Results for 'incompleteness'

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  1. Einstein, Incompleteness, and the Epistemic View of Quantum States.Nicholas Harrigan & Robert W. Spekkens - 2010 - Foundations of Physics 40 (2):125-157.
    Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. We show that representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something (...)
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  2. Incompleteness, Nonlocality, and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics.Michael Redhead - 1987 - Oxford University Press.
    Aiming to unravel the mystery of quantum mechanics, this book is concerned with questions about action-at-a-distance, holism, and whether quantum mechanics gives a complete account of microphysical reality. With rigorous arguments and clear thinking, the author provides an introduction to the philosophy of physics.
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  3.  80
    Incompleteness, non locality and realism. A prolegomenon to the philosophy of quantum mechanics.Michael Redhead - 1987 - Revue Philosophique de la France Et de l'Etranger 180 (4):712-713.
    This book concentrates on research done during the last twenty years on the philosophy of quantum mechanics. In particular, the author focuses on three major issues: whether quantum mechanics is an incomplete theory, whether it is non-local, and whether it can be interpreted realistically. Much of the book is concerned with distinguishing various senses in which these questions can be taken, and assessing the bewildering variety of answers philosophers and physicists have given up to now. The book is self-contained in (...)
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  4.  52
    The Incomplete Universe: Totality, Knowledge, and Truth.Patrick Grim - 1991 - Cambridge: Mass.: Mit Press.
    This is an exploration of a cluster of related logical results. Taken together these seem to have something philosophically important to teach us: something about knowledge and truth and something about the logical impossibility of totalities of knowledge and truth. The book includes explorations of new forms of the ancient and venerable paradox of the :Liar, applications and extensions of Kaplan and Montague's paradox of the Knower, generalizations of Godel's work on incompleteness, and new uses of Cantorian diagonalization. Throughout, (...)
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  5.  69
    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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  6.  35
    Incompleteness Via Paradox and Completeness.Walter Dean - 2020 - Review of Symbolic Logic 13 (3):541-592.
    This paper explores the relationship borne by the traditional paradoxes of set theory and semantics to formal incompleteness phenomena. A central tool is the application of the Arithmetized Completeness Theorem to systems of second-order arithmetic and set theory in which various “paradoxical notions” for first-order languages can be formalized. I will first discuss the setting in which this result was originally presented by Hilbert & Bernays and also how it was later adapted by Kreisel and Wang in order to (...)
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  7. Incompleteness and Inconsistency.Stewart Shapiro - 2002 - Mind 111 (444):817-832.
    Graham Priest's In Contradiction (Dordrecht: Martinus Nijhoff Publishers, 1987, chapter 3) contains an argument concerning the intuitive, or ‘naïve’ notion of (arithmetic) proof, or provability. He argues that the intuitively provable arithmetic sentences constitute a recursively enumerable set, which has a Gödel sentence which is itself intuitively provable. The incompleteness theorem does not apply, since the set of provable arithmetic sentences is not consistent. The purpose of this article is to sharpen Priest's argument, avoiding reference to informal notions, consensus, (...)
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  8. Interactivity, Fictionality, and Incompleteness.Nathan Wildman & Richard Woodward - forthcoming - In Grant Tavinor & Jon Robson (eds.), The Aesthetics of Videogames. Routledge.
  9.  6
    Incomplete Understanding of Concepts.Åsa Wikforss - 2017 - Oxford Handbooks Online: Scholarly Research Reviews.
    This article discusses the thesis that a subject can have a concept, think thoughts containing it, that she incompletely understands. The central question concerns how to construe the distinction between having a concept and understanding it. Two important versions of the thesis are distinguished: a metasemantic version and an epistemic version. According to the first, the subject may have concept C without being a fully competent user, in virtue of deference to other speakers or to the world. According to the (...)
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  10.  28
    Incompleteness of Intuitionistic Propositional Logic with Respect to Proof-Theoretic Semantics.Thomas Piecha & Peter Schroeder-Heister - 2019 - Studia Logica 107 (1):233-246.
    Prawitz proposed certain notions of proof-theoretic validity and conjectured that intuitionistic logic is complete for them [11, 12]. Considering propositional logic, we present a general framework of five abstract conditions which any proof-theoretic semantics should obey. Then we formulate several more specific conditions under which the intuitionistic propositional calculus turns out to be semantically incomplete. Here a crucial role is played by the generalized disjunction principle. Turning to concrete semantics, we show that prominent proposals, including Prawitz’s, satisfy at least one (...)
