and Manley observe the following contrast between (1) and (2): -/- (1) In every race John won. (2) In every race, the colt won. -/- The name 'John' in (1) must intuitively refer to the same single individual for each race. However, the description 'the colt' in (2) has a co-varying reading, i.e. a reading where for each race it refers to a different colt. This observation is a prima facie problem for proponents of (...)
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  2. Wolpert, Chaitin and Wittgenstein 불가능, 불완전 성, 거짓말 쟁이 역설, 신념, 전산 한계, 비 양자 역학적 불확실성 원리 및 -Turing 기계 이론의 궁극적 이론(.Michael Richard Starks - 2020 - In 지구상의 지옥에 오신 것을 환영합니다 : 아기, 기후 변화, 비트 코인, 카르텔, 중국, 민주주의, 다양성, 역학, 평등, 해커, 인권, 이슬람, 자유주의, 번영, 웹, 혼돈, 기아, 질병, 폭력, 인공 지능, 전쟁. Las Vegas, NV USA: Reality Press. pp. 201-209.
    나는 컴퓨터로 계산과 우주의 한계에 대한 많은 최근의 토론을 읽었습니다, polymath 물리학자 및 결정 이론가 데이비드 울퍼트의 놀라운 작품에 대한 몇 가지 의견을 찾을 수 있기를 바라고 있지만 하나의 인용을 발견하지 않은 그래서 나는이 매우 간단한 요약을 제시. Wolpert는 계산을 수행하는 장치와 는 별개이며 물리학법칙과는 무관하므로 컴퓨터, 물리학 및 인간의 행동에 적용되므로 추론(계산)에 대한 제한에 대해 놀라운 불가능또는 불완전성 정리(1992년에서 2008년 참조 arxiv dot org)를 입증했습니다. 그들은 캔터의 대각선화, 거짓말쟁이 역설 및 세계관을 사용하여 튜링 머신 이론의 궁극적 인 정리가 될 (...)
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  3. Saying a Bundle: Meaning, Intention, and Underdetermination.Mark Bowker - 2019 - Synthese 196 (10):4229-4252.
    People often speak loosely, uttering sentences that are plainly false on their most strict interpretation. In understanding such speakers, we face a problem of underdetermination: there is often no unique interpretation that captures what they meant. Focusing on the case of incomplete definite descriptions, this paper suggests that speakers often mean bundles of propositions. When a speaker means a bundle, their audience can know what they mean by deriving any one of its members. Rather than posing a problem for the (...)
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  4. O que significa paraconsistente, indecível, aleatório, computável e incompleto?- Uma revisão da ‘Godel’s Way: exploits into an undecidable world’ (Maneira de Godel: façanhas em um mundo indecidível) por Gregory Chaitin, Francisco A Doria, Newton C.A. da costa 160P (2012) (revisão revisada 2019).Michael Richard Starks - 2019 - In Delírios Utópicos Suicidas no Século XXI Filosofia, Natureza Humana e o Colapso da Civilization- Artigos e Comentários 2006-2019 5ª edição. Las Vegas, NV USA: Reality Press. pp. 168-182.
    Em "Godel's Way", três cientistas eminentes discutem questões como a undecidability, incompletude, aleatoriedade, computabilidade e paraconsistência. Eu abordar estas questões do ponto de vista Wittgensteinian que existem duas questões básicas que têm soluções completamente diferentes. Há as questões científicas ou empíricas, que são fatos sobre o mundo que precisam ser investigados observacionalmente e questões filosóficas sobre como a linguagem pode ser usada inteligìvelmente (que incluem certas questões em matemática e lógica), que precisam ser decidido por olhar uma como nós realmente (...)
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  5. Remarks on Wittgenstein, Gödel, Chaitin, Incompleteness, Impossiblity and the Psychological Basis of Science and Mathematics.Michael Richard Starks - 2019 - In Remarks on Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason in Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, da Costa, Godel, Searle, Rodych, Berto, Floyd, Moyal. Las Vegas, NV USA: Reality Press. pp. 24-38.
    It is commonly thought that such topics as Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were resolved by Wittgenstein over 80 years ago. -/- Wittgenstein also demonstrated the fatal error in regarding mathematics or language or our behavior in general as a unitary coherent logical ‘system,’ rather than as (...)
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  6. Incomplete Descriptions and Indistinguishable Participants.Paul Elbourne - 2016 - Natural Language Semantics 24 (1):1-43.
    The implicit content associated with incomplete definite descriptions is contributed in the form of definite descriptions of situations. A definite description of this kind is contributed by a small structure in the syntax, which is interpreted, in general terms, as ‘the situation that bears R to s’.
