Philosophy Nonexistent Objects
by
Jody Azzouni
  • LAST REVIEWED: 01 December 2022
  • LAST MODIFIED: 27 February 2019
  • DOI: 10.1093/obo/9780195396577-0197

Introduction

The issues that nonexistent entities pose for metaphysics and philosophy of language are among the oldest in philosophy, dating back to Plato and Parmenides. These issues arise because of the very natural view that true statements and false statements have the status they have only because they are about objects—broadly speaking—and they’re true (or false) depending on whether they describe those objects correctly or not. If, however, statements are about something nonexistent, it seems they cannot be true or false because there is nothing for them to be true or false of—the very phrase “something nonexistent” sounds oxymoronic. It even strikes some that attempts to say something meaningful about a nonexistent object (or some nonexistent objects) cannot succeed because there is nothing for such statements to be about. And yet we say meaningful things about nonexistents daily: “Sherlock Holmes is more famous than any real detective,” “There are as many gods as goddesses in Greek mythology,” “Hob and Nob are thinking about the same nonexistent witch.” The philosophical tangles that arise when trying to explain our talk about the nonexistent show up everywhere in philosophy, and not just in discussions of fictions, hallucinations, or dreams. If one is a proponent of nominalism in philosophy of mathematics, for example, then one has to explain (or explain away) the usefulness, the indispensability even, of mathematical statements, because such statements—on the nominalist’s view—are not about anything real. The literature on the nonexistent is a bewildering maze of strategies for circumventing or dissolving the problem of how we talk about what doesn’t exist. The key to understanding how influential concerns with nonexistence have been in philosophy is seeing the wealth of different solutions (often implicit in a particular philosophical tradition) that have been invented to solve the puzzle of how we talk, think about, and even perceive what does not exist.

General Overviews

A general discussion of the philosophical issue of nonexistent objects in the broad sense that we are using here cannot at this time be found either in articles, in books, or online. There are specific online articles, such as Reicher 2014, but despite the breadth of the title (“Nonexistent Objects”) the topic of the article is narrowly focused on Meinongian and Neo-Meinongian solutions to the problem of nonexistent objects. So too, there are books on nonexistent entities, Azzouni 2012, Everett 2013, and Sainsbury 2010, and books with significant discussion of this topic, for example, Crane 2013, but all of these approach the topic from a very specific philosophical framework, and they consider alternative frameworks only in polemical settings.

Anthologies

Some anthologies deal with the problem of nonexistence. Everett and Hofweber 2000 is a good one, although a little dated. Kalderon 2005 and Woods 2010 are specifically dedicated to fictionalism, but this is only one widely taken perspective on the problems of nonexistence.

  • Everett, Anthony, and Thomas Hofweber, eds. Empty Names, Fiction and the Puzzles of Non-existence. Stanford, CA: CSLI, 2000.

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    A good anthology focused primarily on pretense approaches to avoiding ontological commitment to fictional entities. Also some articles on realist approaches to fiction.

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  • Kalderon, Mark Eli, ed. Fictionalism in Metaphysics. Oxford: Oxford University Press, 2005.

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    A good anthology focused primarily on pretense approaches to avoiding ontological commitments.

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  • Woods, John, ed. Fictions and Models: New Essays. Munich: Philosophia Verlag, 2010.

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    A good anthology spanning fictionalist approaches to various areas of philosophy: fiction, metaphysics, philosophy of mathematics, and so on.

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Parmenides and Plato

The problem of the meaningfulness of statements about nonexistent objects seems to have been stated in a fragment from Parmenides 2000. Plato substantially extends discussion of the concern in Plato 1963.

  • Parmenides. Parmenides of Elea: Fragments; A Text and Translation. Toronto: University of Toronto Press, 2000.

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    Contains fragments that deny one can talk meaningfully about what is not.

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  • Plato. “Sophist.” In Plato: The Collected Dialogues. Edited by Edith Hamilton and Huntington Cairns, 957–1017. Princeton, NJ: Princeton University Press, 1963.

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    Explicit about the doctrine that talk about what isn’t cannot be meaningful and cannot have truth values.

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Degrees of Existence

An important doctrine related to the topic of nonexistence that is also found in Plato, and perhaps originates there, is that existence comes in different metaphysical degrees, that things can “partially” exist. A variant of this view is that there are different kinds of existence: mathematical existence, fictional existence, and so on. Russell 2012 suggests a similar kind of division but restricts “existence” to what is in space and time, and “subsistence” to abstract objects such as properties and mathematical entities. The “degrees of existence” doctrine is originally offered in Plato 1963 to handle puzzles about relations, but it has far outlived that origin and still has proponents in the contemporary setting. Philosophers sometimes distinguish “existence” from “reality,” and from that standpoint the views of Plato and many later philosophers should be described as the claim that it is reality (rather than existence) that comes in degrees. In any case, degree views came to play an important role in the metaphysics of nonexistence at the hands of later philosophers, especially because of their connection to claims about the status of existence as a predicate. In addition, they had independent metaphysical interest throughout the classical period and were notably revived in Descartes 1931, particularly in the distinction made by Descartes between formal and objective reality. The contemporary version of the view treats “exist” as an expression with more than one criterion—it is often seen as a discourse-relative and discourse-variable notion, as in Thomasson 2008. A recent development in metaphysics is “fundamentalism,” the view that what really exists is what fundamentally exists, and what is, otherwise, has only derived or derivative existence. Cameron 2010 and Schaffer 2009 argue for positions like these. Quine is a notable proponent of the view that existence comes in only one degree and kind (Quine 1980); this is because he treats existence as expressed only by first-order quantifiers. Parsons 1983 suggests that an alternative notion of existence, subsistence, is expressed by the substitutional interpretation of the first-order quantifiers. Also see Quantifier Variance and Existence as a Predicate.

  • Cameron, Ross. “Quantification, Naturalness and Ontology.” In New Waves in Metaphysics. Edited by Allan Hazlett, 8–26. Basingstoke, UK: Palgrave Macmillan, 2010.

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    Proposes a fundamentalist view of metaphysics. There is what exists, and there is what really exists, what is fundamental.

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  • Descartes, René. “Meditations on First Philosophy.” In The Philosophical Works of Descartes. Translated by Elizabeth S. Haldane and G. R. T. Ross, 131–199. Cambridge, UK: Cambridge University Press, 1931.

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    Classic Cartesian work focused on epistemology. In the course of establishing God’s existence, Descartes propounds a doctrine about degrees of being. First published (in Latin) 1641.

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  • Parsons, Charles. “A Plea for Substitutional Quantification.” In Mathematics in Philosophy: Selected Essays. By Charles Parsons, 63–70. Ithaca, NY: Cornell University Press, 1983.

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    Suggests that substitutional quantification can be interpreted ontologically as involving a kind of “subsistence.”

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  • Plato. “Phaedo.” In Plato: The Collected Dialogues. Edited by Edith Hamilton and Huntington Cairns, 40–98. Princeton, NJ: Princeton University Press, 1963.

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    Classic Platonic dialogue where a propounded doctrine of degrees of reality is clearly motivated by concerns about relations.

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  • Quine, Willard Van Orman. “On What There Is.” In From a Logical Point of View. By Willard Van Orman Quine, 1–19. 2d ed. Cambridge, MA: Harvard University Press, 1980.

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    Opposes treating “existence” as coming in degrees or in kinds. First published 1948.

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  • Russell, Bertrand. The Problems of Philosophy. Oxford: Oxford University Press, 2012.

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    Describes objects that exist as being in space and time. Abstract objects, such as properties and numbers, only “subsist.” First published 1912.

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  • Schaffer, Jonathan. “On What Grounds What.” In Metametaphysics. Edited by David J. Chalmers, David Manley, and Ryan Wasserman, 347–383. Oxford: Oxford University Press, 2009.

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    A recent attempt to distinguish between a lightweight notion of existence and a substantial fundamental notion of existence.

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  • Thomasson, Amie L. “Existence Questions.” Philosophical Studies 141 (2008): 63–78.

    DOI: 10.1007/s11098-008-9263-8Save Citation »Export Citation » Share Citation »

    Claims that sortal terms have application conditions and ties the semantics of “exist” to those application conditions.

