Search results for 'indefinite extensibility' (try it on Scholar)

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  1.  22
    Jared Warren (2017). Quantifier Variance and Indefinite Extensibility. Philosophical Review 126 (1):81-122.
    This essay clarifies quantifier variance and uses it to provide a theory of indefinite extensibility that I call the variance theory of indefinite extensibility. The indefinite extensibility response to the set-theoretic paradoxes sees each argument for paradox as a demonstration that we have come to a different and more expansive understanding of ‘all sets’. But indefinite extensibility is philosophically puzzling: extant accounts are either metasemantically suspect in requiring mysterious mechanisms of domain expansion, (...)
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  2. Gabriel Uzquiano (2015). Varieties of Indefinite Extensibility. Notre Dame Journal of Formal Logic 56 (1):147-166.
    We look at recent accounts of the indefinite extensibility of the concept set and compare them with a certain linguistic model of indefinite extensibility. We suggest that the linguistic model has much to recommend over alternative accounts of indefinite extensibility, and we defend it against three prima facie objections.
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  3.  11
    Jose Luis Bermudez (2009). Truth, Indefinite Extensibility, and Fitch's Paradox. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
    A number of authors have noted that the key steps in Fitch’s argument are not intuitionistically valid, and some have proposed this as a reason for an anti-realist to accept intuitionistic logic (e.g. Williamson 1982, 1988). This line of reasoning rests upon two assumptions. The first is that the premises of Fitch’s argument make sense from an anti-realist point of view – and in particular, that an anti-realist can and should maintain the principle that all truths are knowable. The second (...)
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  4.  56
    Laureano Luna (2012). Grim's Arguments Against Omniscience and Indefinite Extensibility. International Journal for Philosophy of Religion 72 (2):89-101.
    Patrick Grim has put forward a set theoretical argument purporting to prove that omniscience is an inconsistent concept and a model theoretical argument for the claim that we cannot even consistently define omniscience. The former relies on the fact that the class of all truths seems to be an inconsistent multiplicity (or a proper class, a class that is not a set); the latter is based on the difficulty of quantifying over classes that are not sets. We first address the (...)
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  5. Laureano Luna (2013). Indefinite Extensibility in Natural Language. The Monist 96 (2):295-308.
    The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping (...)
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  6.  18
    S. Hewitt, A Note on Gabriel Uzquiano's 'Varieties of Indefinite Extensibility'.
  7.  30
    Graham Priest (2013). Indefinite Extensibility—Dialetheic Style. Studia Logica 101 (6):1263-1275.
    In recent years, many people writing on set theory have invoked the notion of an indefinitely extensible concept. The notion, it is usually claimed, plays an important role in solving the paradoxes of absolute infinity. It is not clear, however, how the notion should be formulated in a coherent way, since it appears to run into a number of problems concerning, for example, unrestricted quantification. In fact, the notion makes perfectly good sense if one endorses a dialetheic solution to the (...)
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  8.  49
    Stewart Shapiro (2003). Prolegomenon to Any Future Neo-Logicist Set Theory: Abstraction and Indefinite Extensibility. British Journal for the Philosophy of Science 54 (1):59--91.
    The purpose of this paper is to assess the prospects for a neo-logicist development of set theory based on a restriction of Frege's Basic Law V, which we call (RV): PQ[Ext(P) = Ext(Q) [(BAD(P) & BAD(Q)) x(Px Qx)]] BAD is taken as a primitive property of properties. We explore the features it must have for (RV) to sanction the various strong axioms of Zermelo–Fraenkel set theory. The primary interpretation is where ‘BAD’ is Dummett's ‘indefinitely extensible’. 1 Background: what and why? (...)
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  9.  74
    S. Shapiro (1998). Induction and Indefinite Extensibility: The Gödel Sentence is True, but Did Someone Change the Subject? Mind 107 (427):597-624.
    Over the last few decades Michael Dummett developed a rich program for assessing logic and the meaning of the terms of a language. He is also a major exponent of Frege's version of logicism in the philosophy of mathematics. Over the last decade, Neil Tennant developed an extensive version of logicism in Dummettian terms, and Dummett influences other contemporary logicists such as Crispin Wright and Bob Hale. The purpose of this paper is to explore the prospects for Fregean logicism within (...)
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  10.  42
    Peter Clark (1998). Dummett's Argument for the Indefinite Extensibility of Set and Real Number. Grazer Philosophische Studien 55:51-63.