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  7. Names Are Predicates.Delia Graff Fara - 2015 - Philosophical Review 124 (1):59-117.
    One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...)
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  8. Incomplete Descriptions and the Underdetermination Problem.Andrei Moldovan - 2015 - Research in Language 13 (4):352–367.
    The purpose of this paper is to discuss two phenomena related to the semantics of definite descriptions: that of incomplete uses of descriptions, and that of the underdetermination of referential uses of descriptions. The Russellian theorist has a way of accounting for incomplete uses of descriptions by appealing to an account of quantifier domain restriction, such as the one proposed in Stanley and Szabó (2000a). But, I argue, the Russellian is not the only one in a position to appeal to (...)
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  9. 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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  10. Incomplete Descriptions and (Reverse) Sobel Sequences.Mirja Annalena Holst - 2013 - Analysis 73 (1):26-32.
    A challenge for theories of incomplete descriptions is to capture the consistency of ‘Sobel sequences’ and to account for an asymmetry in the acceptability of utterances of Sobel sequences and ‘reverse Sobel sequences’. David Lewis’s theory of incomplete descriptions answers, unlike many other theories, the challenge from Sobel sequences, but it does not answer the challenge from reverse Sobel sequences. This article presents another asymmetry in the availability of anaphoric readings of Sobel sequences and reverse Sobel sequences, and proposes an (...)
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  11. A Puzzle About Meaning and Communication.Ray Buchanan - 2010 - Noûs 44 (2):340-371.
  12. Incomplete Descriptions, Incomplete Quantified Expressions (Part of the Dissertation Portfolio Modality, Names and Descriptions).Zsófia Zvolenszky - 2007 - Dissertation, New York University
    This paper offers a unified, quantificational treatment of incomplete descriptions like ‘the table’. An incomplete quantified expression like ‘every bottle’ (as in “Every bottle is empty”) can feature in true utterances despite the fact that the world contains nonempty bottles. Positing a contextual restriction on the bottles being talked about is a straightforward solution. It is argued that the same strategy can be extended to incomplete definite descriptions across the board. ncorporating the contextual restrictions into semantics involves meeting a complex (...)
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  13. Definite and Indefinite.Barbara Abbott - 2006 - In Keith Brown (ed.), Encyclopedia of Language and Linguistics. Elsevier. pp. 3--392.
  14. Über die deskriptive Unerschöpflichkeit der Einzeldinge.Geert Keil - 2006 - In Geert Keil & Udo Tietz (eds.), Phänomenologie und Sprachanalyse. Mentis. pp. 83-125.
    Der Topos von der Unerschöpflichkeit des Gegenstands wird mit der Phänomenologie assoziiert. Den ihm verwandten Topos von der Unaussprechlichkeit des Individuellen haben Goethe und die deutschen Romantiker in die Welt getragen. Der Diktion der analytischen Philosophie sind die Ausdrücke „unerschöpflich“ und „unaussprechlich“ fremd. Dieser Umstand sollte analytische Philosophen nicht davon abhalten, sich den sprachphilosophischen und ontologischen Problemen zuzuwenden, die sich hinter den besagten Formeln verbergen. Husserls Wort für Unerschöpflichkeit ist „Fülle“. Die „Fülle des Gegenstandes“ erläutert Husserl als den „Inbegriff der (...)
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  15. Review of Reimer & Bezuidenhout (2004): Descriptions and Beyond. [REVIEW]John-Michael Kuczynski - 2006 - Pragmatics and Cognition 14 (1):196-204.
    In order to understand a sentence, one must know the relevant semantic rules. Those rules are not learned in a vacuum; they are given to one through one's senses. As a result, knowledge of semantic rules sometimes comes bundled with semantically irrelevant, but cognitively non-innocuous, knowledge of the circumstances in which those rules were learned. Thus, one must work through non-semantic information in order to know what is literally meant by a given sentence-token. A consequence is that one's knowledge of (...)
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  16. Has the Problem of Incompleteness Rested on a Mistake?Ray Buchanan & Gary Ostertag - 2005 - Mind 114 (456):889-913.
    A common objection to Russell's theory of descriptions concerns incomplete definite descriptions: uses of (for example) ‘the book is overdue’ in contexts where there is clearly more than one book. Many contemporary Russellians hold that such utterances will invariably convey a contextually determined complete proposition, for example, that the book in your briefcase is overdue. But according to the objection this gets things wrong: typically, when a speaker utters such a sentence, no facts about the context or the speaker's communicative (...)