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Quantifier Variance

The linguistic counterpart to the idea that existence comes in degrees or kinds is the idea that the notion of “existence” itself is one that is open to different meanings. The contemporary version of this idea also follows Russell and Quine in treating the existence concept as expressed by first-order quantifiers, and the result is “quantifier variance”—the idea that different languages can have different existence concepts because their quantifiers have different ranges. Hirsch 2011 argues that quantifier variance has important implications for ontology, in particular that many ontological debates are purely verbal. The view is—to some extent—anticipated in Carnap 1956 and more recently in Putnam 1990. The implications that Hirsch draws from quantifier variance have been seen as challenges by recent metaphysicians. Sider 2009, for example, argues that ontological debates are not purely verbal, because there is a metaphysically privileged quantifier that picks out the logical joints of the universe. Sider 2011 is a book-length presentation of this view of “structure.” Eklund 2008 and McGrath 2008 offer arguments against quantifier variance.

  • Carnap, Rudolf. “Empiricism, Semantics, and Ontology.” In Meaning and Necessity: A Study in Semantics and Modal Logic. By Rudolf Carnap, 205–221. Chicago: University of Chicago Press, 1956.

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    Seminal article presenting Carnap’s views (as of that date) about the relationship of ontology to language. He draws his important distinction between external questions and internal questions. His view that different languages—useful for different purposes—can have quantifiers with different ranges anticipates the idea of quantifier variance. First published 1950.

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  • Eklund, Matti. “The Picture of Reality as an Amorphous Lump.” In Contemporary Debates in Metaphysics. Edited by Theodore Sider, John Hawthorne, and Dean W. Zimmerman, 383–396. Oxford: Blackwell, 2008.

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    Offers arguments against quantifier variance.

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  • Hirsch, Eli. Quantifier Variance and Realism: Essays in Metaontology. Oxford: Oxford University Press, 2011.

    DOI: 10.1093/acprof:osobl/9780199732111.001.0001Save Citation »Export Citation » Share Citation »

    A collection of related essays arguing for quantifier variance and against anti-realism. Hirsch claims that certain ontological debates are merely verbal, and yet that commonsense ontology is correct.

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  • McGrath, Matthew. “Conciliatory Metaontology and the Vindication of Common Sense.” Noûs 42.3 (2008): 482–508.

    DOI: 10.1111/j.1468-0068.2008.00688.xSave Citation »Export Citation » Share Citation »

    Argues against Hirsch 2011 that certain ontological debates are merely verbal. Claims that Hirsch’s arguments have omitted an important and relevant principle of charity.

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  • Putnam, Hilary. “Truth and Convention.” In Realism with a Human Face. Edited by James Conant, 96–104. Cambridge, MA: Harvard University Press, 1990.

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    One of the many places where Putnam argues both that there are different existence concepts and that such are present in natural language.

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  • Sider, Theodore. “Ontological Realism.” In Metametaphysics: New Essays on the Foundations of Ontology. Edited by David J. Chalmers, David Manley, and Ryan Wasserman, 384–423. Oxford: Oxford University Press, 2009.

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    Argues against the claim that ontological debates are merely verbal, in part by arguing for a metaphysically privileged interpretation of quantifiers.

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  • Sider, Theodore. Writing the Book of the World. Oxford: Oxford University Press, 2011.

    DOI: 10.1093/acprof:oso/9780199697908.001.0001Save Citation »Export Citation » Share Citation »

    Book-length development of the view that there is a fundamental metaphysical meaning for unrestricted quantifiers, where they refer to the “logical joints” of the world.

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Existence as a Predicate

This tortured topic has continued to spawn a gigantic literature for millennia. Part of its interest is due to the role of an “existence predicate” in the ontological proof of God, but surely a great deal of interest turns on the intrinsically surprising and puzzling aspects of words like “exist,” “real,” “actual,” and so on, both logically and linguistically. For Hume 2000 and for Kant 1998, the concern was with whether the attribution of existence to something could be an attribution of a “real” property. At the hands of Russell 1993, the denial of existence being a predicate took a different twist because of Russell’s assimilation of the notion of existence to the existential quantifier. Historically later discussions, for example Austin 1975, Bennett 1966, and Azzouni 2010, show more sensitivity to questions of how the word “exist,” and similarly puzzling words like “real,” operate in natural languages. Nevertheless, the assimilation of the concept of existence to the existential quantifier continues to remain a central plank of contemporary ontology. This is due primarily to the extremely influential Quine 1980. Raley and Burnor 2011 explores the advantages of giving up this central plank in philosophy of science and in philosophy of mathematics.

  • Austin, J. L. Sense and Sensibilia. London: Oxford University Press, 1975.

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    This posthumously published book is primarily concerned with sense data, but it shows genuine sensitivity to and insight about the use of natural-language words like “real” and “exists,” as well as related words like “actual,” “authentic,” and so on.

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  • Azzouni, Jody. “Ontology and the Word ‘Exist’: Uneasy Relations.” Philosophia Mathematica 18.3 (2010): 74–101.

    DOI: 10.1093/philmat/nkp011Save Citation »Export Citation » Share Citation »

    Attempts to diagnose the philosophical puzzles that words like “exist” pose as due to their peculiar and specialized natural-language properties.

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  • Bennett, Jonathan. “Real.” Mind 75.300 (1966): 501–515.

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    Critical of the discussion of “real” in Austin 1975, while offering additional insights about the ordinary use of this word.

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  • Hume, David. A Treatise of Human Nature. Edited by David Fate Norton and Mary J. Norton. Oxford: Oxford University Press, 2000.

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    A major work of the modern period that attempts to empirically ground all our concepts, including the notion of existence (in Treatise 1.2.6). Deeply influential. First published 1739.

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  • Kant, Immanuel. Critique of Pure Reason. Translated and edited by Paul Guyer and Allen W. Wood. Cambridge, UK: Cambridge University Press, 1998.

    DOI: 10.1017/CBO9780511804649Save Citation »Export Citation » Share Citation »

    A major work of the modern period that defies a simple summary. Deeply influential. His famous discussion of a hundred real thalers versus a hundred imaginary thalers occurs during the course of his attempted refutation of the ontological argument in the Transcendental Dialectic (Chapter III, section 4). First published 1781.

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  • Quine, Willard Van Orman. “On What There Is.” In From a Logical Point of View. By Willard Van Orman Quine, 1–19. 2d ed. Cambridge, MA: Harvard University Press, 1980.

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    Systematic argument for why the quantifiers should be exclusively interpreted as indicating what a discourse takes to exist. A fundamental plank in contemporary ontology. First published 1948.

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  • Raley, Yvonne, and Richard N. Burnor. “The Predicate Approach to Ontological Commitment.” Logique et Analyse 54.215 (2011): 359–378.

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    A technical and philosophical exploration of the value of an existence predicate in regimentations of mathematical and scientific theories.

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  • Russell, Bertrand. Introduction to Mathematical Philosophy. London: Routledge, 1993.

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    A rich survey of applications of logic to mathematics and philosophy. Also contains an early discussion of Russell’s assimilation of the existence concept to the existential quantifier. First published 1919.

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The Standard View

The majority position toward nonexistence adopts a version of Plato’s view of the matter. Statements are true or false only by virtue of their saying rightly or wrongly how it is with what they are about—what their terms refer to. The standard view, especially in contemporary philosophy, includes Quine’s criterion—that statements of the form (∃x) . . . x . . . are ontologically committing to xs such that . . . x . . .. Presupposing a version of correspondence truth and Quine’s criterion, as well as a literal interpretation of the statements about apparently nonexistent entities, narrows the solution-space to problems of nonexistence: one can attempt to paraphrase away (or to proxy) the apparent references to what doesn’t exist, one can attempt to isolate the discourse in which references to what doesn’t exist occur, or one can simply accept that items that prima facie don’t exist—fictional entities, for example—actually do exist.

Correspondence Truth

Doctrines of correspondence truth come in many forms. An influential version is derived from Tarski’s seminal presentation of semantics (Tarski 1983): a domain of objects is given, and the truth and falsity of the statements of a specified formal language are characterized in terms of the predicates of, and relations among, those objects. A less technical presentation of Tarski’s views may be found in Tarski 2001. What Tarski has to say about the relationship of his formalized notion of truth to correspondence truth occurs in these two articles. Apart from Tarski’s work, the best way to introduce oneself to the topic of truth—and correspondence truth in particular—is to look through some anthologies. Three good ones for this purpose (although there are many) are Blackburn and Simmons 1999, Lynch 2001, and Schmitt 2004. Also valuable is the online David 2015. Correspondence truth is very closely connected to the notion of truthmakers—one or another kind of something in the world that makes a truth true (and falsehoods false). Beebee and Dodd 2005 is a good anthology of recent articles about the truthmaker debate.