    The paper examines Dummett's argument for the indefinite extensibility of the concepts set, ordinal, real number, set of natural numbers, and natural number. In particular it investigates how the indefinite extensibility of the concept set affects our understanding of the notion of real number and whether the argument to the indefinite extensibility of the reals is cogent. It claims that Dummett is right to think of the universe of sets as an indefinitely extensible domain (...)
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  11. Timothy Williamson (1998). Indefinite Extensibility. Grazer Philosophische Studien 55:1-24.
    Of all the cases made against classical logic, Michael Dummett's is the most deeply considered. Issuing from a systematic and original conception of the discipline, it constitutes one of the most distinctive achievements of twentieth century British philosophy. Although Dummett builds on the work of Brouwer and Heyting, he provides the case against classical logic with a new, explicit and general foundation in the philosophy of language. Dummett's central arguments, widely celebrated if not widely endorsed, concern the implications of the (...)
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  12.  1
    James Walmsley (2002). XIII-Categoricity and Indefinite Extensibility. Proceedings of the Aristotelian Society 102 (3):217-235.
  13.  93
    Crispin Wright, Whence the Paradox? Axiom V and Indefinite Extensibility.
    In a well-known passage in the last chapter of Frege: Philosophy of Mathematics Michael Dummett suggests that Frege’s major “mistake”—the key to the collapse of the project of Grundgesetze—consisted in “his supposing there to be a totality containing the extension of every concept defined over it; more generally [the mistake] lay in his not having the glimmering of a suspicion of the existence of indefinitely extensible concepts” (Dummett [1991, 317]). Now, claims of the form, Frege fell into paradox because……. are (...)
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  14.  18
    James Walmsley (2002). Categoricity and Indefinite Extensibility. Proceedings of the Aristotelian Society 102 (3):217–235.
    Structure is central to the realist view of mathematical disciplines with intended interpretations and categoricity is a model-theoretic notion that captures the idea of the determination of structure by theory. By considering the cases of arithmetic and (pure) set theory, I investigate how categoricity results might offer support from within to the realist view. I argue, amongst other things, that second-order quantification is essential to the support the categoricity results provide. I also note how the findings on categoricity relate to (...)
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  15.  42
    Jeffrey Sanford Russell (forthcoming). Indefinite Divisibility. Inquiry (3):1-25.
    Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of (...)
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  16.  26
    Peter Clark (1994). Poincaré, Richard's Paradox and Indefinite Extensilibity. Psa 2:227--235.
    A central theme in the foundational debates in the early Twentieth century in response to the paradoxes was to invoke the notion of the indefinite extensibility of certain concepts e,g. definability (the Richard paradox) and class (the Zermelo-Russell contradiction). Dummett has recently revived the notion, as the real lesson of the paradoxes and the source of Frege's error in basic law five of the Grundgesetze. The paper traces the historical and conceptual evolution of the concept and critices Dummett's (...)
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  17.  35
    L. Luna & W. Taylor (2014). Taming the Indefinitely Extensible Definable Universe. Philosophia Mathematica 22 (2):198-208.
    In previous work in 2010 we have dealt with the problems arising from Cantor's theorem and the Richard paradox in a definable universe. We proposed indefinite extensibility as a solution. Now we address another definability paradox, the Berry paradox, and explore how Hartogs's cardinality theorem would behave in an indefinitely extensible definable universe where all sets are countable.
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  18.  17
    Laureano Luna (2009). A Note On Formal Reasoning with Extensible Domain. The Reasoner 3 (7):5-6.
    Assuming the indefinite extensibility of any domain of quantification leads to reasoning with extensible domain semantics. It is showed that some theorems (e.g. Thomson's) in conventional semantics logic are not theorems in a logic provided with this new semantics.
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  19. Richard L. Cartwright (1994). Speaking of Everything. Noûs 28 (1):1-20.
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  20.  9
    Santos Gonçalo, Potential Collections.
    The existence of potential collections has been and continues to be the subject of different philosophical debates. In this work I consider three of these debates. I will defend that the collection of all numbers and the collection of all sets need not be understood as potential collections. In contrast, I will defend that the collection of everything can only be understood as a potential collection.
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  21.  48
    J. P. Studd (2012). The Iterative Conception of Set: A (Bi-)Modal Axiomatisation. Journal of Philosophical Logic 42 (5):1-29.
    The use of tensed language and the metaphor of set ‘formation’ found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A (...)
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  22.  42
    Toby Meadows (2016). Sets and Supersets. Synthese 193 (6):1875-1907.
    It is a commonplace of set theory to say that there is no set of all well-orderings nor a set of all sets. We are implored to accept this due to the threat of paradox and the ensuing descent into unintelligibility. In the absence of promising alternatives, we tend to take up a conservative stance and tow the line: there is no universe. In this paper, I am going to challenge this claim by taking seriously the idea that we can (...)