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  11. Revising Incomplete Attitudes.Richard Bradley - 2009 - Synthese 171 (2):235 - 256.
    Bayesian models typically assume that agents are rational, logically omniscient and opinionated. The last of these has little descriptive or normative appeal, however, and limits our ability to describe how agents make up their minds (as opposed to changing them) or how they can suspend or withdraw their opinions. To address these limitations this paper represents the attitudinal states of non-opinionated agents by sets of (permissible) probability and desirability functions. Several basic ways in which such states of mind can be (...)
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  12. The Incompleteness Theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of Mathematical Logic. North-Holland. pp. 821 -- 865.
  13.  57
    Incomplete Events, Intensionality and Imperfective Aspect.Sandro Zucchi - 1999 - Natural Language Semantics 7 (2):179-215.
    I discuss two competing theories of the progressive: the theory proposed in Parsons (1980, 1985, 1989, 1990) and the theory proposed in Landman (1992). These theories differ in more than one way. Landman regards the progressive as an intentional operator, while Parsons doesn't. Moreover, Landman and Parsons disagree on what uninflected predicates denote. For Landman, cross the street has in its denotation complete events of crossing the street; the aspectual contribution of English simple past (perfective aspect) is the identity function. (...)
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  14.  43
    Incompleteness in the Finite Domain.Pavel Pudlák - 2017 - Bulletin of Symbolic Logic 23 (4):405-441.
    Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond NP ≠ coNP. These conjectures formally connect computational complexity with the difficulty of proving some sentences, which means that high computational complexity of a problem associated with a sentence implies that the sentence is not provable in a weak theory, or requires a long proof. Another reason for putting forward these conjectures is that some results in proof complexity seem to (...)
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  15. Incomplete Descriptions.Marga Reimer - 1992 - Erkenntnis 37 (3):347 - 363.
    Standard attempts to defend Russell's Theory of Descriptions against the problem posed by incomplete descriptions, are discussed and dismissed as inadequate. It is then suggested that one such attempt, one which exploits the notion of a contextually delimited domain of quantification, may be applicable to incomplete quantifier expressions which are typically treated as quantificational: expressions of the form AllF's, NoF's, SomeF's, Exactly eightF's, etc. In this way, one is able to retain the plausible claim that such expressions ought to receive (...)
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  16.  64
    Incomplete Definite Descriptions.Scott Soames - 1986 - Notre Dame Journal of Formal Logic 27 (3):349--375.
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  17.  11
    An Incompleteness Theorem for Modal Relevant Logics.Shawn Standefer - 2021 - Notre Dame Journal of Formal Logic 62 (4):669 - 681.
    In this paper, an incompleteness theorem for modal extensions of relevant logics is proved. The proof uses elementary methods and builds upon the work of Fuhrmann.
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  18.  72
    An Incomplete Logic Containing S.Kit Fine - 1974 - Theoria 40 (1):23-29.
  19.  86
    Incomplete Ideal Theory.Amy Berg - 2019 - Social Theory and Practice 45 (4):501-524.
    What is the best way to make sustained societal progress over time? Non-ideal theory done on its own faces the problem of second best, but ideal theory seems unable to cope with disagreement about how to make progress. If ideal theory gives up its claims to completeness, then we can use the method of incompletely theorized agreements to make progress over time.
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  20.  79
    An Incompleteness Theorem in Modal Logic.S. K. Thomason - 1974 - Theoria 40 (1):30-34.
  21.  47
    Incompleteness Results in Kripke Semantics.Silvio Ghilardi - 1991 - Journal of Symbolic Logic 56 (2):517-538.
    By means of models in toposes of C-sets (where C is a small category), necessary conditions are found for the minimum quantified extension of a propositional (intermediate, modal) logic to be complete with respect to Kripke semantics; in particular, many well-known systems turn out to be incomplete.
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  22. 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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  23. Incompletely Theorized Agreements in Constitutional Law.Cass R. Sunstein - 2007 - Social Research: An International Quarterly 74 (1):1-24.