  • Beebee, Helen, and Julian Dodd. Truthmakers: The Contemporary Debate. Oxford: Oxford University Press, 2005.

    DOI: 10.1093/acprof:oso/9780199283569.001.0001Save Citation »Export Citation » Share Citation »

    An anthology of recent papers on the truthmaker debate.

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  • Blackburn, Simon, and Keith Simmons, ed. Truth. Oxford: Oxford University Press, 1999.

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    A good anthology of classic and recent papers arguing for and describing various notions of truth.

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  • David, Marian. “The Correspondence Theory of Truth.” In The Stanford Encyclopedia of Philosophy. Edited by Edward M. Zalta. Stanford, CA: Stanford University, 2015.

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    Valuable online survey with extensive bibliography. Originally published 2002.

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  • Lynch, Michael P., ed. The Nature of Truth: Classic and Contemporary Perspectives. Cambridge, MA: MIT Press, 2001.

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    A good anthology of classic and recent papers arguing for and describing various notions of truth.

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  • Schmitt, Frederick F., ed. Theories of Truth. Oxford: Blackwell, 2004.

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    A good anthology of classic and recent papers arguing for and describing various notions of truth.

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  • Tarski, Alfred. “The Concept of Truth in Formalized Languages.” In Logic, Semantics, Metamathematics. Edited by J. H. Woodger and John Corcoran, 152–278. Indianapolis, IN: Hackett, 1983.

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    English translation of “Der Wahrheitsbegriff in den Sprachen der deduktiven Disziplinen,” first published in 1932. This is the fundamental article in which Tarski first presented his formalized semantic notions, including his famous characterization of truth.

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  • Tarski, Alfred. “The Semantic Conception of Truth and the Foundations of Semantics.” In The Nature of Truth. Edited by Michael P. Lynch, 331–363. Cambridge, MA: MIT Press, 2001.

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    An accessible discussion of the important formal notions that Tarski invented, first published in 1944.

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Quine’s Criterion for Ontological Commitment

Perhaps Quine’s most enduring philosophical accomplishment is presented in Quine 1980. His criterion for what a discourse is ontologically committed to is meant to indicate the ontological commitments of any discourse relative to a regimentation of that discourse in a first-order formal language. More precisely, the ontic commitments of any discourse are recognized by (1) regimenting such a discourse in a first-order language, (2) determining that the aims of the original discourse are served once the range of the objectual quantifiers in the regimentation is minimized, and (3) identifying the ontic commitments of the original discourse with the range of the quantifiers in the regimentation. It’s impossible to overstate the role of Quine’s criterion in contemporary ontology. It is directly challenged by almost no one, even to this day, although a number of philosophers have challenged the specifics of Quine’s criterion, for example, that the regimentation must take place in a first-order language (as opposed to, say, one or another higher-order language). Some early discussion—Scheffler and Chomsky 1958–1959 and Cartwright 1987, for example—probes the meaningfulness and significance of the criterion. Marcus 1993 challenges Quine’s default assumption that the first-order quantifiers should be objectual. Relatedly, there is also a long tradition of attempting to circumvent the criterion by changing either the underlying logic of the discourse in question or the semantics of first-order logic (replacing objectual semantics with substitutional semantics, for example). Gottlieb 1980, Hofweber 2000, and Chihara 1990 are examples. Azzouni 2004 is an attempt to directly deny the criterion, so that even if the quantifiers are given now-standard objectual semantics, they are nevertheless ontologically neutral. Bricker 2014 is an excellent survey of the literature on this topic.

  • Azzouni, Jody. Deflating Existential Consequence: A Case for Nominalism. Oxford: Oxford University Press, 2004.

    DOI: 10.1093/0195159888.001.0001Save Citation »Export Citation » Share Citation »

    A direct challenge to Quine’s criterion for ontological commitment and, correspondingly, a reading of Tarskian semantics according to which they are without ontological commitments.

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  • Bricker, Phillip. “Ontological Commitment.” In The Stanford Encyclopedia of Philosophy. Edited by Edward M. Zalta, Stanford, CA: Stanford University, 2014.

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    An excellent online survey of the issues Quine’s criterion raises.

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  • Cartwright, Richard. “Ontology and the Theory of Meaning.” In Philosophical Essays. By Richard Cartwright, 1–12. Cambridge, MA: MIT Press, 1987.

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    An influential discussion of problems faced by the various formulations of Quine’s criterion for what a discourse is committed to.

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  • Chihara, Charles S. Constructability and Mathematical Existence. Oxford: Oxford University Press, 1990.

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    An attempt to avoid the apparent ontological commitments of mathematics by paraphrasing mathematical statements within a background logical language with modal operators.

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  • Gottlieb, Dale. Ontological Economy: Substitutional Quantification and Mathematics. Oxford: Oxford University Press, 1980.

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    An attempt to circumvent the apparent ontological commitments of mathematics—number theory in particular—by recasting the relevant quantifiers as substitutional.

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  • Hofweber, Thomas. “Quantification and Non-existent Objects.” In Empty Names, Fiction and the Puzzles of Non-existence. Edited by Anthony Everett and Thomas Hofweber, 249–273. Stanford, CA: CSLI, 2000.

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    Argues that natural-language quantifiers are ambiguous: there is a domain-conditions interpretation of them that is ontologically committing, and an inference-role reading of them that is not. Only the latter is relevant to numerical sentences, on Hofweber’s view.

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  • Marcus, Ruth. “Quantification and Ontology.” In Modalities: Philosophical Essays. By Ruth Marcus, 75–87. Oxford: Oxford University Press, 1993.

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    Argues that the substitutional interpretation of first-order quantifiers is ontology-free.

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  • Quine, Willard Van Orman. “On What There Is.” In From a Logical Point of View. By Willard Van Orman Quine, 1–19. 2d ed. Cambridge, MA: Harvard University Press, 1980.

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    The classic discussion of Quine’s criterion for what a discourse is committed to. A fundamental plank in contemporary ontology. First published 1948.

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  • Scheffler, Israel, and Noam Chomsky. “What Is Said to Be.” Proceedings of the Aristotelian Society 59 (1958–1959): 71–82.

    DOI: 10.1093/aristotelian/59.1.71Save Citation »Export Citation » Share Citation »

    An early and insightful challenge to the significance of Quine’s criterion for what a discourse is committed to.

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Paraphrase and Proxying

An early response to statements that refer to or quantify over prima facie nonexistent entities is to attempt to paraphrase such statements into other statements without the unwanted ontological commitments. The simplest, and most demanding, version takes the requirement to be that, given a sentence that refers to or otherwise quantifies over nonexistents, e.g., “Mickey Mouse was invented by Walt Disney” or “Most of the hobbits depicted in the novel The Lord of the Rings are nameless,” an alternative sentence must be provided that does not refer to or otherwise quantify over nonexistents, for example, “Mickey Mouse cartoons were invented by Walt Disney” or “In the novel The Lord of the Rings, there are pretended to be many nameless hobbits.” As the examples just given intimate, providing alternative sentences with the same truth conditions is not easy. Quine 2013 (first published in 1960) contains a subtle and nuanced discussion of methods of paraphrasing. It has been suggested in Alston 1958 that a requirement for paraphrase should be the preservation of meaning, but this is denied by Quine. Van Inwagen 2000 argues that paraphrase isn’t possible with statements that quantify over fictions. A weaker requirement than paraphrase, proxying, is that such suitable paraphrases need not be available to be used by speakers—rather, it only need be established that they exist. In this case, one can continue to use the statements the paraphrases are of to stand for (or to proxy for) those paraphrases. Although this second (weaker) requirement has only recently emerged clearly, it does seem to have been anticipated in Quine 2013. Field 2016 is an ambitious attempt to show that any deduction of purely empirical content from mixed empirical and mathematical assumptions is a convenient shorthand for a deduction of that empirical content from purely empirical assumptions. Yablo 2010 develops a proxy view that treats mathematical statements as analogous to statements containing figurative speech; the statements referring to mathematical entities are literally false but stand for (proxy for) statements—perhaps otherwise inexpressible ones—that don’t refer to mathematical entities. Melia 2000 suggests that in uttering statements that quantify over or refer to mathematical entities, one can “weasel” out of the apparent ontological implications of the statements by saying that one didn’t mean the statement to have those implications because there was some other (possibly inexpressible) statement that was meant. Raley 2012 argues that weaseling faces fatal dilemmas and Knowles and Liggins 2015 defend weaseling. Colyvan 2010 argues that none of the easy ways of avoiding ontological commitments will work. Azzouni 2009 describes and evaluates the various proxying and paraphrase strategies.

