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Summary For Quine, 'to be is to be the value of a variable': serious theoretical claims about what there is, or what exists, are most perspicuously articulated using the quantifier of first-order logic. On this view, one incurs ontological commitment to whatever one's first-order theory quantifies over. Others have different attitudes towards the relationship between ontological inquiry and first-order quantification, including: those who claim that being is distinct from existence; those who hold that other expressions (e.g. predicates) can incur ontological commitment; those who reject the idea that all serious talk about being and existence can be captured by the first-order quantifier, and those who deny that first-order languages are the best vehicles for articulating metaphysical theories. 
Key works Meinong 1960 Quine 1951 Alston 1958 Quine 1961 Routley 1982 Boolos 1984 Lewis 1990 Melia 1995 Yablo 1998 Azzouni 1998 Rayo & Yablo 2001 Manley 2009   
Introductions Rayo 2007 Hofweber 2008 van Inwagen 2009
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  1. R. B. Angell (1986). Truth-Functional Conditionals and Modern Vs. Traditional Syllogistic. Mind 95 (378):210-223.
  2. Jody Azzouni (2010). Talking About Nothing: Numbers, Hallucinations, and Fictions. Oxford University Press.
    Numbers -- Hallucinations -- Fictions -- Scientific languages, ontology, and truth -- Truth conditions and semantics.
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  3. Jody Azzouni (2006). Deflating Existential Consequence: A Case for Nominalism. Oup Usa.
    If we must take mathematical statements to be true, must we also believe in the existence of abstract eternal invisible mathematical objects accessible only by the power of pure thought? Jody Azzouni says no, and he claims that the way to escape such commitments is to accept (as an essential part of scientific doctrine) true statements which are about objects that don't exist in any sense at all. Azzouni illustrates what the metaphysical landscape looks like once we avoid a militant (...)
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  4. Stephen Barker (2015). Expressivism About Reference and Quantification Over the Non-Existent Without Meinongian Metaphysics. Erkenntnis 80 (S2):215-234.
    Can we believe that there are non-existent entities without commitment to the Meinongian metaphysics? This paper argues we can. What leads us from quantification over non-existent beings to Meinongianism is a general metaphysical assumption about reality at large, and not merely quantification over the non-existent. Broadly speaking, the assumption is that every being we talk about must have a real definition. It’s this assumption that drives us to enquire into the nature of beings like Pegasus, and what our relationship as (...)
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  5. Arvid Båve (2011). How To Precisify Quantifiers. 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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  6. Francesco Berto (2012). Existence as a Real Property. Synthèse Library, Springer.
    This book is both an introduction to and a research work on Meinongianism. “Meinongianism” is taken here, in accordance with the common philosophical jargon, as a general label for a set of theories of existence – probably the most basic notion of ontology. As an introduction, the book provides the first comprehensive survey and guide to Meinongianism and non-standard theories of existence in all their main forms. As a research work, the book exposes and develops the most up-to-date Meinongian theory (...)
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  7. G. Boolos (1998). Is Hume's Principle Analytic? Logic, Logic, and Logic:301--314.
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  8. George Boolos (1998). Logic, Logic, and Logic. Harvard University Press.
    This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; ...
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  9. George S. Boolos (1975). On Second-Order Logic. Journal of Philosophy 72 (16):509-527.
  10. Lajos L. Brons (2013). What Does It Mean for Something to Exist? The Science of Mind 51 (1):53-74.
    (First paragraph.) Ontology is often described as the inquiry into what exists, but there is some disagreement among (meta-) ontologists about what “existence” means and whether there are different kinds or senses of “existence” or just one; that is, whether “existence” is equivocal or univocal. Furthermore, there is a growing number of philosophers (many of whom take inspiration from Aristotle’s metaphysical writings) who argue that ontology should not be concerned so much with what exists, but with what is fundamental or (...)
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  11. Lajos L. Brons (2012). Bare and Indexical Existence: Integrating Logic and Sensibility in Ontology. In S. Watanabe (ed.), Logic and Sensibility. Keio University Press.
  12. Francesco F. Calemi (forthcoming). Linceo e la presbiopia ontologica. Considerazioni sul nominalismo di Achille Varzi. Isonomía.
