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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
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  1. Some Proof Theoretical Remarks on Quantification in Ordinary Language.Michele Abrusci & Christian Retoré - manuscript
    This paper surveys the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this general setting departs from empirical linguistic data, and give some hints for a different view based on proof theory, which on many aspects gets closer to the language itself. We stress the importance of Hilbert's oper- ator epsilon and tau for, respectively, existential and universal quantifications. Indeed, these operators help a lot to construct semantic representation close to (...)
  2. The Logic of 'Almost All'.Ernest W. Adams - 1974 - Journal of Philosophical Logic 3 (1/2):3 - 17.
  3. 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 (...)
  4. The Semantics of Generic The.John Bacon - 1973 - Journal of Philosophical Logic 2 (3):323 - 339.
  5. Quantification, Negation, and Focus: Challenges at the Conceptual-Intentional Semantic Interface.Tista Bagchi - manuscript
    Quantification, Negation, and Focus: Challenges at the Conceptual-Intentional Semantic Interface Tista Bagchi National Institute of Science, Technology, and Development Studies (NISTADS) and the University of Delhi Since the proposal of Logical Form (LF) was put forward by Robert May in his 1977 MIT doctoral dissertation and was subsequently adopted into the overall architecture of language as conceived under Government-Binding Theory (Chomsky 1981), there has been a steady research effort to determine the nature of LF in language in light of structurally (...)
  6. Un punto a favor de Russell.Pierre Baumann - 2015 - Retorno 1 (1):35-48.
  7. Are Quantifier Phrases Always Quantificational? The Case of 'Every F'.Pierre Baumann - 2013 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 20 (2):143-172.
    This paper argues that English quantifier phrases of the form ‘every F’ admit of a literal referential interpretation, contrary to the standard semantic account of this expression, according to which it denotes a set and a second-order relation. Various arguments are offered in favor of the referential interpretation, and two likely objections to it are forestalled.
  8. 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 (...)
  9. 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 (...)
  10. Fallacies in Predicate Logic?David Bell - 1971 - Mind 80 (317):145-147.
  11. The Quantified Argument Calculus.Hanoch Ben-Yami - 2014 - Review of Symbolic Logic 7 (1):120-146.
    I develop a formal logic in which quantified arguments occur in argument positions of predicates. This logic also incorporates negative predication, anaphora and converse relation terms, namely, additional syntactic features of natural language. In these and additional respects, it represents the logic of natural language more adequately than does any version of Frege’s Predicate Calculus. I first introduce the system’s main ideas and familiarize it by means of translations of natural language sentences. I then develop a formal system built on (...)
  12. 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 (...)
  13. 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 (...)
  14. 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 (...)
  15. Quantification in Eskimo: A Challenge for Compositional Semantics.Maria Bittner - 1995 - In E. Bach, E. Jelinek, A. Kratzer & B. Partee (eds.), Quantification in Natural Languages. Kluwer Academic Publishers. pp. 59--80.
    This paper describes quantificational structures in Greenlandic Eskimo (Kalaallisut), a language where familiar quantificational meanings are expressed in ways that are quite different from English. Evidence from this language thus poses some formidable challenges for cross-linguistic theories of compositional semantics.
  16. On the Semantics of the Greenlandic Antipassive and Related Constructions.Maria Bittner - 1987 - International Journal of American Linguistics 53:194–231.
    : This study describes a new field method, suited for investigating scope relations — and other aspects of truth conditional meaning — with native speaker consultants who may speak no other language and have no background in linguistics or logic. This method revealed a surprising scope contrast between the antipassive and the ergative construction in Greenlandic Eskimo. The results of this field work are described in detail and a crosslinguistic scope generalization is proposed based on Greenlandic Eskimo, Basque, Polish, Russian, (...)
  17. Exceptional Wide Scope as Anaphora to Quantificational Dependencies.Adrian Brasoveanu & Donka F. Farkas - manuscript
    The paper proposes a novel account to the problem of exceptional scope (ES) of (in)definites, e.g. the widest and intermediate scope readings of the sentence Every student of mine read every poem that a famous Romanian poet wrote before World War II. We propose that ES readings are available when the sentence is interpreted as anaphoric to quantificational domains and quantificational dependencies introduced in the previous discourse. For example, the two every quantifiers and the indefinite elaborate on the sets of (...)
  18. Unrestricted Exportation: No Toying with Pragmatic English as English Itself.Adam Cuevas - manuscript
  19. ‘Two Examiners Marked Six Scripts.’ Interpretations of Numerically Quantified Sentences.Martin Davies - 1989 - Linguistics and Philosophy 12 (3):293 - 323.
  20. 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.
  21. Existence as a Real Predicate.Paulo Faria - 2010 - Veritas – Revista de Filosofia da Pucrs 55 (2):33-41.
  22. 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 (...)
  23. Flaws in Dummett’s Syntactical Account of Singular Terms.Danny Frederick - manuscript
    Dummett defines a ‘predicate’ as that which combines with one or more singular terms to form a sentence. His account of ‘singular term’ is syntactical, involving three necessary conditions. He discusses a fourth, ‘Aristotelian’, criterion before propounding a criterion of predicate quantification which he claims to be superior to it. He tentatively proposes that the three necessary conditions plus the criterion of predicate quantification yield sufficient conditions for being a singular term. I show that Dummett’s necessary conditions fail with regard (...)