    How is constitutionalism possible, when people disagree on so many questions about what is good and what is right? The answer lies in two kinds of incompletely theorized agreement - both reached amidst the sharpest disagreements about the fundamental issues in social life. The first consist of agreements on abstract formulations ; these agreements are crucial to constitution-making as a social practice. The second consist of agreements on particular doctrines and practices; these agreements are crucial to life and law under (...)
     
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  24.  40
    Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History.Saul A. Kripke - 2021 - History and Philosophy of Logic 43 (2):175-182.
    In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long ‘search’ for a purely mathematical incompleteness result in first-order Peano arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a number-theoretic form.
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  25.  34
    The Incompleteness of the Economy and Business: A Forceful Reminder. [REVIEW]Paul H. Dembinski - 2011 - Journal of Business Ethics 100 (S1):29-40.
    Many different but related arguments developed in the Caritas in Veritate converge on one central, yet not clearly stated, conclusion or thesis: economic and business activities are ‘incomplete’. This article will explore the above-mentioned ‘incompleteness’ thesis or argument from three different perspectives: the role, the practice and the purpose of economic and business activities in contemporary societies. In doing so, the paper will heavily draw on questions and, still not fully learned, lessons derived from the present financial and economic (...)
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  26. Incomplete Understanding, Deference, and the Content of Thought.Mark Greenberg - unknown
    Tyler Burge’s influential arguments have convinced most philosophers that a thinker can have a thought involving a particular concept without fully grasping or having mastery of that concept. In Burge’s (1979) famous example, a thinker who lacks mastery of the concept of arthritis nonetheless has thoughts involving that concept. It is generally supposed, however, that this phenomenon – incomplete understanding, for short – does not require us to reconsider in a fundamental way what it is for a thought to involve (...)
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  27.  77
    Incomplete Symbols — Definite Descriptions Revisited.Norbert Gratzl - 2015 - Journal of Philosophical Logic 44 (5):489-506.
    We investigate incomplete symbols, i.e. definite descriptions with scope-operators. Russell famously introduced definite descriptions by contextual definitions; in this article definite descriptions are introduced by rules in a specific calculus that is very well suited for proof-theoretic investigations. That is to say, the phrase ‘incomplete symbols’ is formally interpreted as to the existence of an elimination procedure. The last section offers semantical tools for interpreting the phrase ‘no meaning in isolation’ in a formal way.
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  28. Incompletely Theorized Agreements in Constitutional Law.Cass Sunstein - 2007 - Social Research: An International Quarterly 74:1-24.
    How is constitutionalism possible, when people disagree on so many questions about what is good and what is right? The answer lies in two kinds of incompletely theorized agreement - both reached amidst the sharpest disagreements about the fundamental issues in social life. The first consist of agreements on abstract formulations ; these agreements are crucial to constitution-making as a social practice. The second consist of agreements on particular doctrines and practices; these agreements are crucial to life and law under (...)
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  29. Incompleteness, Mechanism, and Optimism.Stewart Shapiro - 1998 - Bulletin of Symbolic Logic 4 (3):273-302.
  30. Incompleteness for Quantified Relevance Logics.Kit Fine - 1989 - In J. Norman & Richard Sylvan (eds.), Directions in Relevant Logic. Springer, Dordrecht. pp. 205-225.
    In the early seventies, several logicians developed a semantics for propositional systems of relevance logic. The essential ingredients of this semantics were a privileged point o, an ‘accessibility’ relation R and a special operator * for evaluating negation. Under the truth- conditions of the semantics, each formula A(Pl,…,Pn) could be seen as expressing a first order condition A+(pl,…,pn, o, R,*) on sets p1,…,pn and o, R, *, while each formula-scheme could be regarded as expressing the second-order condition ∀p1,…,∀pn A+(p1,…,pn, o, (...)
     
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  31.  24
    The Incompleteness Theorems After 70 Years.Henryk Kotlarski - 2004 - Annals of Pure and Applied Logic 126 (1-3):125-138.
    We give some information about new proofs of the incompleteness theorems, found in 1990s. Some of them do not require the diagonal lemma as a method of construction of an independent statement.
