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  1. Truthmaker Semantics, Ground, and Generality.Kit Fine & Louis DeRosset - forthcoming - Topoi.
    Our aim in this paper is to extend the semantics for the kind of logic of ground developed in (deRosset and Fine, 2023). In that paper, we very briefly suggested a way of treating universal and existential quantification over a fixed domain of objects. Here we explore some options for extending the treatment to allow for a variable domain of objects.
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  2. Stratified Restricted Universals.Michael Calasso & Shay Allen Logan - 2023 - Asian Journal of Philosophy 2 (2):44.
    Jc Beall has made several contributions to the theory of restricted quantification in relevant logics. This paper examines these contributions and proposes an alternative account of restricted universals. The alternative is not, however, a theory of relevant restricted universals in any real sense. It is, however, a theory of restricted universals phrased in the most plausible general quantificational theory for relevant logics—Kit Fine’s stratified semantics. The motivation both for choosing this semantic framework and for choosing the particular theory of restricted (...)
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  3. The Constituents of the Propositions of Logic.Kevin C. Klement - 2015 - In Donovan Wishon & Bernard Linsky (eds.), Acquaintance, Knowledge, and Logic: New Essays on Bertrand Russell's The Problems of Philosophy. Stanford: CSLI Publications. pp. 189–229.
    In he Problems of Philosophy and other works of the same period, Russell claims that every proposition must contain at least one universal. Even fully general propositions of logic are claimed to contain “abstract logical universals”, and our knowledge of logical truths claimed to be a species of a priori knowledge of universals. However, these views are in considerable tension with Russell’s own philosophy of logic and mathematics as presented in Principia Mathematica. Universals generally are qualities and relations, but if, (...)
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  4. Cross-linguistic insights in the theory of semantics and its interface with syntax.Anna Szabolcsi - forthcoming - Theoretical Linguistics.
    This paper highlights a small selection of cases where crosslinguistic insights have been important to big questions in the theory of semantics and the syntax/semantics interface. The selection includes (i) the role and representation of Speaker and Addressee in the grammar; (ii) mismatches between form and interpretation motivating high-placed silent operators for functional elements; and (iii) the explanation of semantic universals, including universals pertaining to inventories, in terms of learnability and the trade-off between informativeness and simplicity.
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  5. An Expressivist Theory of Taste Predicates.Dilip Ninan - forthcoming - Philosophers' Imprint.
    Simple taste predications come with an `acquaintance requirement': they require the speaker to have had a certain kind of first-hand experience with the object of predication. For example, if I tell you that the crème caramel is delicious, you would ordinarily assume that I have actually tasted the crème caramel and am not simply relying on the testimony of others. The present essay argues in favor of a lightweight expressivist account of the acquaintance requirement. This account consists of a recursive (...)
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  6. Against Fregean Quantification.Bryan Pickel & Brian Rabern - 2023 - Ergo: An Open Access Journal of Philosophy 9 (37):971-1007.
    There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. (...)
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  7. What’s Positive and Negative about Generics: A Constrained Indexical Approach.Junhyo Lee & Anthony Nguyen - 2022 - Philosophical Studies 179 (5):1739-1761.
    Nguyen argues that only his radically pragmatic account and Sterken’s indexical account can capture what we call the positive data. We present some new data, which we call the negative data, and argue that no theory of generics on the market is compatible with both the positive data and the negative data. We develop a novel version of the indexical account and show that it captures both the positive data and the negative data. In particular, we argue that there is (...)
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  8. An Inferential Impasse in the Theory of Implicatures.Savas L. Tsohatzidis - manuscript
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  9. Invariance and Necessity.Gila Sher - 2019 - In Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. Berlin, Boston: De Gruyter. pp. 55-70.
    Properties and relations in general have a certain degree of invariance, and some types of properties/relations have a stronger degree of invariance than others. In this paper I will show how the degrees of invariance of different types of properties are associated with, and explain, the modal force of the laws governing them. This explains differences in the modal force of laws/principles of different disciplines, starting with logic and mathematics and proceeding to physics and biology.
