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About this topic
Summary This category can be used for any consideration of quantifiers collectively or, perhaps more appropriately, specific quantifiers (other than existential and universal), such as are present in natural language but not present in another category under Quantifiers.  (I would use the top category for a consideration of quantifiers collectively.)  It can also be used for a consideration of, say, both restricted and unrestricted quantification, or both objectual and substitutional quantification.
Key works An excellent example of a quantifier ever-present in natural language, which is one way to explain the ubiquity of vagueness in natural language (and in our thinking) is Grim 2005.  There really aren't key works, though, given how many topics are covered in a miscellaneous category.
Introductions Likewise, and most certainly, there are no introductory works for any specific quantifier, although some works, such as the one cited above, do not need a great deal of technical sophistication to appreciate (in both senses of that word). Standard logic textbooks are the best introductions to the existential and universal quantifiers, which is why most discussions of these really do not fit here.
Related categories

87 found
1 — 50 / 87
  1. added 2018-09-06
    Logic & Natural Language on Plural Reference and its Semantic and Logical Significance.Hanoch Ben-Yami - 2004 - Routledge.
    Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus' place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language in its fundamental semantic characteristics, primarily in (...)
  2. added 2018-08-06
    Categories of First-Order Quantifiers.Urszula Wybraniec-Skardowska - 2018 - In Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present. Basel, Switzerland: pp. 575-597.
    One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...)
  3. added 2018-03-09
    Tractarian First-Order Logic: Identity and the N-Operator: Tractarian First-Order Logic.Brian Rogers & Kai F. Wehmeier - 2012 - Review of Symbolic Logic 5 (4):538-573.
    In the Tractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called “N” by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on early work of Hintikka’s, (...)
  4. added 2018-03-08
    Singular Terms, Predicates and the Spurious ‘Is’ of Identity.Danny Frederick - 2013 - Dialectica 67 (3):325-343.
    Contemporary orthodoxy affirms that singular terms cannot be predicates and that, therefore, ‘is’ is ambiguous as between predication and identity. Recent attempts to treat names as predicates do not challenge this orthodoxy. The orthodoxy was built into the structure of modern formal logic by Frege. It is defended by arguments which I show to be unsound. I provide a semantical account of atomic sentences which draws upon Mill's account of predication, connotation and denotation. I show that singular terms may be (...)
  5. added 2018-02-17
    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 (...)
  6. added 2017-10-11
    Ideology in a Desert Landscape.Alessandro Torza - 2017 - Philosophical Issues 27 (1):383-406.
    On one influential view, metaphysical fundamentality can be understood in terms of joint-carving. Ted Sider has recently argued that some first order quantifier is joint-carving, and modal notions are not joint-carving. After vindicating the theoretical indispensability of quantification against recent criticism, I will defend a logical result due to Arnold Koslow which implies that and are incompatible. I will therefore consider an alternative understanding of Sider's metaphysics to the effect that some first order quantifier is joint-carving, and intensional notions are (...)
  7. added 2017-07-28
    Semantics and Proof Theory of the Epsilon Calculus.Richard Zach - 2017 - In Sujata Ghosh & Sanjiva Prasad (eds.), Logic and Its Applications. ICLA 2017. Berlin, Heidelberg: Springer. pp. 27-47.
    The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and accessible presentations of its theory on the other. One significant early result for the original axiomatic proof system for the epsilon-calculus is the first epsilon theorem, for which a proof is sketched. The system itself is discussed, also relative to possible semantic interpretations. The problems facing (...)
  8. added 2017-03-03
    Quantification, Pronouns, and VP Anaphora.Barbara Partee & Emmon Bach - 1984 - In Truth, Interpretation and Information,. Amsterdam: Foris Publications. pp. 99-130.
  9. added 2017-02-27
    The Epsilon Calculus.Jeremy Avigad & Richard Zach - 2008 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University.
    The epsilon calculus is a logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics. The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. Specifically, in the calculus, a term εx A denotes some x satisfying A(x), if there is one. In Hilbert's Program, the epsilon terms play the role of ideal elements; the aim of Hilbert's finitistic consistency proofs is to give a procedure which removes such terms (...)
  10. added 2016-12-30
    Quantifier Variance and Indefinite Extensibility.Jared Warren - 2017 - 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, or metaphysically suspect in requiring nonstandard assumptions about (...)