  • Alston, William P. “Ontological Commitments.” Philosophical Studies 9.1–2 (1958): 8–17.

    DOI: 10.1007/BF00797866Save Citation »Export Citation » Share Citation »

    An early criticism of Quine’s approach to paraphrase. Uses the meaning-equivalence condition on paraphrase to argue that paraphrase cannot be used for purposes of ontological parsimony as Quine intends.

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  • Azzouni, Jody. “Evading Truth Commitments: The Problem Reanalyzed.” Logique et Analyse 52.206 (2009): 139–176.

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    Lays out the various proxying and paraphrase strategies and evaluates them.

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  • Colyvan, Mark. “There Is No Easy Road to Nominalism.” Mind 119.474 (2010): 285–306.

    DOI: 10.1093/mind/fzq014Save Citation »Export Citation » Share Citation »

    Argues that the various ways of being nominalists (“easy roads”) without engaging in the hard work of paraphrasing statements so that they don’t refer to or quantify over mathematical entities won’t work. Argues that the hard road of a Field-style program is the only possibility for serious nominalists.

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  • Field, Hartry. Science without Numbers. 2d ed. Oxford: Oxford University Press, 2016.

    DOI: 10.1093/acprof:oso/9780198777915.001.0001Save Citation »Export Citation » Share Citation »

    An influential attempt to deflect the apparent indispensability of quantification over mathematical entities in applied mathematics. The second edition contains a short introduction discussing a few of the criticisms raised in response to the earlier work. The first edition was published 1980.

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  • Knowles, Robert, and David Liggins. “Good Weasel Hunting.” Synthese 192.10 (2015): 3397–3412.

    DOI: 10.1007/s11229-015-0711-7Save Citation »Export Citation » Share Citation »

    Defends Melia’s weaseling strategy against critics such as Colyvan and Raley.

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  • Melia, Joseph. “Weaseling Away the Indispensability Argument.” Mind 109 (2000): 455–480.

    DOI: 10.1093/mind/109.435.455Save Citation »Export Citation » Share Citation »

    Claims that scientists can assert sentences or theories that have substantial ontological commitments as implications, but they can subsequently deny those commitments without inconsistency. Melia calls this “weaseling.”

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  • Raley, Yvonne. “Why the Weasel Fails.” Philosophia Mathematica 20.3 (2012): 339–345.

    DOI: 10.1093/philmat/nks017Save Citation »Export Citation » Share Citation »

    Argues that Melia’s weaseling strategy faces a fatal dilemma.

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  • Quine, Willard Van Orman. Word and Object. Cambridge, MA: MIT Press, 2013.

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    Chapters 5 and 7 of this work are especially concerned with canvassing the various strategies for regimenting ordinary language statements (finding appropriate first-order versions of them) that don’t, according to Quine’s criterion, have undesirable ontological commitments. First published 1960.

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  • van Inwagen, Peter. “Quantification and Fictional Discourse.” In Empty Names, Fiction and the Puzzles of Non-existence. Edited by Anthony Everett and Thomas Hofweber, 235–247. Stanford, CA: CSLI, 2000.

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    Argues that the quantifiers of ordinary language are first-order objectual ones, and that reasoning about fictional objects requires quantification over such entities. Draws a realist conclusion about fictional entities.

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  • Yablo, Stephen. “Go Figure: A Path through Fictionalism.” In Things: Philosophical Papers. Vol. 2. By Stephen Yablo, 177–199. Oxford: Oxford University Press, 2010.

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    Argues that apparent references to mathematical objects are figurative or metaphorical. First published 2001.

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Quantifying In

Quantifying in—a phenomenon first publicized widely in Quine 1976, and discussed by David Kaplan in groundbreaking work, for example Kaplan 1969 and Kaplan 1986—is the nature of quantification into propositional-attitude contexts. The logic of the interaction of quantification and propositional attitude contexts is widely contested and extremely hard to understand. Much of the voluminous literature in this area is concerned with designing a set of coherent principles to govern quantification into intentional contexts. A related issue that has arisen specifically with regard to nonexistents is that statements involving quantifiers and intentional contexts seem to be ontologically committing if the quantifier takes wide scope but not if an intentional operator does. Consider a context like “It is pretended that—.” If we say, for example, “John is pretending that there is someone running on the beach carrying a basketball,” the statement in question does not commit the speaker to there actually being someone running on the beach. On the other hand, “There is someone running on the beach such that John is pretending that he is carrying a basketball” does commit the speaker to there being someone running on the beach, although not to his carrying a basketball. A number of idioms (intentional idioms) have a similarly nullifying effect on quantification: “thinks,” “hopes,” “believes,” and so on. Important statements about fictions or hallucinations or statements describing the beliefs of individuals about nonexistent entities, however, do not seem amenable to a form in which an intentional operator takes wide scope. This is argued for, by the use of examples, in van Inwagen 2000, Parsons 1980, and Chisholm 2008, among other works. Lewis 1983 attempts to handle fictional discourse by eliminating quantifying in. Evans 1982 shows a keen awareness of the issues pretense views face with respect to quantifying in and out, and attempts to handle them with a set of rules governing pretense.

  • Chisholm, Roderick. “Beyond Being and Nonbeing.” In Metaphysics: The Big Questions. Edited by Peter van Inwagen and Dean W. Zimmerman, 40–50. Oxford: Blackwell, 2008.

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    Deftly shows a number of examples where we seem to refer to nonexistent objects, and illustrates how hard it is to paraphrase these in ways where the references to them vanish. First published 1973.

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  • Evans, Gareth. The Varieties of Reference. Edited by John McDowell. Oxford: Oxford University Press, 1982.

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    Chapter 10, especially, shows a keen appreciation of the problems quantifying in raises for attempts to pretense-characterize fictional and hallucinatory talk.

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  • Kaplan, David. “Quantifying In.” In Words and Objections: Essays on The Work of W. V. Quine. Edited by Donald Davidson and Jaakko Hintikka, 206–242. Dordrecht, The Netherlands: D. Reidel, 1969.

    DOI: 10.1007/978-94-010-1709-1_14Save Citation »Export Citation » Share Citation »

    A presentation of a groundbreaking theory of quantifying into propositional-attitude contexts in response to Quine 1976.

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  • Kaplan, David. “Opacity.” In The Philosophy of W. V. Quine. Edited by Lewis Edwin Hahn and Paul Arthur Schilpp, 229–289. La Salle, IL: Open Court, 1986.

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    An important revisiting of the themes of Kaplan 1969 and Quine 1976.

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  • Lewis, David. “Truth in Fiction.” In Philosophical Papers. Vol. 1. By David Lewis, 261–280. Oxford: Oxford University Press, 1983.

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    Endeavors to handle fictional truth via a wide-scope fiction operator.

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  • Parsons, Terence. Nonexistent Objects. New Haven, CT: Yale University Press, 1980.

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    An early and important presentation of a Meinongian-inspired approach to fictional discourse. Shows that many of our references to nonexistents cannot be treated as implicitly involving an intensional operator.

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  • Quine, Willard Van Orman. “Quantifiers and Propositional Attitudes.” In The Ways of Paradox and Other Essays. By Willard Van Orman Quine, 185–196. Rev. ed. Cambridge, MA: Harvard University Press, 1976.

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    An extremely influential seminal discussion of quantifying into propositional-attitude contexts. Originally published 1966.

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  • van Inwagen, Peter. “Quantification and Fictional Discourse.” In Empty Names, Fiction and the Puzzles of Non-existence. Edited by Anthony Everett and Thomas Hofweber, 235–247. Stanford, CA: CSLI, 2000.

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    Discusses quantifying over fictional entities and illustrates cases of reasoning that look extremely hard to paraphrase away.