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  32. Incomplete Fictions and Imagination.J. Robert G. Williams - unknown
    *Note that this project is now being developed in joint work with Rich Woodward* -/- Some things are left open by a work of fiction. What colour were the hero’s eyes? How many hairs are on her head? Did the hero get shot in the final scene, or did the jailor complete his journey to redemption and shoot into the air? Are the ghosts that appear real, or a delusion? Where fictions are open or incomplete in this way, we can (...)
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  33. Essentially Incomplete Descriptions.Carlo Penco - 2010 - European Journal of Analytic Philosophy 6 (2):47 - 66.
    In this paper I offer a defence of a Russellian analysis of the referential uses of incomplete (mis)descriptions, in a contextual setting. With regard to the debate between a unificationist and an ambiguity approach to the formal treatment of definite descriptions (introduction), I will support the former against the latter. In 1. I explain what I mean by "essentially" incomplete descriptions: incomplete descriptions are context dependent descriptions. In 2. I examine one of the best versions of the unificationist “explicit” approach (...)
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  34.  34
    Two Incomplete Anti-Realist Modal Epistemic Logics.Timothy Williamson - 1990 - Journal of Symbolic Logic 55 (1):297-314.
  35.  4
    Incomplete Utterances as Critical Assessments.Jacob Kline & Innhwa Park - 2020 - Discourse Studies 22 (4):441-459.
    Using video recordings of draft meetings conducted as part of an intramural basketball program as data, this conversation analytic study examines the use of an incomplete utterance in a joint evaluative activity. In particular, we focus on how the participants, volunteer coaches, who meet to draft players for their respective teams, produce a syntactically incomplete utterance as a means to critically assess a player, a non-present third party to the interaction. Analysis reveals that the participants use an incomplete utterance as (...)
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  36.  84
    Incomplete Contracts and Complexity Costs.Luca Anderlini & Leonardo Felli - 1999 - Theory and Decision 46 (1):23-50.
    This paper investigates, in a simple risk-sharing framework, the extent to which the incompleteness of contracts could be attributed to the complexity costs associated with the writing and the implementation of contracts. We show that, given any measure of complexity in a very general class, it is possible to find simple contracting problems such that, when complexity costs are explicitly taken into account, the contracting parties optimally choose an incomplete contract which coincides with the ‘default’ division of surplus. Optimal (...)
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  37.  60
    Incompleteness and the Barcan Formula.M. J. Cresswell - 1995 - Journal of Philosophical Logic 24 (4):379 - 403.
    A (normal) system of propositional modal logic is said to be complete iff it is characterized by a class of (Kripke) frames. When we move to modal predicate logic the question of completeness can again be raised. It is not hard to prove that if a predicate modal logic is complete then it is characterized by the class of all frames for the propositional logic on which it is based. Nor is it hard to prove that if a propositional modal (...)
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  38. An Incomplete Inclusion of Non-Cooperators Into a Rawlsian Theory of Justice.Chong-Ming Lim - 2016 - Res Philosophica 93 (4):893-920.
    John Rawls’s use of the “fully cooperating assumption” has been criticized for hindering attempts to address the needs of disabled individuals, or non-cooperators. In response, philosophers sympathetic to Rawls’s project have extended his theory. I assess one such extension by Cynthia Stark, that proposes dropping Rawls’s assumption in the constitutional stage (of his four-stage sequence), and address the needs of non-cooperators via the social minimum. I defend Stark’s proposal against criticisms by Sophia Wong, Christie Hartley, and Elizabeth Edenberg and Marilyn (...)
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  39. Externalism and Incomplete Understanding.Asa Maria Wikforss - 2004 - Philosophical Quarterly 54 (215):287-294.
    Sarah Sawyer has challenged my claim that social externalism depends on the assumption that individuals have an incomplete grasp of their own concepts. Sawyer denies that Burge's later sofa thought-experiment relies on this assumption: the unifying principle behind the thought-experiments supporting social externalism, she argues, is just that referents play a role in the individuation of concepts. I argue that Sawyer fails to show that social externalism need not rely on the assumption of incomplete understanding. To establish the content externalist (...)
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  40. Incompleteness and Reasoned Choice.Amartya Sen - 2004 - Synthese 140 (1-2):43 - 59.
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  41.  25
    Kripke Incomplete Logics Containing KTB.Yutaka Miyazaki - 2007 - Studia Logica 85 (3):303-317.