  11. added 2016-12-08
    The Logic of Failures of the Cinematic Imagination: Two Case Studies – and a Logical Puzzle and Solution in Just One.Joseph S. Fulda - 2013 - Pragmatics and Society 4 (1):105-111.
    This piece is intended to explicate - by providing a precising definition of - the common cinematic figure which I term “the failure of the cinematic imagination,“ while presenting a logical puzzle and its solution within a simple Gricean framework. -/- It should be noted that this is neither fully accurate nor fully precise, because of the audience; one should examine the remaining articles in the issue to understand what I mean.
  12. added 2016-09-30
    The Antinomy of the Variable: A Tarskian Resolution.Bryan Pickel & Brian Rabern - 2016 - Journal of Philosophy 113 (3):137-170.
    Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables ‘x’ (...)
  13. added 2016-09-21
    Reply to Fine.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):571-583.
  14. added 2016-08-10
    Un punto a favor de Russell.Pierre Baumann - 2015 - Retorno 1 (1):35-48.
  15. added 2016-07-18
    NASSLLI 2016 Dynamic Semantics (5): Quantification.Maria Bittner - unknown
    Featured course on "Dynamic Semantics" at NASSLLI 2016. Day 5: Quantification. Abstract: In discourse, quantifiers can function as antecedents or anaphors. We analyze a sample discourse in Dynamic Plural Logic (DPlL, van den Berg 1993, 1994), which represents not only current discourse referents, but also current relations by means of plural information states. This makes it possible to analyze quantification as structured discourse reference. Finally, the DPlL analysis is transposed into Update with Centering, to simplify the formalism and relate quantification (...)
  16. added 2016-07-05
    On Logical Relativity.Achille C. Varzi - 2002 - Philosophical Issues 12 (1):197-219.
    One logic or many? I say—many. Or rather, I say there is one logic for each way of specifying the class of all possible circumstances, or models, i.e., all ways of interpreting a given language. But because there is no unique way of doing this, I say there is no unique logic except in a relative sense. Indeed, given any two competing logical theories T1 and T2 (in the same language) one could always consider their common core, T, and settle (...)
  17. added 2016-03-15
    Transparent Knowledge Once Again.Jaakko Hintikka - 1973 - Philosophical Studies 24 (2):125 - 127.
  18. added 2016-02-18
    Deixis and Anaphora.François Recanati - 2002 - In Zoltán Gendler Szabó (ed.), Semantics Versus Pragmatics. Oxford University Press. pp. 286--316.
    A defence of the 'pragmatic' theory of anaphora (which stresses the analogy between anaphora and deixis) against an argument put forward by Gareth Evans.
  19. added 2015-12-04
    Introduction.Alessandro Torza - 2015 - In Quantifiers, Quantifiers, and Quantifiers. Themes in Logic, Metaphysics and Language. (Synthese Library vol 373). Springer. pp. 1-15.
  20. added 2015-11-26
    The Incompleteness of the World and Its Consequences.Jan Westerhoff - 2013 - Metaphysica 14 (1):79-92.
    In the recent literature we find various arguments against the possibility of absolutely general quantification. Far from being merely a technical question in the philosophy of logic, the impossibility of absolutely general quantification (if established) would have severe consequence for ontology, for it would imply the non-existence of the world as traditionally conceived. This paper will investigate these implications for ontology and consider some possible ways of addressing them.
  21. added 2015-10-15
    Spectra of Formulae with Henkin Quantifiers.Joanna Golińska & Konrad Zdanowski - 2003 - In A. Rojszczak, J. Cachro & G. Kurczewski (eds.), Philosophical Dimensions of Logic and Science. Kluwer Academic Publishers. pp. 29--45.
    It is known that various complexity-theoretical problems can be translated into some special spectra problems (see e.g. Fagin [Fa74] or Blass and Gurevich, [Bl-Gu86]). So questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quanti fiers in the empty vocabulary. This problem has been investigated fi rstly by Krynicki and Mostowski in [Kr-Mo 92] and [Kr- Mo 95]. All presented results can be (...)
  22. added 2015-10-08
    Compositionality Without Word Boundaries: (The) More and (the) Most.Anna Szabolcsi - 2012 - Proceedings of Semantics and Linguistic Theory (SALT) 22.