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Geach’s Hob Nob

Peter Geach’s Hob Nob example (Geach 1972) has created a small literature all on its own. Hob and Nob may be thinking of the same nonexistent witch, without their thinking agreeing on much else. Versions of the problem not only exemplify the problem of quantifying into intentional contexts but the fact that co-referring names (that nevertheless refer to something nonexistent) can occur in such contexts. No particular solution has convinced even a sizable minority of the philosophers worried about this problem. Salmon 2005 uses Hob Nob cases to press the case for ephemeral intentional objects that are brought into existence by our thinking of them. Salmon’s paper is a far-ranging and thorough examination of the drawbacks of previous approaches to the sentences, as well as a defense of his own approach. Burge 1983 attempts to characterize Hob Nob sentences in terms of indexing terms within intentional contexts. Asher 1987 applies discourse representation theory to the problem, and Edelberg 1986 offers the suggestion that existential quantifiers are capable of either ranging over thought objects or functioning as terms referring to those thought objects. King 1993 generalizes the number of examples a theory of Hob Nob sentences is supposed to explain, and treats the relevant pronouns in “Generalized Geach sentences” as context-dependent quantifiers. Neale 1990 is a milestone in the study of descriptions; Neale applies his theory to Hob Nob sentences in an important note.

  • Asher, Nicholas. “A Typology for Attitude Verbs and Their Anaphoric Properties.” Linguistics and Philosophy 10.2 (1987): 125–197.

    DOI: 10.1007/BF00584317Save Citation »Export Citation » Share Citation »

    An extension of Hans Kamp’s discourse representation theory, which is applied to Geach sentences.

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  • Burge, Tyler. “Russell’s Problem and Intentional Identity.” In Agent, Language, and the Structure of the World: Essays Presented to Hector-Neri Castañeda, with His Replies. Edited by James E. Tomberlin, 79–110. Indianapolis, IN: Hackett, 1983.

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    Develops a theory to handle reference failure, and applies it to Hob Nob statements. Suggests that different people’s nonreferring referential devices are sometimes to be quasi-anaphorically linked despite their disagreements. Suggests that the matter is often dependent on pragmatic considerations and is often vague.

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  • Edelberg, Walter. “A New Puzzle about Intentional Identity.” Journal of Philosophical Logic 15.1 (1986): 1–25.

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    An approach to the problem posed by Geach sentences by treating existential quantifiers as capable of either ranging over thought objects or being terms referring to those thought objects.

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  • Geach, Peter. “Intentional Identity.” In Logic Matters. By Peter Geach, 146–153. Berkeley, CA: University of California Press, 1972.

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    Offers the example of Hob Nob sentences and describes the drawbacks of various approaches to semantically characterizing them.

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  • King, Jeffrey C. “Intentional Identity Generalized.” Journal of Philosophical Logic 22.1 (1993): 61–93.

    DOI: 10.1007/BF01049181Save Citation »Export Citation » Share Citation »

    Shows that the problem Geach’s Hob Nob examples exhibit are specific instances of a more general problem exhibited by what he calls Generalized Geach sentences. Offers a theory on which the relevant pronouns in Generalized Geach sentences are context-dependent quantifiers. Criticizes previous approaches, for example those of Asher 1987 and Edelberg 1986.

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  • Neale, Stephen. Descriptions. Cambridge, MA: MIT Press, 1990.

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    In note 66 on page 221, Neale applies his general theory of descriptions to a version of the Hob Nob sentences.

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  • Salmon, Nathan. “Mythical Objects.” In Metaphysics, Mathematics, and Meaning. By Nathan Salmon, 91–107. Oxford: Oxford University Press, 2005.

    DOI: 10.1093/0199284717.003.0004Save Citation »Export Citation » Share Citation »

    A substantial and important discussion of Hob Nob sentences, including a survey of previous approaches. Salmon argues that to capture the semantics of Hob Nob sentences it is required that such statements be taken to be about ephemeral abstracta. Criticizes previous approaches, such as those of Neale 1990 and Burge 1983.

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Negative Existentials

A specific problem that arises with nonexistent entities occurs with statements that simply deny the existence of such—“Pegasus doesn’t exist” or “There are no flying horses,” for example. The problem is that standard approaches to the semantics of such statements seem to give them the wrong truth conditions, and approaches that give them the right truth conditions raise problems for the other kinds of statements we make about nonexistents. Quine 1980 replaces names (“Pegasus”) with definite descriptions (“the flying horse of Greek mythology”), and handles their truth conditions via Russell’s theory of descriptions (Russell 2008). But philosophers have not been satisfied with the truth conditions that Quine’s approach imposes on negative existentials. Burge 1974 handles them using a negative free logic, and Sainsbury 2005 is a book-length presentation of a descendent view. Everett 2000 and Taylor 2000 import pragmatic elements to illuminate the particular semantic theories (ones that treat terms referring to nonexistents as semantically empty) they presuppose as governing proper names. Donnellan 1974 is an early discussion of negative existentials that attempts to handle them compatibly with a causal/historical theory of proper names.

  • Burge, Tyler. “Truth and Singular Terms.” Noûs 8.4 (1974): 309–325.

    DOI: 10.2307/2214437Save Citation »Export Citation » Share Citation »

    Argues that negative free logic is the appropriate logic for languages containing empty singular terms.

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  • Donnellan, Keith. “Speaking of Nothing.” Philosophical Review 83.1 (1974): 3–31.

    DOI: 10.2307/2183871Save Citation »Export Citation » Share Citation »

    An important early discussion of negative existentials, with an attempt to handle their truth conditions compatibly with a historical/causal theory of names.

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  • Everett, Anthony. “Referential and Empty Names.” In Empty Names, Fiction and the Puzzles of Non-existence. Edited by Anthony Everett and Thomas Hofweber, 37–60. Stanford, CA: CSLI, 2000.

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    Attempts to show that empty names can explain the truth values of negative existentials because they offer a degenerate semantic contribution by failing to provide an object. Attempts to show that nonreferring names can nevertheless thinly be about the same thing if they share a source.

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  • Quine, Willard Van Orman. “On What There Is.” In From a Logical Point of View. By Willard Van Orman Quine, 1–19. 2d ed. Cambridge, MA: Harvard University Press, 1980.

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    Relying on Russell 2008, offers the suggestion that “Pegasus doesn’t exist” be regimented as “There is no unique something that is the flying horse of ancient Greek mythology.” First published 1948.

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  • Russell, Bertrand. “On Denoting.” In The Philosophy of Language. Edited by Aloysius P. Martinich, 230–238. 5th ed. Oxford: Oxford University Press, 2008.

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    Extremely influential article offering an interpretation of definite descriptions that replaces them with an existential quantifier and a uniqueness condition. Provides a way of giving gapless truth conditions for definite descriptions. First published 1905.

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  • Sainsbury, Richard Mark. Reference without Referents. Oxford: Oxford University Press, 2005.

    DOI: 10.1093/0199241805.001.0001Save Citation »Export Citation » Share Citation »

    Book-length treatment of a negative free-logic approach to negative existentials that was originally pioneered in Burge 1974.

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  • Taylor, Kenneth. “Emptiness without Compromise.” In Empty Names, Fiction and the Puzzles of Non-existence. Edited by Anthony Everett and Thomas Hofweber, 17–36. Stanford, CA: CSLI, 2000.

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    Attempts to resolve the apparent contradiction between the apparent expression of singular statements like “Pegasus doesn’t exist” with a semantics where “Pegasus” doesn’t refer, by invoking a nonliteral interpretation of what is said by “Pegasus doesn’t exist” that is pragmatically relevant.

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Realisms

A common solution to the problem of nonreferring terms is simply to deny that they are as they appear to be: nonreferring. Instead there are, perhaps strange, objects to which fictional terms, mathematical terms, and so on, refer. Colyvan 2001, for example, claims that indispensability arguments definitely show that Platonism is true: mathematical terms refer to mathematical abstracta. Van Inwagen 2004 runs an indispensability argument to show the existence of properties. Deutsche 2000 argues that fictional terms refer to fictional entities, which are abstracta possessing certain properties. Important variants of this popular position vis-à-vis fictional entities are also argued for in Salmon 2005, among many other works. Lewis and Lewis 1983 argues in a dialogue that realism vis-à-vis a kind of entity involves a balancing act among several differently tugging intellectual virtues, illustrating the point with holes. Dummett 1978 is a classic article arguing that bivalence is the hallmark of realism; to deny realism toward a kind of object requires the changing of logic. Quine 1981 echoes the view and develops the claim that bivalence is a reason for realism across the board. Quine’s discussion anticipates Lewis and Lewis 1983 on balancing conflicting intellectual virtues.