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  23. George Boolos (1993). Whence the Contradiction? Aristotelian Society Supplementary Volume 67:211--233.
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  24. Laureano Luna & William Taylor (2010). Cantor's Proof in the Full Definable Universe. Australasian Journal of Logic 9:11-25.
    Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the (...)
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  25.  28
    Laureano Luna (2008). Can We Consistently Say That We Cannot Speak About Everything? The Reasoner 2 (9):5-7.
    Following an idea from Gödel and Carnap we show how we can speak with absolute generality even if we cannot quantify with absolute generality.
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  26.  61
    Gonçalo Santos (2010). A Not So Fine Version of Generality Relativism. Theoria 25 (2):149-161.
    The generality relativist has been accused of holding a self-defeating thesis. Kit Fine proposed a modal version of generality relativism that tries to resist this claim. We discuss his proposal and argue that one of its formulations is self-defeating.
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  27. Peter Clark (1993). Sets and Indefinitely Extensible Concepts and Classes. Aristotelian Society Supplementary Volume 67:235--249.
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  28.  2
    Benjamin W. McCraw (2016). Recent Objections to Perfect Knowledge and Classical Approaches to Omniscience in Advance. Philosophy and Theology 28 (1):259-270.
    Recently Patrick Grim and Einar Duenger Bohn have argued that there can be no perfectly knowing Being. In particular, they urge that the object of omniscience is logically absurd (Grim) or requires an impossible maximal point of all knowledge (Bohn). I argue that, given a more classical notion of omniscience found in Aquinas and Augustine, we can shift the focus of perfect knowledge from what that being must know to the mode of that being’s understanding. Since Grim and Bohn focus (...)
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  29.  1
    Laureano Luna (2016). Physicalism, Truth, and the Pinocchio Paradox. Mind and Matter 14 (1):77-86.
    We develop an argument sketched by Luna (2011) based on the Pinocchio paradox, which was proposed by Eldridge-Smith and Eldridge- Smith (2010). We show that, upon plausible assumptions, the claim that mental states supervene on bodily states leads to the conclusion that some proposition is both paradoxical and not paradoxical. In order to show how the presence of paradoxes can be harnessed for philosophical argumentation, we present as well a couple of related arguments.
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  30.  25
    Daniel J. Velleman (1993). Constructivism Liberalized. Philosophical Review 102 (1):59-84.
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  31.  50
    A. W. Moore (1998). More on 'The Philosophical Significance of Gödel's Theorem'. Grazer Philosophische Studien 55:103-126.
    In Michael Dummett's celebrated essay on Gödel's theorem he considers the threat posed by the theorem to the idea that meaning is use and argues that this threat can be annulled. In my essay I try to show that the threat is even less serious than Dummett makes it out to be. Dummett argues, in effect, that Gödel's theorem does not prevent us from "capturing" the truths of arithmetic; I argue that the idea that meaning is use does not require (...)
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  32.  2
    Laureano Luna (2016). Rescuing Poincaré From Richard’s Paradox. History and Philosophy of Logic 38 (1):57-71.
    Poincaré in a 1909 lecture in Göttingen proposed a solution to the apparent incompatibility of two results as viewed from a definitionist perspective: on the one hand, Richard’s proof that the definitions of real numbers form a countable set and, on the other, Cantor’s proof that the real numbers make up an uncountable class. Poincaré argues that, Richard’s result notwithstanding, there is no enumeration of all definable real numbers. We apply previous research by Luna and Taylor on Richard’s paradox, (...) extensibility and unrestricted quantification to evaluate Poincaré’s proposal. We emphasize that Poincaré’s solution involves an early recourse to indefinite extensibility and argue that his proposal, if it is to completely avoid Richard’s paradox, requires rejecting absolutely unrestricted quantification: Richard’s paradox provides a context in which paradox seems inescapable if unrestricted quantification is possible. In proposing his solution to the apparent conflict between Richard’s and Canto... (shrink)
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  33.  10
    Eduardo Alejandro Barrio (2011). Teorías de la Verdad Sin Modelos Estándar: Un Nuevo Argumento Para Adoptar Jerarquías. Análisis Filosófico 31 (1):7-32.
    En este artículo, tengo dos objetivos distintos. En primer lugar, mostrar que no es una buena idea tener una teoría de la verdad que, aunque consistente, sea omega-inconsistente. Para discutir este punto, considero un caso particular: la teoría de Friedman-Sheard FS. Argumento que en los lenguajes de primer orden omega inconsistencia implica que la teoría de la verdad no tiene modelo estándar. Esto es, no hay un modelo cuyo dominio sea el conjunto de los números naturales en el cual esta (...)