    This paper seeks to illustrate the advantages of not treating phonological words as distinguished building blocks in compositional semantics. Following Bobaljik 2012, we derive the relative readings of amount superlatives in two steps, [[[d-many] comparative] superlative]. The existence of two comparative constructions is revealed, involving more vs. the more. Each builds a different superlative construction, explaining the conflicting intuitions about superlatives in the literature, as well as puzzles relating to the definite article in superlatives.
  23. added 2015-10-08
    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 (...)
  24. added 2015-09-25
    Quantifiers and Referential Use.Mario Gomez-Torrente - 2015 - In Alessandro Torza (ed.), Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language. Springer. pp. 97-124.
    Referential uses of quantified determiner phrases other than descriptions have not been extensively considered. In this paper they are considered in some detail, and related to referential uses of descriptions. The first aim is to develop the observation that, contrary to the currently received view that it is only for descriptions that referential uses are frequent and standard, arising in run-of-the-mill contextual scenarios, this is in fact the case for all usual kinds of quantifier phrases. A second aim is to (...)
  25. added 2015-09-13
    A Sequent Calculus for Urn Logic.Rohan French - 2015 - Journal of Logic, Language and Information 24 (2):131-147.
    Approximately speaking, an urn model for first-order logic is a model where the domain of quantification changes depending on the values of variables which have been bound by quantifiers previously. In this paper we introduce a model-changing semantics for urn-models, and then give a sequent calculus for urn logic by introducing formulas which can be read as saying that “after the individuals a1,..., an have been drawn, A is the case”.
  26. added 2015-05-28
    What Do Quantifier Particles Do?Anna Szabolcsi - 2015 - Linguistics and Philosophy 38 (2):159-204.
    In many languages, the same particles that form quantifier words also serve as connectives, additive and scalar particles, question markers, roots of existential verbs, and so on. Do these have a unified semantics, or do they merely bear a family resemblance? Are they aided by silent operators in their varied roles―if yes, what operators? I dub the particles “quantifier particles” and refer to them generically with capitalized versions of the Japanese morphemes. I argue that both MO and KA can be (...)
  27. added 2015-03-12
    A Pragmatic, Truth-Functional Solution to a Logical Difficulty with Biconditionals Absent in Conditionals.Joseph S. Fulda - 2005 - Journal of Pragmatics 37 (9/12):1419-1425/2120.
    Solves what is sometimes, but not always, referred to as the third paradox of material implication. Readers downloading this piece should please also download the corrigendum. Note that "pragmatic" is here used in its original sense of context-sensitive, that is, adjacency. (This comment is made in response to an article in a student journal published in the western U.S. which claimed that I said that because something involves translation it must be pragmatic; that is so, in the original sense; only (...)
  28. added 2015-03-12
    Counterfactuals Revisited.Joseph Fulda - 1996 - Sorites 5:35-38.
    This paper presents an ontologically leaner, mathematically cleaner, and logically keener explication of counterfactuals and possible worlds than the standard Lewis-Stalnaker account.
  29. added 2015-03-12
    Denied Conditionals Are Not Negated Conditionals.Joseph Fulda - 1995 - Sorites 2:45-45.
    This note addresses the problems that arise from denying conditionals in classical logic and concludes that such problems result from using propositional logic where predicate logic with quantification over cases is indicated.
  30. added 2014-12-08
    Hintikka on the Foundations of Mathematics: IF Logic and Uniformity Concepts.André Bazzoni - 2015 - Journal of Philosophical Logic 44 (5):507-516.
    The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic is the real logic of mathematics is supported in that article by an argument relying on uniformity concepts taken from real analysis. I show that the central point of his argument is a simple logical mistake. Second and more generally, I conclude, based on the previous remarks and on another standard fact (...)
  31. added 2014-11-20
    Variable-Binders as Functors.Achille C. Varzi - 1995 - Poznan Studies in the Philosophy of the Sciences and the Humanities 40:303-19.
    This work gives an extended presentation of the treatment of variable-binding operators adumbrated in [3:1993d]. Illustrative examples include elementary languages with quantifiers and lambda-equipped categorial languages. Some remarks are also offered to illustrate the philosophical import of the resulting picture. Particularly, a certain conception of logic emerges from the account: the view that logics are true theories in the model-theoretic sense, i.e. the result of selecting a certain class of models as the only “admissible” interpretation structures (for a given language).