    It is shown that there is a Kripke incomplete logic in NExt(KTB ⊕ □2 p → □3 p). Furthermore, it is also shown that there exists a continuum of Kripke incomplete logics in NExt(KTB ⊕ □5 p → □6 p).
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  42.  37
    Evaluatively Incomplete States of Affairs.Michael J. Zimmerman - 1983 - Philosophical Studies 43 (2):211 - 224.
    The main point of this paper has been to show that the concept of evaluative incompleteness deserves consideration. In addition, I have suggested that it is plausible to accept that certain states of affairs in fact are evaluatively incomplete. But I have not sought to prove that this is so; indeed, I do not know how such proof might be given. Just which states of affairs, if any, are evaluatively incomplete is an extremely vexed question, and it is not (...)
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  43. The Alleged Incompleteness of Public Reason.Andrew Williams - 2000 - Res Publica 6 (2):199-211.
    According to John Rawls's ideal of liberal public reason, comprehensive moral, religious and philosophical doctrines should play no more than an auxiliary or marginal role in the political life of constitutional democracies. David Reidy has recently claimed that since liberal public reason is incomplete, comprehensive doctrines, and non-public reasons, must play a wider role than Rawls admits. In response, I argue that Reidy's arguments do not establish that liberal public reason is incomplete. Furthermore, even if the substantive values embodied in (...)
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  44.  77
    Incomplete Understanding of Concepts: The Case of the Derivative.Sheldon R. Smith - 2015 - Mind 124 (496):1163-1199.
    Many philosophers have discussed the ability of thinkers to think thoughts that the thinker cannot justify because the thoughts involve concepts that the thinker incompletely understands. A standard example of this phenomenon involves the concept of the derivative in the early days of the calculus: Newton and Leibniz incompletely understood the derivative concept and, hence, as Berkeley noted, they could not justify their thoughts involving it. Later, Weierstrass justified their thoughts by giving a correct explication of the derivative concept. This (...)
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  45. Incompleteness and Computability: An Open Introduction to Gödel's Theorems.Richard Zach - 2019 - Open Logic Project.
    Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.
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  46.  2
    Hierarchical Incompleteness Results for Arithmetically Definable Extensions of Fragments of Arithmetic.Rasmus Blanck - 2021 - Review of Symbolic Logic 14 (3):624-644.
    There has been a recent interest in hierarchical generalizations of classic incompleteness results. This paper provides evidence that such generalizations are readily obtainable from suitably formulated hierarchical versions of the principles used in the original proofs. By collecting such principles, we prove hierarchical versions of Mostowski’s theorem on independent formulae, Kripke’s theorem on flexible formulae, Woodin’s theorem on the universal algorithm, and a few related results. As a corollary, we obtain the expected result that the formula expressing “ $\mathrm (...)
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  47. 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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  48.  53
    On Proofs of the Incompleteness Theorems Based on Berry's Paradox by Vopěnka, Chaitin, and Boolos.Makoto Kikuchi, Taishi Kurahashi & Hiroshi Sakai - 2012 - Mathematical Logic Quarterly 58 (4-5):307-316.
    By formalizing Berry's paradox, Vopěnka, Chaitin, Boolos and others proved the incompleteness theorems without using the diagonal argument. In this paper, we shall examine these proofs closely and show their relationships. Firstly, we shall show that we can use the diagonal argument for proofs of the incompleteness theorems based on Berry's paradox. Then, we shall show that an extension of Boolos' proof can be considered as a special case of Chaitin's proof by defining a suitable Kolmogorov complexity. We (...)
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  49. The Incompleteness of Dispositional Predicates.Sungho Choi - 2008 - Synthese 163 (2):157 - 174.
    Elizabeth Prior claims that dispositional predicates are incomplete in the sense that they have more than one argument place. To back up this claim, she offers a number of arguments that involve such ordinary dispositional predicates as ‘fragile’, ‘soluble’, and so on. In this paper, I will first demonstrate that one of Prior’s arguments that ‘is fragile’ is an incomplete predicate is mistaken. This, however, does not immediately mean that Prior is wrong that ‘fragile’ is an incomplete predicate. On the (...)
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  50. On Interpreting Chaitin's Incompleteness Theorem.Panu Raatikainen - 1998 - Journal of Philosophical Logic 27 (6):569-586.
    The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure (...)
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