    According to Varzi's nominalism properties are typical examples of ontological hallucinations. In this brief paper I'll focus on an interesting argument that Varzi puts forward against the Realists’ tenet according to which predicates have properties as ontological correlates. I’ll argue that even if Varzi's argument is not convincing, the metalinguistic nominalism he espouses has sufficient resources to meet the realists' challenge concerning the phenomenon of predication. Furthermore, I'll make some methodological remarks about the relationship holding between the «dot quote» analysis (...)
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  13. Ross Cameron, Quantification, Naturalness and Ontology.
    Quine said that the ontological question can be asked in three words, ‘What is there?’, and answered in one, ‘everything’. He was wrong. We need an extra word to ask the ontological question: it is ‘What is there, really?’; and it cannot be answered truthfully with ‘everything’ because there are some things that exist but which don’t really exist (and maybe even some things that really exist but which don’t exist).
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  14. Massimiliano Carrara, Alessandra Arapinis & Friederike Moltmann (eds.) (forthcoming). Unity and Plurality. Philosophy, Logic, and Semantics. Oxford University Press.
    This volume brings together new work on the logic and ontology of plurality and a range of recent articles exploring novel applications to natural language semantics. The contributions in this volume in particular investigate and extend new perspectives presented by plural logic and non-standard mereology and explore their applications to a range of natural language phenomena. Contributions by P. Aquaviva, A. Arapinis, M. Carrara, P. McKay, F. Moltmann, O. Linnebo, A. Oliver and T. Smiley, T. Scaltsas, P. Simons, and B.-Y. (...)
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  15. Richard L. Cartwright (1994). Speaking of Everything. Noûs 28 (1):1-20.
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  16. D. Chalmers, D. Manley & R. Wasserman (eds.) (2009). Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press.
  17. Saloua Chatti & Fabien Schang (2013). The Cube, the Square and the Problem of Existential Import. History and Philosophy of Logic 34 (2):101 - 132.
    (2013). The Cube, the Square and the Problem of Existential Import. History and Philosophy of Logic: Vol. 34, No. 2, pp. 101-132. doi: 10.1080/01445340.2013.764962.
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  18. Nino Cocchiarella (1969). A Second Order Logic of Existence. Journal of Symbolic Logic 34 (1):57-69.
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  19. Nino Cocchiarella (1968). Some Remarks on Second Order Logic with Existence Attributes. Noûs 2 (2):165-175.
    Some internal and philosophical remarks are made regarding a system of a second order logic of existence axiomatized by the author. Attributes are distinguished in the system according as their possession entails existence or not, The former being called e-Attributes. Some discussion of the special principles assumed for e-Attributes is given as well as of the two notions of identity resulting from such a distinction among attributes. Non-Existing objects are of course indiscernible in terms of e-Attributes. In addition, However, Existing (...)
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  20. Cristian Cocos (2008). Fear of Commitment. Revue Roumaine de Philosophie 52:65-76.
    Starting from an exercise in Quinean hermeneutics targeting the notion of ontological commitment, the paper focuses on Quine's reasons for avoiding higher-order quantification. The argument goes further to support the idea of types of existence, which is then shown to accommodate higher-order logical frameworks, via accepting multiple identity/individuation standards.
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  21. Fabrice Correia & Sven Rosenkranz (2015). Presentism Without Presentness. Thought: A Journal of Philosophy 4 (1):19-27.
    We argue that presentism, understood as a view about time and existence, can perspicuously be defined in opposition to all other familiar contenders without appeal to any notion of presentness or cognate notions such as concreteness. Given recent worries about the suitability of such notions to cut much metaphysical ice, this should be welcomed by presentism's defenders. We also show that, irrespective of its sparse ideology, the proposed formulation forestalls any deviant interpretation at odds with the view it aims to (...)
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  22. Tim Crane, Existence and Quantification Reconsidered.
    The currently standard philosophical conception of existence makes a connection between three things: certain ways of talking about existence and being in natural language; certain natural language idioms of quantification; and the formal representation of these in logical languages. Thus a claim like ‘Prime numbers exist’ is treated as equivalent to ‘There is at least one prime number’ and this is in turn equivalent to ‘Some thing is a prime number’. The verb ‘exist’, the verb phrase ‘there is’ and the (...)