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  10. Quantifier particles and compositionality.Anna Szabolcsi - 2013 - Proceedings of the 19th Amsterdam Colloquium.
    In many languages, the same particles build quantifier words and serve as connectives, additive and scalar particles, question markers, existential verbs, and so on. Do the roles of each particle form a natural class with a stable semantics? Are the particles aided by additional elements, overt or covert, in fulfilling their varied roles? I propose a unified analysis, according to which the particles impose partial ordering requirements (glb and lub) on the interpretations of their hosts and the immediate larger contexts, (...)
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  11. Generic one, arbitrary PRO, and the first person.Friederike Moltmann - 2006 - Natural Language Semantics 14 (3):257–281.
    The generic pronoun 'one' (or its empty counterpart, arbitrary PRO) exhibits a range of properties that show a special connection to the first person, or rather the relevant intentional agent (speaker, addressee, or described agent). The paper argues that generic 'one' involves generic quantification in which the predicate is applied to a given entity ‘as if’ to the relevant agent himself. This is best understood in terms of simulation, a central notion in some recent developments in the philosophy of mind (...)
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  12. Boguslawski's Analysis of Quantification in Natural Language.John-Michael Kuczynski - 2010 - Journal of Pragmatics 42 (10):2836-2844.
    The semantic rules governing natural language quantifiers (e.g. "all," "some," "most") neither coincide with nor resemble the semantic rules governing the analogues of those expressions that occur in the artificial languages used by semanticists. Some semanticists, e.g. Peter Strawson, have put forth data-consistent hypotheses as to the identities of the semantic rules governing some natural-language quantifiers. But, despite their obvious merits, those hypotheses have been universally rejected. In this paper, it is shown that those hypotheses are indeed correct. Moreover, data-consistent (...)
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  13. Nominal quantification as top-level anaphora.Maria Bittner - manuscript
    So far, we have focused on discourse reference to atomic individuals and specific times, events, and states. The basic point of the argument was that all types of discourse reference involve attention-guided anaphora (in the sense of Bittner 2012: Ch. 2). We now turn to discourses involving anaphora to and by quantificational expressions. Today, we focus on quantification over individuals but the analysis we develop will directly generalize to other semantic types. The basic idea is that quantification is one more (...)
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  14. Ways of Scope Taking.Anna Szabolcsi (ed.) - 1997 - Kluwer Academic Publishers.
    Ways of Scope Taking is concerned with syntactic, semantic and computational aspects of scope. Its starting point is the well-known but often neglected fact that different types of quantifiers interact differently with each other and other operators. The theoretical examination of significant bodies of data, both old and novel, leads to two central claims. (1) Scope is a by-product of a set of distinct Logical Form processes; each quantifier participates in those that suit its particular features. (2) Scope interaction is (...)
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  15. Quantification as reference: Evidence from Q-verbs.Maria Bittner & Naja Trondhjem - 2008 - In Lisa Matthewson (ed.), Quantification: A Cross-Linguistic Perspective. Emerald. pp. 7-66.
    Formal semantics has so far focused on three categories of quantifiers, to wit, Q-determiners (e.g. 'every'), Q-adverbs (e.g. 'always'), and Q-auxiliaries (e.g. 'would'). All three can be analyzed in terms of tripartite logical forms (LF). This paper presents evidence from verbs with distributive affixes (Q-verbs), in Kalaallisut, Polish, and Bininj Gun-wok, which cannot be analyzed in terms of tripartite LFs. It is argued that a Q-verb involves discourse reference to a distributive verbal dependency, i.e. an episode-valued function that sends different (...)
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  16. Mass nouns, Count nouns and Non-count nouns.Henry Laycock - 2005 - In Alex Barber (ed.), Encyclopedia of Language and Linguistics. Elsevier.