  32. added 2014-11-07
    Unrestricted Exportation: No Toying with Pragmatic English as English Itself.Adam Cuevas - manuscript
  33. added 2014-10-11
    Sulla relatività logica.Achille C. Varzi - 2004 - In Massimiliano Carrara & Pierdaniele Giaretta (eds.), Filosofia e logica. Rubbettino Editore. pp. 135–173.
  34. added 2014-04-02
    Propositions and Compositionality.Juhani Yli-Vakkuri - 2013 - Philosophical Perspectives 27 (1):526-563.
  35. added 2014-04-02
    Quantified Concealed Questions.Ilaria Frana - 2013 - Natural Language Semantics 21 (2):179-218.
    This paper presents a novel treatment of quantified concealed questions , examining different types of NP predicates and deriving the truth conditions for pair-list and set readings. A generalization is proposed regarding the distribution of the two readings, namely that pair-list readings arise from CQs with relational head nouns, whereas set readings arise from CQs whose head nouns are not relational. It is shown that set readings cannot be derived under the ‘individual concept’ approach, one of the most influential analyses (...)
  36. added 2014-03-30
    If-Logic and Truth-Definition.Gabriel Sandu - 1998 - Journal of Philosophical Logic 27 (2):143-164.
    In this paper we show that first-order languages extended with partially ordered connectives and partially ordered quantifiers define, under a certain interpretation, their own truth-predicate. The interpretation in question is in terms of games of imperfect information. This result is compared with those of Kripke and Feferman.
  37. added 2014-03-29
    Quantification.Anna Szabolcsi - 2010 - Cambridge University Press.
    Machine generated contents note: 1. What this book is about and how to use it; 2. Generalized quantifiers and their elements: operators and their scopes; 3. Generalized quantifiers in non-nominal domains; 4. Some empirically significant properties of quantifiers and determiners; 5. Potential challenges for generalized quantifiers; 6. Scope is not uniform and not a primitive; 7. Existential scope versus distributive scope; 8. Distributivity and scope; 9. Bare numeral indefinites; 10. Modified numerals; 11. Clause-internal scopal diversity; 12. Towards a compositional semantics (...)
  38. added 2014-03-26
    The Meaning of Free Choice.Anastasia Giannakidou - 2001 - Linguistics and Philosophy 24 (6):659-735.
    In this paper, I discuss the distribution and interpretation of free choice items (FCIs) in Greek, a language exhibiting a lexical paradigm of such items distinct from that of negative polarity items. Greek differs in this respect from English, which uniformly employs any. FCIs are grammatical only in certain contexts that can be characterized as nonveridical (Giannakidou 1998, 1999), and although they yield universal-like interpretations in certain structures, they are not, I argue, universal quantifiers. Evidence will be provided that FCIsare (...)
  39. added 2014-03-26
    The Semantics of Scandinavian Free Choice Items.Kjell Johan Saeboe - 2001 - Linguistics and Philosophy 24 (6):737-788.
    I present an analysis of Free Choice Items (FCIs), based on Scandinavian, where FCIs are complex and distinct from polarity sensitive items. Scandinavian FCIs are argued to have two components. One is a universal quantifying into modal contexts. The other is an operator mapping a type (s,t) expression onto itself, adjoining to the closest type t or (s,t) expression. Thus invoking Intensional Functional Application, this operator requires the presence of a modal in the scope of the universal quantifier. Facts concerning (...)
  40. added 2014-03-23
    Quantification and Second Order Monadicity.Paul M. Pietroski - 2003 - Philosophical Perspectives 17 (1):259–298.
  41. added 2014-03-21
    First Order Quantifiers in Monadic Second Order Logic.H. Jerome Keisler & Wafik Boulos Lotfallah - 2004 - Journal of Symbolic Logic 69 (1):118-136.
    This paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the toolkit of Janin and Marcinkowski [JM01]. We introduce an operation $esists_{n}(S)$ on properties S that says "there are n components having S". We use this operation to show that under natural strictness conditions, adding a first order quantifier word u to the beginning of a prefix class V increases the expressive power monotonically in u. As a corollary, (...)