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  23. Richard Creath (1980). Nominalism by Theft. American Philosophical Quarterly 17 (4):311 - 318.
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  24. Louis deRosset (forthcoming). Analyticity and Ontology. Oxford Studies in Metaphysics.
    /Analyticity theorists/, as I will call them, endorse the /doctrine of analyticity in ontology/: if some truth P analytically entails the existence of certain things, then a theory that contains P but does not claim that those things exist is no more ontologically parsimonious than a theory that also claims that they exist. Suppose, for instance, that the existence of a table in a certain location is analytically entailed by the existence and features of certain particles in that location. The (...)
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  25. Cian Dorr (2014). Quantifier Variance and the Collapse Theorems. The Monist 97:503-570.
  26. Cian Dorr (2008). There Are No Abstract Objects. In Theodore Sider, John Hawthorne & Dean W. Zimmerman (eds.), Contemporary Debates in Metaphysics. Blackwell.
    I explicate and defend the claim that, fundamentally speaking, there are no numbers, sets, properties or relations. The clarification consists in some remarks on the relevant sense of ‘fundamentally speaking’ and the contrasting sense of ‘superficially speaking’. The defence consists in an attempt to rebut two arguments for the existence of such entities. The first is a version of the indispensability argument, which purports to show that certain mathematical entities are required for good scientific explanations. The second is a speculative (...)
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  27. Cian Dorr (2005). What We Disagree About When We Disagree About Ontology. In Mark Eli Kalderon (ed.), Fictionalism in Metaphysics. Oxford University Press. 234--86.
    In this paper I attempt two things. First, I argue that one can coherently imagine different communities using languages structurally similar to English, but in which the meanings of the quantifiers vary, so that the answers to ontological questions, such as ‘Under what circumstances do some things compose something?’, are different. Second, I argue that nevertheless, one can make sense of the idea that of the various possible assignments of meanings to the quantifiers, one is especially fundamental, so that there (...)
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  28. Matti Eklund, Existence, Quantification, and Shallow Ontology.
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  29. Matti Eklund, Carnapian Theses in Metaontology and Metaethics.
    In contemporary debates about ontology, one prominent skeptical view emphasizes the existence of different possible languages for doing ontology. Eli Hirsch, in recent years the most prominent proponent of a view like this, has defended the claim that “many familiar questions about the ontology of physical objects are merely verbal. Nothing is substantively at stake in these questions beyond the correct use of language” and the claim that “quantifier expressions can have different meaning in different languages”.1 Ted Sider, while critical (...)
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  30. Matti Eklund (2011). Book Review. Quantifier Variance and Realism: Essays in Metaontology. Eli Hirsch. [REVIEW] Notre Dame Philosophical Review.
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  31. Paulo Faria (2010). Existence as a Real Predicate. Veritas 55 (2):33-41.
  32. Kit Fine (2009). The Question of Ontology. In David John Chalmers, David Manley & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. 157--177.
  33. Kit Fine (2006). Relatively Unrestricted Quantification. In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press. 20-44.
    There are four broad grounds upon which the intelligibility of quantification over absolutely everything has been questioned—one based upon the existence of semantic indeterminacy, another on the relativity of ontology to a conceptual scheme, a third upon the necessity of sortal restriction, and the last upon the possibility of indefinite extendibility. The argument from semantic indeterminacy derives from general philosophical considerations concerning our understanding of language. For the Skolem–Lowenheim Theorem appears to show that an understanding of quanti- fication over absolutely (...)
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  34. Kit Fine (2001). The Question of Realism. Philosophers' Imprint 1 (1):1-30.
    This paper distinguishes two kinds of realist issue -- the issue of whether the propositions of a given domain are factual and the issue of whether they are fundamental. It criticizes previous accounts of what these issues come to and suggests that they are to be understood in terms of a basic metaphysical concept of reality. This leaves open the question of how such issues are to be resolved; and it is argued that this may be done through consideration of (...)
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  35. Akiko Frischhut & Alexander Skiles (2013). Time, Modality, and the Unbearable Lightness of Being. Thought 2 (1):264-273.