  • Colyvan, Mark. The Indispensability of Mathematics. Oxford: Oxford University Press, 2001.

    DOI: 10.1093/019513754X.001.0001Save Citation »Export Citation » Share Citation »

    Book-length defense of Platonism. Argues that attempts to treat mathematical terms as referring to nonexistents fail in light of the indispensability argument.

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  • Deutsche, Harry. “Making Up Stories.” In Empty Names, Fiction and the Puzzles of Non-existence. Edited by Anthony Everett and Thomas Hofweber, 149–181. Stanford, CA: CSLI, 2000.

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    Argues for a fictional plenitude in which all the items occur to which all our fictional terms refer.

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  • Dummett, Michael. “Realism.” In Truth and Other Enigmas. By Michael Dummett, 145–165. Cambridge, MA: Harvard University Press, 1978.

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    Classic presentation of the view that a classical bivalent logic determines realism as the metaphysical correlate of its areas of application.

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  • Lewis, David, and Stephanie Lewis. “Holes.” In Philosophical Papers. Vol. 1. By David Lewis, 3–9. Oxford: Oxford University Press, 1983.

    DOI: 10.1093/0195032047.003.0001Save Citation »Export Citation » Share Citation »

    Nice dialogue illustrates that the need to apparently commit oneself ontologically to holes turns on questions of economy and familiarity: on the sorts of costs in terms of which various kinds of realisms must be evaluated. First published 1970.

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  • Quine, Willard Van Orman. “What Price Bivalence?” In Theories and Things. By Willard Van Orman Quine, 31–37. Cambridge, MA: Harvard University Press, 1981.

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    Evaluates the cost of realism via evaluating the cost of the imposition of a bivalent logic.

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  • Salmon, Nathan. “Nonexistence.” In Metaphysics, Mathematics, and Meaning. By Nathan Salmon, 50–90. Oxford: Oxford University Press, 2005.

    DOI: 10.1093/0199284717.003.0003Save Citation »Export Citation » Share Citation »

    Argues for real intentional objects that are the relata of terms that we prima facie take to be nonreferring.

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  • van Inwagen, Peter. “A Theory of Properties.” In Oxford Studies in Metaphysics. Vol. 1. Edited by Dean W. Zimmerman, 107–138. Oxford: Oxford University Press, 2004.

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    Motivates a realist metaphysics of properties based on an indispensability argument.

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Meinongianism and Neo-Meinongianism

Meinong’s philosophical work stems directly from his thinking about intentionality. Our thought and speech seems directed toward entities that do not exist and even toward entities that cannot exist. Meinong claims that there are three kinds of objects: those that exist, those that subsist, and those that neither subsist nor exist. The round square is an example of the last sort of item. The entities that neither subsist nor exist are described in Findlay 1963 (cited under Meinong) as “absisting.” Although Russell was initially quite sympathetic to Meinong’s views, he became hostile to them after he invented his theory of descriptions. Nevertheless, Meinongian views flourished during the course of the 20th century and continue to flourish in 21st-century metaphysics.

Meinong

Only some of Meinong’s work has been translated into English: Meinong 1980 is an important presentation of his view that is available in English. However, many good studies of Meinong’s views are available, including Chisholm 2008, Findlay 1963, and Grossman 1974. Russell 1973a and Russell 1973b are excellent reviews of Meinong, the first very sympathetic. Russell 2008 presents Russell’s theory of descriptions, an approach to definite descriptions that enabled Russell to take a more hostile view toward Meinong’s views.

  • Chisholm, Roderick. “Beyond Being and Nonbeing.” In Metaphysics: The Big Questions. Edited by Peter van Inwagen and Dean W. Zimmerman, 40–50. Oxford: Blackwell, 2008.

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    A clear presentation of Meinongian themes and motivations. First published 1973.

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  • Findlay, John Niemeyer. Meinong’s Theory of Objects and Values. 2d ed. Oxford: Oxford University Press, 1963.

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    Sympathetic book-length study of Meinong’s theory of objects.

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  • Grossman, Reinhardt. Meinong. London: Routledge & Kegan Paul, 1974.

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    Sympathetic book-length study of Meinong’s views.

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  • Meinong, Alexius. “The Theory of Objects.” In Realism and the Background of Phenomenology. Edited by Roderick M. Chisholm, 76–117. Atascadero, CA: Ridgeview, 1980.

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    English translation of “Über Gegenstandstheorie,” first published in 1904. Meinong argues that because we can think about things that do not exist, they have some sort of being.

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  • Russell, Bertrand. “Meinong’s Theory of Complexes and Assumptions.” In Essays in Analysis. Edited by Douglas Lackey, 21–76. New York: George Braziller, 1973a.

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    An early and substantial review of Meinong’s theory. Russell is quite sympathetic to Meinong’s views at this stage in his career. First published 1904.

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  • Russell, Bertrand. “Review of A. Meinong, Untersuchungen zur Gegenstandstheorie und Psychologie.” In Essays in Analysis. Edited by Douglas Lackey, 77–88. New York: George Braziller, 1973b.

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    A much more hostile discussion of Meinong’s view. Raises for the first time many of the objections to Meinong’s theory that subsequently recur in the literature. First published 1905.

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  • Russell, Bertrand. “On Denoting.” In The Philosophy of Language. Edited by Aloysius P. Martinich, 230–238. 5th ed. Oxford: Oxford University Press, 2008.

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    This seminal article presents Russell’s theory of descriptions, which he used against Meinongian views. First published 1905.

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Contemporary Meinongianism and Neo-Meinongianism

Meinongianism and Neo-Meinongianism, despite Russell’s famous ridiculing, flourished throughout the 20th century, and they continue to flourish in the 21st century. Routley 1980 is a major work developing in enormous detail a Meinongian approach, one which the author calls “noneism.” Priest 2005 is a contemporary work in the neo-Meinongian tradition, strongly influenced by Routley 1980. Priest attempts to solve the important characterization problem. Parsons 1980 distinguishes the properties of nonexistent objects into two kinds, following an approach found in Meinong. Parsons applies his approach to fictional discourse. Smith 2002 is focused on the problem of illusion and the problem of hallucination; Smith argues that the problem of hallucination requires treating the hallucinated objects as Meinongian objects. Zalta 1983 and Zalta 1988 are book-length treatments of Zalta’s particular form of Meinongianism, which distinguishes two modes of predication, one that relates existing objects to their properties and the other that relates nonexisting objects to their properties. Zalta applies his theory to a number of different kinds of nonexistents. The author of McGinn 2008 motivates his own neo-Meinongian position by arguing that the logical quantifiers are not used to express the existence concept.

  • McGinn, Colin. “Existence.” In Logical Properties: Identity, Existence, Predication, Necessity, Truth. By Colin McGinn, 15–51. Oxford: Oxford University Press, 2008.

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    Argues that the logical quantifiers should not be used to express the existence concept.

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  • Parsons, Terence. Nonexistent Objects. New Haven, CT: Yale University Press, 1980.

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    A book-length treatment of Parsons’ particular Meinongian theory. There are two kinds of properties nonexistent objects have, nuclear and extranuclear, but there is only one mode of predication that both existent and nonexistent objects share.

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  • Priest, Graham. Towards Non-being: The Logic and Metaphysics of Intentionality. Oxford: Oxford University Press, 2005.

    DOI: 10.1093/0199262543.001.0001Save Citation »Export Citation » Share Citation »

    A book-length treatment of noneism. Attempts to solve the characterization problem that noneism faces, which is that it seems that a nonexistent object has those properties it is characterized as having, but this cannot be correct because it seems to validate the ontological proof of God. Worse, an unrestricted version of the characterization condition for nonexistent entities seems to allow the proof of any statement.

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  • Routley, Richard. Exploring Meinong’s Jungle: An Investigation of Noneism and the Theory of Items. Departmental Monograph 3. Canberra, Australia: Australian National University, 1980.

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    A major work. Concrete objects exist, according to Routley’s version of Meinongianism, but everything else, e.g., abstracta, possible objects, fictional entities, simply doesn’t exist. Objects that don’t exist, however, have properties. He calls his view “noneism.”

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  • Smith, A. D. The Problem of Perception. Cambridge, MA: Harvard University Press, 2002.

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    Concerned with the problem of illusion and the problem of hallucination. Argues that Meinongian objects are needed to handle the problem of hallucination.