    I present a high-level account of the semantical distinction between count nouns and non-count nouns. The basic idea is that count nouns are semantically either singular or plural and non-count nouns are neither.
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  17. First-Order Quantifiers.G. Aldo Antonelli - manuscript
    In §21 of Grundgesetze der Arithmetik asks us to consider the forms: a a2 = 4 and a a > 0 and notices that they can be obtained from a φ(a) by replacing the function-name placeholder φ(ξ) by names for the functions ξ2 = 4 and ξ > 0 (and the placeholder cannot be replaced by names of objects or of functions of 2 arguments).
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  18. What Mary Did Yesterday: Reflections on Knowledge-wh.Berit Brogaard - 2009 - Philosophy and Phenomenological Research 78 (2):439 - 467.
    Reductionists about knowledge-wh hold that "s knows-wh" (e.g. "John knows who stole his car") is reducible to "there is a proposition p such that s knows that p, and p answers the indirect question of the wh-clause." Anti-reductionists hold that "s knows-wh" is reducible to "s knows that p, as the true answer to the indirect question of the wh-clause." I argue that both of these positions are defective. I then offer a new analysis of knowledge-wh as a special kind (...)
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  19. Quantifiers and propositional attitudes: Quine revisited.Sean Crawford - 2008 - Synthese 160 (1):75 - 96.
    Quine introduced a famous distinction between the ‘notional’ sense and the ‘relational’ sense of certain attitude verbs. The distinction is both intuitive and sound but is often conflated with another distinction Quine draws between ‘dyadic’ and ‘triadic’ (or higher degree) attitudes. I argue that this conflation is largely responsible for the mistaken view that Quine’s account of attitudes is undermined by the problem of the ‘exportation’ of singular terms within attitude contexts. Quine’s system is also supposed to suffer from the (...)
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  20. Variables, generality and existence.Henry Laycock - 2006 - In Paulo Valore (ed.), Topics on General and Formal Ontology. Polimetrica. pp. 27.
    So-called mass nouns, however precisely they are defined, are in any case a subset of non-count nouns. Count nouns are either singular or plural; to be non-count is hence to be neither singular nor plural. This is not, as such, a metaphysically significant contrast: 'pieces of furniture' is plural whereas 'furniture' itself is non-count. This contrast is simply between 'the many / few' and 'the much / little' - between counting and measuring. However not all non-count nouns are, like 'furniture', (...)
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  21. Words without objects: semantics, ontology, and logic for non-singularity.Henry Laycock - 2006 - New York: Oxford University Press.
    A picture of the world as chiefly one of discrete objects, distributed in space and time, has sometimes seemed compelling. It is however one of the main targets of Henry Laycock's book; for it is seriously incomplete. The picture, he argues, leaves no space for "stuff" like air and water. With discrete objects, we may always ask "how many?," but with stuff the question has to be "how much?" Laycock's fascinating exploration also addresses key logical and linguistic questions about the (...)
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  22. Scope and binding.Anna Szabolcsi - 2011 - In von Heusinger, Maienborn & Portner (eds.), Semantics: An International Handbook of Natural Language Meaning, Vol. 2. de Gruyter Mouton.
    The first part of this article (Sections 1–5) focuses on the classical notions of scope and binding and their formal foundations. It argues that once their semantic core is properly understood, it can be implemented in various different ways: with or without movement, with or without variables. The second part (Sections 6–12) takes up the empirical issues that have redrawn the map in the past two decades. It turns out that scope is not a primitive. Existential scope and distributive scope (...)
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Generalized Quantifiers
  1. Reference to singular kinds in Germanic and Romance.Samuel Jambrović - 2023 - Proceedings of the 2023 Annual Conference of the Canadian Linguistic Association.