    We develop a theory about the metaphysics of time and modality that combines the conceptual resources devised in recent sympathetic work on ontological pluralism (the thesis that there are fundamentally distinct kinds of being) with the thought that what is past, future, and merely possible is less real than what is present and actual (albeit real enough to serve as truthmakers for statements about the past, future, and merely possible). However, we also show that despite being a coherent, distinctive, and (...)
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  36. Joseph S. Fulda (1988). The Logic of Skolem Functions: A Subtle Construction and a Subtle Error. Association for Automated Reasoning Newsletter 10:5-6.
    The full-text of the entire issue is available on the Web; readers seeing this should ensure that there is permission to download. It would be quite difficult to separate just my piece from the others.
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  37. Michael Glanzberg (2004). Quantification and Realism. 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 (...)
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  38. Dale Gottlieb (1980). Ontological Economy: Substitutional Quantification and Mathematics. Oxford University Press.
  39. Dale Gottlieb (1976). A Method for Ontology, with Applications to Numbers and Events. Journal of Philosophy 73 (18):637-651.
  40. Dale Gottlieb & Timothy McCarthy (1979). Substitutional Quantification and Set Theory. Journal of Philosophical Logic 8 (1):315 - 331.
  41. Theodore Hailperin (2011). Logic Semantics with the Potential Infinite. History and Philosophy of Logic 31 (2):145-159.
    A form of quantification logic referred to by the author in earlier papers as being 'ontologically neutral' still made use of the actual infinite in its semantics. Here it is shown that one can have, if one desires, a formal logic that refers in its semantics only to the potential infinite. Included are two new quantifiers generalizing the sentential connectives, equivalence and non-equivalence. There are thus new avenues opening up for exploration in both quantification logic and semantics of the infinite.
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  42. Bob Hale & Crispin Wright (2009). The Metaontology of Abstraction. In David John Chalmers, David Manley & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press.
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  43. Xiaoqiang Han (2009). Why Cannot We Dispense with the Subject-Predicate Form Without Losing Something More? Florida Philosophy Review 9 (2):79-89.
    It has been suggested that there may exist languages that contain only feature-placing sentences, and hence the conceptual scheme implied by such languages is radically different from the one with which we are more familiar. Contrary to what some philosophers believe, I argue that with such languages, we may not be able to say things having approximately the force of the things we actually say, that is, to express the so-called ordinary matters merely at the expense of simplicity. For one (...)
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  44. Katherine Hawley (2007). Neo‐Fregeanism and Quantifier Variance. Aristotelian Society Supplementary Volume 81 (1):233 - 249.
    In his paper in the same volume, Sider argues that, of maximalism and quantifier variance, the latter promises to let us make better sense of neo-Fregeanism. I argue that neo-Fregeans should, and seemingly do, reject quantifier variance. If they must choose between these two options, they should choose maximalism.
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  45. Jaakko Hintikka (2009). A Proof of Nominalism: An Exercise in Successful Reduction in Logic. In A. Hieke & H. Leitgeb (eds.), Reduction - Abstraction - Analysis. Ontos.
  46. Eli Hirsch (2013). Charity to Charity. Philosophy and Phenomenological Research 86 (1):435-442.
  47. Eli Hirsch (2008). Language, Ontology, and Structure. Noûs 42 (3):509-528.
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  48. Eli Hirsch (2005). Physical-Object Ontology, Verbal Disputes, and Common Sense. Philosophy and Phenomenological Research 70 (1):67–97.
    Two main claims are defended in this paper: first, that typical disputes in the literature about the ontology of physical objects are merely verbal; second, that the proper way to resolve these disputes is by appealing to common sense or ordinary language. A verbal dispute is characterized not in terms of private idiolects, but in terms of different linguistic communities representing different positions. If we imagine a community that makes Chisholm's mereological essentialist assertions, and another community that makes Lewis's four-dimensionalist (...)
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  49. Eli Hirsch (2004). Comments on Theodore Sider's Four Dimensionalism. [REVIEW] Philosophy and Phenomenological Research 68 (3):658–664.
  50. Eli Hirsch (2002). Quantifier Variance and Realism. Philosophical Issues 12 (1):51-73.
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