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  • Zalta, Edward. Abstract Objects: An Introduction to Axiomatic Metaphysics. Dordrecht, The Netherlands: Reidel, 1983.

    DOI: 10.1007/978-94-009-6980-3Save Citation »Export Citation » Share Citation »

    Offers a distinctive Meinongian position that distinguishes two modes of predication. Although ordinary existing objects exemplify their properties, nonexistent ones instead “encode” their properties.

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  • Zalta, Edward. Intensional Logic and the Metaphysics of Intentionality. Cambridge, MA: MIT Press, 1988.

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    Revisits, amplifies, and develops the Meinongian theory offered in Zalta 1983.

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The Phenomenological Tradition and Existentialism

The phenomenological tradition is closely associated with Meinong historically, as are many of its themes. This is because phenomenology attempts to study intentional phenomena. Brentano 1995 and Husserl 2000, for example, are both influenced by the psychology of the time when they were written, and they raise philosophical concerns with how our mental life is directed toward the nonexistent. The same is true of the existential tradition that followed this work and was influenced by it, for example Heidegger 2008 and Sartre 2009.

  • Brentano, Franz. Psychology from an Empirical Standpoint. Edited by Linda L. McAlister. Translated by Antos C. Rancurello, D. B. Terrell, and Linda L. McAlister. London: Routledge, 1995.

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    English translation of Psychologie vom empirischen Standpunkte, first published in 1874. Introduced the notion of intentionality into contemporary philosophy. A major influence on both existential and analytic philosophical traditions.

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  • Heidegger, Martin. Being and Time. Translated by John Macquarrie and Edward Robinson. New York: HarperPerennial/Modern Thought, 2008.

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    English translation of Sein und Zeit, first published in 1927. A principal text of existentialism.

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  • Husserl, Edmund. Logical Investigations. 2 vols. Translated by J. N. Findlay. London: Humanity Books, 2000.

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    English translation of Logische Untersuchungen, 1900 (2nd German edition of Volume 2, Part 1 published in 1913; 2nd German edition of Volume 2, Part 2 published in 1921). Especially relevant is Investigation V.

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  • Sartre, Jean-Paul. Being and Nothingness. Translated by Hazel E. Barnes. London: Routledge, 2009.

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    English translation of L’Être et le Néant (Paris: Gallimard, 1943). A principal text of existentialism.

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Fictionalism

Fictionalism toward a subject area is the claim that the statements in that subject area are not true; more accurately, that the existential quantifications are false, the universal quantifications are true, and statements with empty singular terms have truth values according to one or another approach to them. Fictionalism, as described, dictates no particular strategy for handling statements about the nonexistent; it is compatible either with pretense approaches or with paraphrase approaches. See Pretense Approaches to Nonexistence and Paraphrase and Proxying. Good anthologies on fictionalism are Kalderon 2005 and Woods 2010. An important distinction between revolutionary fictionalism and hermeneutic fictionalism is drawn in Stanley 2001. Revolutionary fictionalists, like Hartry Field (Field 1980), reconceptualize a subject area, such as mathematical discourse, to render it unproblematical (as not involving talk about nonexistents). Hermeneutic fictionalists, on the other hand, like Stephen Yablo (Yablo 2005), try to show that an area of discourse already involves pretense or metaphor, and so is unproblematic to begin with: it does not really talk about nonexistents but only appears to. Eklund 2015 is an excellent online guide to this large literature. Many philosophers who self-regard their approach as “fictionalist” simultaneously regard their approach as a “pretense” one. See Pretense Approaches to Nonexistence.

  • Eklund, Matti. “Fictionalism.” In The Stanford Encyclopedia of Philosophy. Edited by Edward M. Zalta. Stanford, CA: Stanford University, 2015.

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    A nice survey of fictionalist approaches to various philosophical subject areas. Extensive bibliography.

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  • Field, Hartry. Science without Numbers. Princeton, NJ: Princeton University Press, 1980.

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    Explores the strategy of avoiding the Platonistic conclusion of the indispensability argument in the case of a small portion of Newtonian physics by treating the language as literally false but as open to reconceptualization in nominalist terms.

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  • Kalderon, Mark Eli, ed. Fictionalism in Metaphysics. Oxford: Oxford University Press, 2005.

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    A good anthology focused on fictionalist approaches to ontological commitments.

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  • Stanley, Jason. “Hermeneutic Fictionalism.” Midwest Studies in Philosophy 25 (2001): 36–71.

    DOI: 10.1111/1475-4975.00039Save Citation »Export Citation » Share Citation »

    Draws an important distinction between revolutionary fictionalism and hermeneutic fictionalism.

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  • Woods, John, ed. Fictions and Models: New Essays. Munich: Philosophia Verlag, 2010.

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    A good anthology spanning fictionalist approaches to various areas of philosophy, such as fiction, metaphysics, and philosophy of mathematics.

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  • Yablo, Stephen. “The Myth of the Seven.” In Fictionalism in Metaphysics. Edited by Mark Eli Kalderon, 88–115. Oxford: Oxford University Press, 2005.

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    An example of hermeneutic fictionalism. Argues that our talk of mathematical entities is metaphorical.

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Pretense Approaches to Nonexistence

Pretense views, broadly speaking, handle apparent talk of the nonexistent by treating it as nonliteral in one way or another. Speakers who speak of the nonexistent are pretending to talk about those entities. On some pretense views they are nonliterally indicating other literal statements that instead do not talk about the nonexistent. On other pretense views they are even pretending to utter meaningful propositions. Walton 1973 is a very influential presentation of the view, building pretense psychologically out of children’s games. Walton 1990 is an important book-length discussion of the view. Evans 1982 is a sophisticated presentation and development of the view, applied especially to talk about hallucinatory experience. Armour-Garb and Woodbridge 2015 is a good book-length defense of a pretense approach that distinguishes between “pretend content” (proxy content) and “serious content” (proxy target content) (see Paraphrase and Proxying). Everett 2013 is a book-length pretense-theoretic approach based on the cognitive account due to Stephen Stich and Shaun Nichols. Crimmins 1998 applies pretense to solve problems raised by attitude ascriptions. Kroon 2000 is an application of the author’s pragmatic pretense approach to negative existentials; Kroon 2004 is an application of that approach to Frege-Russell problems. Yablo 2005 applies a pretense approach to talk of mathematical entities. Many philosophers who self-regard their approach as “fictionalist” simultaneously self-regard their approach as a “pretense” one (see Fictionalism).

Neutralism

Neutralism is the view that the quantifiers, both the ordinary language expressions and the formal devices, are ontologically neutral—to say “there are mice such that . . .” without context is neither to affirm nor not to affirm the existence of mice. The view is not the same as Meinongian views that offer a kind of quantifier that ranges over what does not exist (see Meinongianism and Neo-Meinongianism), nor is it the same as views that separate existence into different kinds of being—existence and reality, say—and allow that quantifiers can range over one but not the other (see Degrees of Existence). Azzouni 2004 is a book-length study and application of the neutral perspective of the quantifiers, specifically in the defense of nominalism (see nonexistents in the context of Philosophy of Mathematics). Azzouni 2010 extends neutralism to singular terms. Bueno 2005 defends neutralism, but Bueno 2008 argues that neutralism is compatible with agnostic nominalism, a position of epistemic neutrality with respect to whether mathematical objects exist or not. Raley 2007 attacks Quine’s criterion by way of support for neutralism. Lane 2011 evaluates neutralism for its value in application to philosophical puzzles in philosophy of religion. Asay 2010 tries to show that Azzouni’s brand of neutralism does not apply to natural languages.

  • Asay, Jamin. “How to Express Ontological Commitment in the Vernacular.” Philosophia Mathematica 18.3 (2010): 293–310.

    DOI: 10.1093/philmat/nkq005Save Citation »Export Citation » Share Citation »

    Tries to show that, contrary to the neutralist perspective on ordinary language quantifiers, negative existential claims in the vernacular deny ontological commitments.

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  • Azzouni, Jody. Deflating Existential Consequence: A Case for Nominalism. Oxford: Oxford University Press, 2004.

    DOI: 10.1093/0195159888.001.0001Save Citation »Export Citation » Share Citation »

    The first book-length treatment of the neutralist approach to quantifiers, applied in particular against Platonism.

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  • Azzouni, Jody. Talking about Nothing: Numbers, Hallucinations, and Fictions. Oxford: Oxford University Press, 2010.