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  17. On a Unitary Semantical Analysis for Definite and Indefinite Descriptions.Peter Ludlow & Gabriel Segal - 2004 - In Marga Reimer & Anne Bezuidenhout (eds.), Descriptions and Beyond. Oxford University Press. pp. 420-437.
  18. Dynamic Definite Descriptions, Implicit Arguments, and Familiarity.A. ter Meulen - 2004 - In Marga Reimer & Anne Bezuidenhout (eds.), Descriptions and Beyond. Oxford University Press.
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  19. The Indefinability of €œOne”.Laurence Goldstein - 2002 - Journal of Philosophical Logic 31 (1):29-42.
    Logicism is one of the great reductionist projects. Numbers and the relationships in which they stand may seem to possess suspect ontological credentials – to be entia non grata – and, further, to be beyond the reach of knowledge. In seeking to reduce mathematics to a small set of principles that form the logical basis of all reasoning, logicism holds out the prospect of ontological economy and epistemological security. This paper attempts to show that a fundamental logicist project, that of (...)
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  20. A Companion to Philosophical Logic.Dale Jacquette (ed.) - 2002 - Wiley-Blackwell.
    This collection of newly comissioned essays by international contributors offers a representative overview of the most important developments in contemporary philosophical logic. Presents controversies in philosophical implications and applications of formal symbolic logic. Surveys major trends and offers original insights.
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  21. Descriptions and Logical Form.Gary Ostertag - 2002 - In Dale Jacquette (ed.), A Companion to Philosophical Logic.
  22. Descriptions and Situations.Francois Recanati - 2002 - In Marga Reimer & Anne Bezuidenhout (eds.), Descriptions and Beyond. Clarendon Press. pp. 15-40.
  23. The Semantics and Pragmatics of Complex Demonstratives.Ernest Lepore & Kirk Ludwig - 2000 - Mind 109 (434):199-240.
    Complex demonstratives, expressions of the form 'That F', 'These Fs', etc., have traditionally been taken to be referring terms. Yet they exhibit many of the features of quantified noun phrases. This has led some philosophers to suggest that demonstrative determiners are a special kind of quantifier, which can be paraphrased using a context sensitive definite description. Both these views contain elements of the truth, though each is mistaken. We advance a novel account of the semantic form of complex demonstratives that (...)
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  24. On Quantifier Domain Restriction.Jason Stanley & Zoltán Gendler Szabó - 2000 - Mind and Language 15 (2-3):219--61.
  25. A Scorekeeping Error.Gary Ostertag - 1999 - Philosophical Studies 96 (2):123-146.
  26. Quantification and Context.Marga Reimer - 1998 - Linguistics and Philosophy 21 (1):95-115.
  27. Parts and Wholes in Semantics (TOC).Friederike Moltmann - 1997 - Oxford University Press.
    This book present a unified semantic theory of expressions involving the notions of part and whole. It develops a theory of part structures which differs from traditional (extensional) mereological theories in that the notion of an integrated whole plays a central role and in that the part structure of an entity is allowed to vary across different situations, perspectives, and dimensions. The book presents a great range of empirical generalizations involving plurals, mass nouns, adnominal and adverbial modifiers such as 'whole', (...)
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  28. Indexicals and Descriptions.Fernando Garcia-Murga - 1995 - Sorites 2:46-56.
    Reference is a common feature to indexicals, definite descriptions and, at least some uses of indefinite descriptions. A referential expression triggers a search for a referent, which ranges over the linguistic context, physical environment or encyclopedic knowledge. I argue for a unified theory of reference within which indexicals and definite descriptions refer to salient objects while indefinite descriptions refer to non salient objects. The descriptive content attached to each expression provides information making it possible for the addressee to find an (...)
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  29. Descriptions.Stephen Neale - 1990 - MIT Press.
    When philosophers talk about descriptions, usually they have in mind singular definite descriptions such as ‘the finest Greek poet’ or ‘the positive square root of nine’, phrases formed with the definite article ‘the’. English also contains indefinite descriptions such as ‘a fine Greek poet’ or ‘a square root of nine’, phrases formed with the indefinite article ‘a’ (or ‘an’); and demonstrative descriptions (also known as complex demonstratives) such as ‘this Greek poet’ and ‘that tall woman’, formed with the demonstrative articles (...)
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  30. How to Refer with Vague Descriptions.Manfred Pinkal - 1979 - In Rainer Bäuerle, Urs Egli & Arnim von Stechow (eds.), Semantics From Different Points of View. Springer Verlag. pp. 32--50.
  31. Definite Descriptions and Context-Dependence.Alan Brinton - 1977 - Noûs 11 (4):397-407.
  32. On Referring.P. F. Strawson - 1950 - Mind 59 (235):320-344.