    The need for the definite article to express a singular kind ("the cat") in the Germanic languages is predicted by Borer's (2005) structural approach to the mass-count distinction. Chierchia's (1998) "down" operator can apply to nPs to derive mass kinds ("rice") and to DivPs to derive plural kinds ("cats"), but there is no determinerless structure that exclusively denotes properties of atomic individuals to which this same operator can apply to derive singular kinds. The only alternative is the process that Chierchia (...)
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  2. Asymmetry Effects in Generic and Quantified Generalizations.Kevin Reuter, Eleonore Neufeld & Guillermo Del Pinal - 2023 - Proceedings of the 45Th Meeting of the Cognitive Science Society 45:1-6.
    Generic statements (‘Tigers have stripes’) are pervasive and early-emerging modes of generalization with a distinctive linguistic profile. Previous experimental work found that generics display a unique asymmetry between their acceptance conditions and the implications that are typically drawn from them. This paper presents evidence against the hypothesis that only generics display an asymmetry. Correcting for limitations of previous designs, we found a generalized asymmetry effect across generics, various kinds of explicitly quantified statements (‘most’, ‘some’, ‘typically’, ‘usually’), and variations in types (...)
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  3. Update rules and semantic universals.Luca Incurvati & Giorgio Sbardolini - 2023 - Linguistics and Philosophy 46 (2):259-289.
    We discuss a well-known puzzle about the lexicalization of logical operators in natural language, in particular connectives and quantifiers. Of the many logically possible operators, only few appear in the lexicon of natural languages: the connectives in English, for example, are conjunction _and_, disjunction _or_, and negated disjunction _nor_; the lexical quantifiers are _all, some_ and _no_. The logically possible nand (negated conjunction) and Nall (negated universal) are not expressed by lexical entries in English, nor in any natural language. Moreover, (...)
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  4. Nothing, Everything, Something!Achille C. Varzi - 2022 - In Fosca Mariani-Zini (ed.), The Meaning of Something: Rethinking the Logic and the Unity of Metaphysics. Springer.
    Universalist and nihilist answers to philosophical questions may be extreme, but they are clear enough. Aliquidist answers, by contrast, are typically caught between the Scylla of vagueness and indeterminacy and the Charybdis of ungroundedness and arbitrariness, and steering a proper middle course—saying exactly where in the middle one is going to settle—demands exceptional navigating powers. I myself tend to favor extreme answers precisely for this reason. Here, however, I consider one sense in which Something may claim superiority over its polar (...)
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  5. What is Logical in First-Order Logic?Boris Čulina - manuscript
    In this article, logical concepts are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the universal and existential quantifiers form a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language.
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  6. The incompleteness of extensional object languages of physics and time reversal. Part 2.Andrew Holster - manuscript
    This continues from Part 1. It is shown how an intensional interpretation of physics object languages can be formalised, and how a syntactic compositional time reversal operator can subsequently be defined. This is applied to solve the problems used as examples in Part 1. A proof of a general theorem that such an operator must be defineable is sketched. A number of related issues about the interpretation of theories of physics, including classical and quantum mechanics and classical EM theory are (...)
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  7. Truth and Generalized Quantification.Bruno Whittle - 2019 - Australasian Journal of Philosophy 97 (2):340-353.
    Kripke [1975] gives a formal theory of truth based on Kleene's strong evaluation scheme. It is probably the most important and influential that has yet been given—at least since Tarski. However, it has been argued that this theory has a problem with generalized quantifiers such as All—that is, All ϕs are ψ—or Most. Specifically, it has been argued that such quantifiers preclude the existence of just the sort of language that Kripke aims to deliver—one that contains its own truth predicate. (...)
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  8. Vagueness and Quantification.Andrea Iacona - 2016 - Journal of Philosophical Logic 45 (5):579-602.
    This paper deals with the question of what it is for a quantifier expression to be vague. First it draws a distinction between two senses in which quantifier expressions may be said to be vague, and provides an account of the distinction which rests on independently grounded assumptions. Then it suggests that, if some further assumptions are granted, the difference between the two senses considered can be represented at the formal level. Finally, it outlines some implications of the account provided (...)