  24. 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 (...)
  25. 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. 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.
  27. 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.
  28. 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.
  29. 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 (...)
  30. Material Implications.Joseph S. Fulda - 1992 - American Mathematical Monthly 99 (5):480.
  31. Epistemic Operators in Dependence Logic.Pietro Galliani - 2013 - Studia Logica 101 (2):367-397.
    The properties of the ${\forall^{1}}$ quantifier defined by Kontinen and Väänänen in [13] are studied, and its definition is generalized to that of a family of quantifiers ${\forall^{n}}$ . Furthermore, some epistemic operators δ n for Dependence Logic are also introduced, and the relationship between these ${\forall^{n}}$ quantifiers and the δ n operators are investigated.The Game Theoretic Semantics for Dependence Logic and the corresponding Ehrenfeucht- Fraissé game are then adapted to these new connectives.Finally, it is proved that the ${\forall^{1}}$ quantifier (...)
  32. 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 (...)
  33. 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 (...)
  34. 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.
  35. Definite Descriptions and Quantifier Scope: Some Mates Cases Reconsidered.Michael Glanzberg - 2007 - European Journal of Analytic Philosophy 3 (2):133-158.
  36. Quantification and Realism.Michael Glanzberg - 2004 - Philosophy and Phenomenological Research 69 (3):541–572.
    This paper argues for the thesis that, roughly put, it is impossible to talk about absolutely everything. To put the thesis more precisely, there is a particular sense in which, as a matter of semantics, quantifiers always range over domains that are in principle extensible, and so cannot count as really being ‘absolutely everything’. The paper presents an argument for this thesis, and considers some important objections to the argument and to the formulation of the thesis. The paper also offers (...)
  37. Quantifiers.Michael Glanzberg - unknown
    Quantified terms are terms of generality. They are also provide some of our prime examples of the phenomenon of scope. The distinction between singular and general terms, as well as the ways that general terms enter into scope relations, are certainly fundamental to our understanding of language. Yet when we turn to natural language, we encounter a huge and apparently messy collection of general terms; not just every and some, but most, few, between five and ten, and many others. Natural-language (...)
  38. 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 (...)
  39. Spectra of Formulae with Henkin Quantifiers.Joanna Golinska-Pilarek & Konrad Zdanowski - 2003 - In A. Rojszczak, J. Cachro & G. Kurczewski (eds.), Philosophical Dimensions of Logic and Science. Kluwer Academic Publishers.
    It is known that various complexity-theoretical problems can be translated into some special spectra problems. Thus, 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 quantifiers in the empty vocabulary.
  40. 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 (...)
  41. The Buried Quantifier: An Account of Vagueness and the Sorites.Patrick Grim - 2005 - Analysis 65 (2):95–104.
  42. What's So Logical About the “Logical” Axioms?J. H. Harris - 1982 - Studia Logica 41 (2-3):159 - 171.
    Intuitionists and classical logicians use in common a large number of the logical axioms, even though they supposedly mean different things by the logical connectives and quantifiers — conquans for short. But Wittgenstein says The meaning of a word is its use in the language. We prove that in a definite sense the intuitionistic axioms do indeed characterize the logical conquans, both for the intuitionist and the classical logician.
  43. Mass and Count Quantifiers.Jim Higginbotham - 1994 - Linguistics and Philosophy 17 (5):447 - 480.
  44. Transparent Knowledge Once Again.Jaakko Hintikka - 1973 - Philosophical Studies 24 (2):125 - 127.
  45. Do We Need Quantification?Philip Hugly & Charles Sayward - 1984 - Notre Dame Journal of Formal Logic 25 (4):289-302.
    The standard response is illustrated by E, J. Lemmon's claim that if all objects in a given universe had names and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex proposition. It is because these two requirements are not always met that we need universal quantification. This paper is partly in agreement with Lemmon and partly in disagreement. From the point of view of syntax and semantics we can (...)
  46. 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 (...)
  47. Syllogisms with Fractional Quantifiers.Fred Johnson - 1994 - Journal of Philosophical Logic 23 (4):401 - 422.
    Aristotle's syllogistic is extended to include denumerably many quantifiers such as 'more than 2/3' and 'exactly 2/3.' Syntactic and semantic decision procedures determine the validity, or invalidity, of syllogisms with any finite number of premises. One of the syntactic procedures uses a natural deduction account of deducibility, which is sound and complete. The semantics for the system is non-classical since sentences may be assigned a value other than true or false. Results about symmetric systems are given. And reasons are given (...)
  48. 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, (...)
  49. Quantifiers as Modal Operators.Steven T. Kuhn - 1980 - Studia Logica 39 (2-3):145 - 158.
    Montague, Prior, von Wright and others drew attention to resemblances between modal operators and quantifiers. In this paper we show that classical quantifiers can, in fact, be regarded as S5-like operators in a purely propositional modal logic. This logic is axiomatized and some interesting fragments of it are investigated.
  50. Intensional First-Order Logic with Types.Shalom Lappin - unknown
    The paper presents Property Theory with Curry Typing (PTCT) where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting fine-grained intensionality, the basic theory is essentially first-order, so that implementations using the theory can apply standard first-order theorem proving techniques. Some extensions to the type theory are discussed, type polymorphism, and enriching the system with sufficient number theory to account for quantifiers of proportion, such as “most.”.
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