  42. added 2014-03-17
    The Elusive Scope of Descriptions.Daniel Rothschild - 2007 - Philosophy Compass 2 (6):910–927.
    (1) Every miner went to a meeting. It seems that (1) can mean either that there was one meeting that every miner went to, or that every miner went to at least one meeting with no guarantee that they all went to the same meeting. In the language of first-order logic we can represent these two readings as a matter of the universal and existential quantifiers having different scope with respect to each other.
  43. added 2014-03-15
    Definite Descriptions and Quantifier Scope: Some Mates Cases Reconsidered.Michael Glanzberg - 2007 - European Journal of Analytic Philosophy 3 (2):133-158.
  44. added 2014-03-12
    Aristotle's Logic and the Quest for the Quantification of the Predicate.Bert Mosselmans - 2008 - Foundations of Science 13 (3-4):195-198.
    This paper examines the quest for the quantification of the predicate, as discussed by W.S. Jevons, and relates it to the discussion about universals and particulars between Plato and Aristotle. We conclude that the quest for the quantification of the predicate can only be achieved by stripping the syllogism from its metaphysical heritage.
  45. added 2014-03-10
    Branching Quantification V. Two-Way Quantification.Nina Gierasimczuk & Jakub Szymanik - 2009 - Journal of Semantics 26 (4):329-366.
    Next SectionWe discuss the thesis formulated by Hintikka (1973) that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.
  46. added 2014-03-07
    Certain Verbs Are Syntactically Explicit Quantifiers.Anna Szabolcsi - 2011 - The Baltic International Yearbook of Cognition, Logic and Communication 6:5.
    Quantification over individuals, times, and worlds can in principle be made explicit in the syntax of the object language, or left to the semantics and spelled out in the meta-language. The traditional view is that quantification over individuals is syntactically explicit, whereas quantification over times and worlds is not. But a growing body of literature proposes a uniform treatment. This paper examines the scopal interaction of aspectual raising verbs (begin), modals (can), and intensional raising verbs (threaten) with quantificational subjects in (...)
  47. added 2014-03-07
    Global Domains Versus Hidden Indexicals.Christopher Gauker - 2010 - Journal of Semantics 27 (2):243-270.
    Jason Stanley has argued that in order to obtain the desired readings of certain sentences, such as “In most of John’s classes, he fails exactly three Frenchmen”, we must suppose that each common noun is associated with a hidden indexical that may be either bound by a higher quantifier phrase or interpreted by the context. This paper shows that the desired readings can be obtained as well by interpreting nouns as expressing relations and without supposing that nouns are associated with (...)
  48. added 2014-03-06
    The Logical Form of Universal Generalizations.Alice Drewery - 2005 - Australasian Journal of Philosophy 83 (3):373 – 393.
    First order logic does not distinguish between different forms of universal generalization; in this paper I argue that lawlike and accidental generalizations (broadly construed) have a different logical form, and that this distinction is syntactically marked in English. I then consider the relevance of this broader conception of lawlikeness to the philosophy of science.
  49. added 2014-03-05
    The Meaning of 'Most': Semantics, Numerosity and Psychology.Paul Pietroski, Jeffrey Lidz, Tim Hunter & Justin Halberda - 2009 - Mind and Language 24 (5):554-585.
    The meaning of 'most' can be described in many ways. We offer a framework for distinguishing semantic descriptions, interpreted as psychological hypotheses that go beyond claims about sentential truth conditions, and an experiment that tells against an attractive idea: 'most' is understood in terms of one-to-one correspondence. Adults evaluated 'Most of the dots are yellow', as true or false, on many trials in which yellow dots and blue dots were displayed for 200 ms. Displays manipulated the ease of using a (...)
  50. added 2014-03-04
    How To Precisify Quantifiers.Arvid Båve - 2011 - Journal of Philosophical Logic 40 (1):103-111.
    I here argue that Ted Sider's indeterminacy argument against vagueness in quantifiers fails. Sider claims that vagueness entails precisifications, but holds that precisifications of quantifiers cannot be coherently described: they will either deliver the wrong logical form to quantified sentences, or involve a presupposition that contradicts the claim that the quantifier is vague. Assuming (as does Sider) that the “connectedness” of objects can be precisely defined, I present a counter-example to Sider's contention, consisting of a partial, implicit definition of the (...)
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