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  9. Life on the Range.G. Aldo Antonelli - 2015 - In A. Torza (ed.), Quantifiers, Quantifiers, and Quantifiers. Synthese LIbrary. pp. 171-189.
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  10. A solution to the donkey sentence problem.Adam Morton - 2015 - Analysis 75 (4):554-557.
    The problem concerns quantifiers that seem to hover between universal and existential readings. I argue that they are neither, but a different quantifier that has features of each. NOTE the published paper has a mistake. I have corrected this in the version on this site. A correction note will appear in Analysis.
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  11. 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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  12. Background notions in lattice theory and generalized quantifiers.Anna Szabolcsi - 1997 - In Ways of Scope Taking. Kluwer Academic Publishers. pp. 1--27.
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  13. Quantifiers in pair-list readings.Anna Szabolcsi - 1997 - In Ways of Scope Taking. Kluwer Academic Publishers. pp. 311--347.
    Section 1 provides a brief summary of the pair-list literature singling out some points that are particularly relevant for the coming discussion. -/- Section 2 shows that the dilemma of quantifi cation versus domain restriction arises only in extensional complement interrogatives. In matrix questions and in intensional complements only universals support pairlist readings, whence the simplest domain restriction treatment suffices. Related data including conjunction, disjunction, and cumulative readings are discussed -/- Section 3 argues that in the case of extensional complements (...)
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  14. The Square of Opposition and Generalized Quantifiers.Duilio D'Alfonso - 2012 - In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser. pp. 219--227.
    In this paper I propose a set-theoretical interpretation of the logical square of opposition, in the perspective opened by generalized quantifier theory. Generalized quantifiers allow us to account for the semantics of quantificational Noun Phrases, and of other natural language expressions, in a coherent and uniform way. I suggest that in the analysis of the meaning of Noun Phrases and Determiners the square of opposition may help representing some semantic features responsible to different logical properties of these expressions. I will (...)
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  15. Quantification and Logical Form.Andrea Iacona - 2015 - In Alessandro Torza (ed.), Quantifiers, Quantifiers, and Quantifiers. Springer. pp. 125-140.
    This paper deals with the logical form of quantified sentences. Its purpose is to elucidate one plausible sense in which quantified sentences can adequately be represented in the language of first-order logic. Section 1 introduces some basic notions drawn from general quantification theory. Section 2 outlines a crucial assumption, namely, that logical form is a matter of truth-conditions. Section 3 shows how the truth-conditions of quantified sentences can be represented in the language of first-order logic consistently with some established undefinability (...)
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  16. The Semantics of Together.Friederike Moltmann - 2004 - Natural Language Semantics 12 (4):289-318.
    The semantic function of the modifier 'together' in adnominal position has generally been considered to be that of preventing a distributive reading of the predicate. This paper will argue that this view is mistaken. The semantic function of adnominal 'together' rather is that of inducing a cumulative measurement of the group that together is associated with. The measurement-based analysis of adnominal together that I propose can also, with some modifications, be extended to adverbial occurrences of together.
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  17. Response to Westerstahl.Hanoch Ben-Yami - 2012 - Logique Et Analyse 55 (217):47-55.
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  18. Modal Ontology and Generalized Quantifiers.Peter Fritz - 2013 - Journal of Philosophical Logic 42 (4):643-678.
    Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with so-called inner and outer (...)
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  19. Quantification.Anna Szabolcsi - 2010 - New York: Cambridge University Press.
    This book surveys research in quantification starting with the foundational work in the 1970s. It paints a vivid picture of generalized quantifiers and Boolean semantics. It explains how the discovery of diverse scope behavior in the 1990s transformed the view of quantification, and how the study of the internal composition of quantifiers has become central in recent years. It presents different approaches to the same problems, and links modern logic and formal semantics to advances in generative syntax. A unique feature (...)