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  34.  21
    Alexander Paseau (2005). On an Application of Categoricity. Proceedings of the Aristotelian Society 105 (3):411–415.
    James Walmsley in “Categoricity and Indefinite Extensibility” argues that a realist about some branch of mathematics X (e.g. arithmetic) apparently cannot use the categoricity of an axiomatisation of X to justify her belief that every sentence of the language of X has a truth-value. My note corrects Walmsley’s formulation of his claim, and shows that his argument for it hinges on the implausible idea that grasping that there is some model of the axioms amounts to grasping that there (...)
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  35.  57
    Christy Mag Uidhir (ed.) (2013). Art & Abstract Objects. Oxford University Press.
    TABLE OF CONTENTS Introduction: Art, Metaphysics, & The Paradox of Standards (Christy Mag Uidhir) GENERAL ONTOLOGICAL ISSUES 1. Must Ontological Pragmatism be Self-Defeating? (Guy Rohrbaugh) 2. Indication, Abstraction, & Individuation (Jerrold Levinson) 3. Destroying Artworks (Marcus Rossberg) INFORMATIVE COMPARISONS 4. Artworks & Indefinite Extensibility (Roy T. Cook) 5. Historical Individuals Like Anas platyrhynchos & ‘Classical Gas’ (P.D. Magnus) 6. Repeatable Artworks & Genericity (Shieva Kleinschmidt & Jacob Ross) ARGUMENTS AGAINST & ALTERNATIVES TO 7. Against Repeatable Artworks (Allan Hazlett) (...)
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  36.  5
    Luisa Martí (2008). The Semantics of Plural Indefinite Noun Phrases in Spanish and Portuguese. Natural Language Semantics 16 (1):1-37.
    In this paper I provide a decompositional analysis of three kinds of plural indefinites in two related languages, European Spanish and Brazilian Portuguese. The three indefinites studied are bare plurals, the unos (Spanish)/uns (Portuguese) type, and the algunos (Spanish)/alguns (Portuguese) type. The paper concentrates on four properties: semantic plurality, positive polarity, partitivity, and event distribution. The logic underlying the analysis is that of compositionality, applied at the subword level: as items become bigger in form (with the addition of morphemes), they (...)
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  37.  5
    M. Kirchbach (2003). Quantum States of Indefinite Spins: From Baryons to Massive Gravitino. [REVIEW] Foundations of Physics 33 (5):781-812.
    One of the long-standing problems in particle physics is the covariant description of higher spin states. The standard formalism is based upon totally symmetric Lorentz invariant tensors of rank-K with Dirac spinor components, $\psi _{\mu _1 \cdots \mu _K } $ , which satisfy the Dirac equation for each space time index. In addition, one requires $\partial ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } = 0{\text{ }}and{\text{ }}\gamma ^{\mu _1 } \psi _{\mu _1 \cdots \mu _K } (...)
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  38.  87
    Barbara Abbott, The Difference Between Definite and Indefinite Descriptions.
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  39.  28
    Paul Dekker (2002). Meaning and Use of Indefinite Expressions. Journal of Logic, Language and Information 11 (2):141-194.
    Sentences containing pronouns and indefinite noun phrases can be said toexpress open propositions, propositions which display gaps to be filled.This paper addresses the question what is the linguistic content ofthese expressions, what information they can be said to provide to ahearer, and in what sense the information of a speaker can be said tosupport their utterance. We present and motivate first order notions ofcontent, update and support. The three notions are each defined in acompositional fashion and brought together within (...)
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  40.  19
    Isabelle Bruno (2009). The “Indefinite Discipline” of Competitiveness Benchmarking as a Neoliberal Technology of Government. Minerva 47 (3):261-280.
    Working on the assumption that ideas are embedded in socio-technical arrangements which actualize them, this essay sheds light on the way the Open Method of Co-ordination (OMC) achieves the Lisbon strategic goal: to become the most competitive and dynamic knowledge-based economy in the world . Rather than framing the issue in utilitarian terms, it focuses attention on quantified indicators, comparable statistics and common targets resulting from the increasing practice of intergovernmental benchmarking, in order to tackle the following questions: how does (...)