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  20. Jaap van der Does & Jan Van Eijk, eds., Quantifiers, Logic, and Language[REVIEW]Varol Akman - 1998 - Natural Language Engineering 4 (4):363-382.
    This is a review of Quantifiers, Logic, and Language, edited by Jaap van der Does and Jan van Eijk, published by CSLI (Center for the Study of Language and Information) Publications, Stanford, CA, in 1996.
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  21. Descriptions: Predicates or quantifiers?Berit Brogaard - 2007 - Australasian Journal of Philosophy 85 (1):117 – 136.
    In this paper I revisit the main arguments for a predicate analysis of descriptions in order to determine whether they do in fact undermine Russell's theory. I argue that while the arguments without doubt provide powerful evidence against Russell's original theory, it is far from clear that they tell against a quantificational account of descriptions.
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  22. Sharvy's theory of definite descriptions revisited.Berit Brogaard - 2007 - Pacific Philosophical Quarterly 88 (2):160–180.
    The paper revisits Sharvy's theory of plural definite descriptions. An alternative account of plural definite descriptions building on the ideas of plural quantification and non-distributive plural predication is developed. Finally, the alternative is extrapolated to account for generic uses of definite descriptions.
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  23. The but not all: A partitive account of plural definite descriptions.Berit Brogaard - 2007 - Mind and Language 22 (4):402–426.
    A number of authors in favor of a unitary account of singular descriptions have alleged that the unitary account can be extrapolated to account for plural definite descriptions. In this paper I take a closer look at this suggestion. I argue that while the unitary account is clearly onto something right, it is in the end empirically inadequate. At the end of the paper I offer a new partitive account of plural definite descriptions that avoids the problems with both the (...)
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  24. The syntax of scope.Anna Szabolcsi - 2000 - In Mark Baltin & Chris Collins (eds.), Handbook ... Syntax. Blackwell. pp. 607--633.
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Plural Quantification
  1. The Argument from Determinate Vagueness.Jaime Castillo-Gamboa - forthcoming - Oxford Studies in Metaphysics.
    The Lewis-Sider argument from vagueness is one of the most powerful objections against restricted composition. Many have resisted the argument by rejecting its key premise, namely that existence is not vague. In this paper, I argue that this strategy is ineffective as a response to vagueness-based objections against restricted composition. To that end, I formulate a new argument against restricted composition: the argument from determinate vagueness. Unlike the Lewis-Sider argument, my argument doesn’t require accepting that existence is not vague, but (...)
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  2. On Type Distinctions and Expressivity.Salvatore Florio - 2023 - Proceedings of the Aristotelian Society 123 (2):150-172.
    Quine maintained that philosophical and scientific theorizing should be conducted in an untyped language, which has just one style of variables and quantifiers. By contrast, typed languages, such as those advocated by Frege and Russell, include multiple styles of variables and matching kinds of quantification. Which form should our theories take? In this article, I argue that expressivity does not favour typed languages over untyped ones.
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  3. Ultimate V.Sam Roberts - manuscript
    Potentialism is the view that the universe of sets is inherently potential. It comes in two main flavours: height-potentialism and width-potentialism. It is natural to think that height and width potentialism are just aspects of a broader phenomenon of potentialism, that they might both be true. The main result of this paper is that this is mistaken: height and width potentialism are jointly inconsistent. Indeed, I will argue that height potentialism is independently committed to an ultimate background universe of sets, (...)
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  4. Special Quantification: Substitutional, Higher-Order, and Nominalization Approaches.Friederike Moltmann - forthcoming - In Alex Grzankowski & Anthony Savile (eds.), Thought: its Origin and Reach. Essays in Honour of Mark Sainsbury. Routledge.
    Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like 'something' permit a replacement, preserving grammaticality or the same reading of the verb: (1) a. John claims that he won. b. ??? John claims a proposition / some thing. c. John claims something. In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other (...)
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