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  41.  93
    Irene Heim (1982). The Semantics of Definite and Indefinite Noun Phrases. Dissertation, UMass Amherst
  42.  23
    A. Cohen (2001). On the Generic Use of Indefinite Singulars. Journal of Semantics 18 (3):183-209.
    The distribution of indefinite singular generics is much more restricted than that of bare plural generics. The former, unlike the latter, seem to require that the property predicated of their subject be, in some sense, ‘definitional’. Moreover, the two constructions exhibit different scopal behaviour, and differ in their felicity in conjunctions, questions, and expressions describing the speaker's confidence. I propose that the reason is that the two expressions, in fact, have rather different meanings. Carlson (1995) makes a distinction between (...)
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  43.  33
    Paul Thom (2008). Al-Fārābī on Indefinite and Privative Names. Arabic Sciences and Philosophy 18 (2):193-209.
    In his Short Treatise and his Commentary on the Peri hermeneias, al-Fbī offers two different but related accounts of indefinite terms and the propositions that contain them. In both works he presents a series of different senses that an indefinite term may have, commencing with a sense in which such a term would be equivalent to a privative term, and concluding with a sense in which it would determine the logical complement of the corresponding definite term. I offer (...)
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  44.  42
    Frank Jackson & Robert Pargetter (1973). Indefinite Probability Statements. Synthese 26 (2):205 - 217.
    Indefinite probability statements can be analysed in terms of statements which attribute probability to propositions. Therefore, there is no need to find a special place in probability theory for them; once we have an adequate account of statements that straightforwardly attribute probability to propositions, we will automatically have an adequate account of indefinite probability statements.
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  45.  68
    John Bigelow & Robert Pargetter (1987). An Analysis of Indefinite Probability Statements. Synthese 73 (2):361 - 370.
    An analysis of indefinite probability statements has been offered by Jackson and Pargetter (1973). We accept that this analysis will assign the correct probability values for indefinite probability claims. But it does so in a way which fails to reflect the epistemic state of a person who makes such a claim. We offer two alternative analyses: one employing de re (epistemic) probabilities, and the other employing de dicto (epistemic) probabilities. These two analyses appeal only to probabilities which are (...)
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  46.  32
    Anastasia Giannakidou & Jason Merchant, On the Interpretation of Null Indefinite Objects in Greek.
    In this paper, we examine the properties of a novel kind of nominal ellipsis in Greek, which we call indefinite argument drop (IAD), concentrating on its manifestation in object positions. We argue that syntactically these null objects are present as pro, and we show that semantically they are licensed only by weak DP antecedents (in the sense of Milsark 1974). We compare IAD with NP- internal ellipsis, as attested also in English among many other languages, and show that IAD (...)
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  47.  15
    K. Schwabe (2001). On Shared Indefinite NPs in Coordinative Structures. Journal of Semantics 18 (3):243-269.
    Indefinite NPs in shared constituents of coordinative structures in German exhibit different referential options with respect to scope and specificity. These options are restricted by the informational status of the indefinite: A focused indefinite NP can receive all referential options, while a non‐focused one can only get the narrow scope non‐specific reading. Our analysis assumes that the information structure of the coordination determines the syntactic representation of the construction in terms of deletion or right‐node‐raising. Dependent on the (...)
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  48.  18
    Enrique Alvarez & Manuel Correia (2012). Syllogistic with Indefinite Terms. History and Philosophy of Logic 33 (4):297-306.
    This paper presents a restructured set of axioms for categorical logic. In virtue of it, the syllogistic with indefinite terms is deduced and proved, within the categorical logic boundaries. As a result, the number of all the conclusive syllogisms is deduced through a simple and axiomatic methodology. Moreover, the distinction between immediate and mediate inferences disappears, which reinstitutes the unity of Aristotelian logic.
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  49.  17
    Arnold Nat (1979). First-Order Indefinite and Uniform Neighbourhood Semantics. Studia Logica 38 (3):277 - 296.
    The main purpose of this paper is to define and study a particular variety of Montague-Scott neighborhood semantics for modal propositional logic. We call this variety the first-order neighborhood semantics because it consists of the neighborhood frames whose neighborhood operations are, in a certain sense, first-order definable. The paper consists of two parts. In Part I we begin by presenting a family of modal systems. We recall the Montague-Scott semantics and apply it to some of our systems that have hitherto (...)
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  50.  7
    Stephen Barker (2009). Indefinite Descriptions as Referring Terms. Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 16 (4):569-586.
    I argue that indefinite descriptions are referring terms. This is not the ambiguity thesis: that sometimes they are referring terms and sometimes something else, such as quantifiers . No. On my view they are always referring terms; and never quantifiers. I defend this thesis by modifying the standard conception of what a referring term is: a modification that needs to be made anyway, irrespective of the treatment of indefinites. I derive this approach from my speech-act theoretic semantics . The (...)
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