    DOI: 10.1093/acprof:oso/9780199738946.001.0001Save Citation »Export Citation » Share Citation »

    Book-length treatment of the view that the quantifiers of natural language are ontologically neutral, and that the same is true of names and demonstrative expressions in natural languages. The corresponding expressions in formal languages are open to a semantical approach on which they are ontologically neutral as well.

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  • Bueno, Otávio. “Dirac and the Dispensability of Mathematics.” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (September 2005): 465–490.

    DOI: 10.1016/j.shpsb.2005.03.002Save Citation »Export Citation » Share Citation »

    An application of the neutralist perspective to a case study in the history of science.

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  • Bueno, Otávio. “Nominalism and Mathematical Intuition.” In Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism. Edited by Gerhard Preyer and Georg Peter, 89–107. Frankfurt: Ontos Verlag, 2008.

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    A defense of agnostic nominalism.

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  • Lane, William Craig. “A Nominalist Perspective on God and Abstract Objects.” In Special Issue: God and Abstract Objects. Edited by Paul Gould. Philosophia Christi 13 (2011): 305–318.

    DOI: 10.5840/pc201113228Save Citation »Export Citation » Share Citation »

    Argues that there are reasons to adopt the neutralist perspective on the quantifiers in order to meet the challenge to belief in God posed by abstract objects.

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  • Raley, Yvonne. “Ontology, Commitment, and Quine’s Criterion.” Philosophia Mathematica 15.3 (2007): 271–290.

    DOI: 10.1093/philmat/nkm018Save Citation »Export Citation » Share Citation »

    Attacks the view that Quine’s criterion should be used to characterize the ontic capacities of quantifiers. Claims that objectual first-order semantics for the quantifiers is ontologically neutral.

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Specializations in Philosophy Where Nonexistence Is Problematic

Especially in the 20th century, subspecialties in philosophy have arisen—“philosophy of science,” “philosophy of mathematics,” and “philosophy of perception,” for example—where although philosophical issues specific to the area are discussed (the status of laws in the case of philosophy of science, issues about perceptual content in the case of philosophy of perception), there are nevertheless problems that cross disciplines. The problem of thinking about and referring to what doesn’t exist is one of these trans-specialist problems. This problem has emerged with particular force in four subspecialties: the Philosophy of Mathematics, the Philosophy of Science, the Philosophy of Fiction, and the Philosophy of Perception—the last specifically with regard to hallucinatory experience. Specialized concerns with nonexistents have also arisen in metaphysics and philosophy of language, specifically the ontological status of possible worlds and propositions.

Philosophy of Mathematics

In philosophy of mathematics, the indispensability thesis, also due to Quine 1981, and discussed in more detail in Putnam 1975 (often called the “Quine-Putnam indispensability thesis,” e.g., in Field 2016 and Colyvan 2001), seems to require quantification over mathematical entities, and therefore to require an ontological commitment to those entities even if we are otherwise convinced they do not exist. Different versions of the argument have emerged, because Putnam and Quine were not explicit about the assumptions of the indispensability arguments they were arguing for. Resnik 1997 offers one version of the argument, while Maddy 2007 criticizes a different version. Field’s nominalization project (Field 2016) is motivated by the indispensability argument, Colyvan 2001 discusses the argument at length, and Azzouni 2009 distinguishes several versions of the argument that differ greatly in the strength of their assumptions. Panza and Sereni 2015 attempts a full characterization of the family of indispensability arguments.

  • Azzouni, Jody. “Evading Truth Commitments: The Problem Reanalyzed.” Logique et Analyse 52.206 (2009): 139–176.

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    Distinguishes several versions of the indispensability argument and evaluates them.

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  • Colyvan, Mark. The Indispensability of Mathematics. Oxford: Oxford University Press, 2001.

    DOI: 10.1093/019513754X.001.0001Save Citation »Export Citation » Share Citation »

    Book-length treatment of the indispensability argument. Argues that the argument is sound and generates a commitment to Platonism.

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  • Field, Hartry. Science without Numbers. 2d ed. Oxford: Oxford University Press, 2016.

    DOI: 10.1093/acprof:oso/9780198777915.001.0001Save Citation »Export Citation » Share Citation »

    Explores the strategy of avoiding the Platonistic conclusion of the indispensability argument in the case of a small portion of Newtonian physics.

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  • Maddy, Penelope. Second Philosophy: A Naturalistic Method. Oxford: Oxford University Press, 2007.

    DOI: 10.1093/acprof:oso/9780199273669.001.0001Save Citation »Export Citation » Share Citation »

    A book-length treatment of her “science-first” view of philosophy. Attacks one version of the Quine-Putnam indispensability thesis.

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  • Panza, Marco, and Andrea Sereni. “On the Indispensable Premises of the Indispensability Argument.” In From Logic to Practice: Italian Studies in the Philosophy of Mathematics. Edited by Gabriele Lolli, Marco Panza, and Giorgio Venturi, 241–276. Cham, Switzerland: Springer, 2015.

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    Attempts a full characterization of the family of indispensability arguments in mathematics.

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  • Putnam, Hilary. “Philosophy of Logic.” In Mathematics, Matter and Method: Philosophical Papers. Vol. 1. By Hilary Putnam, 324–357. Cambridge, UK: Cambridge University Press, 1975.

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    Influential work where Putnam lays out details of the indispensability argument, illustrating how Newton’s law of gravitation apparently requires quantification over mathematical objects.

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  • Quine, Willard Van Orman. “Success and Limits of Mathematization.” In Theories and Things. By Willard Van Orman Quine, 148–156. Cambridge, MA: Harvard University Press, 1981.

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    One place, among many, where Quine briefly describes his allegiance to what has come to be called “the Quine-Putnam indispensability thesis.”

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  • Resnik, Michael. Mathematics as a Science of Patterns. Oxford: Oxford University Press, 1997.

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    Offers a characterization of the indispensability argument and defends it. Attempts to develop a Platonistic view of mathematics that takes mathematics to be a science of patterns, which are abstract objects.

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Philosophy of Science

Scientific realism/anti-realism debates are a key place where issues about nonexistents arise in philosophy of science. One early (positivistic) view was that theoretical entities do not exist, although observable entities do. The scientific theories that nevertheless quantify over theoretical entities were to be interpreted instrumentally, as in classical operationism. But this was perceived to face drawbacks because of the role of theoretical entities in theories; see Boyd, et al. 1991 for a historical discussion. An influential attempt to sustain the view (called “constructive empiricism”) that in scientific theories one can remain committed only to observational entities may be found in van Fraassen 1980. Bueno 2011 is a recent attempt to defend constructive empiricism with respect to challenging cases raised by non-observational but detailed tracking of nanoscale entities. Fine 1996 is an attempt to move beyond the realism/anti-realism debate altogether. Valuable for an understanding of scientific realism/anti-realism debates are scientific works that indicate milestones during which scientists shifted from an instrumentalist view of a non-observational phenomenon to a realist view of it. Perrin 1990 is an excellent example of this, with respect to atoms. Van Fraassen 2009 focuses on the Perrin case, which scientific realists have used to bolster their position and tries to show that Perrin’s results and methodology are compatible with constructive empiricism, an irrealist position. Psillos 1999 is an excellent textbook discussion of the issues in scientific realism, including some important historical case studies.

  • Boyd, Richard, Philip Gasper, and J. D. Trout. “Introduction.” In The Philosophy of Science. Edited by Richard Boyd, Philip Gasper, and J. D. Trout, xi–xiv. Cambridge, MA: MIT Press, 1991.

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    A good analytical summary of how contemporary philosophy of science has moved past the influential positivist paradigm.

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  • Bueno, Otávio. “When Physics and Biology Meet: The Nanoscale Case.” Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 42.2 (2011): 180–189.

    DOI: 10.1016/j.shpsc.2010.11.025Save Citation »Export Citation » Share Citation »

    A contemporary attempt to defend constructive empiricism with attention to an important scientific case.

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  • Fine, Arthur. The Shaky Game: Einstein, Realism, and the Quantum Theory. 2d ed. Chicago: University of Chicago Press, 1996.

    DOI: 10.7208/chicago/9780226923260.001.0001Save Citation »Export Citation » Share Citation »

    A scientifically informed attempt to move beyond the realism/anti-realism debate.

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  • Perrin, Jean. Atoms. Translated by Dalziel Llewellyn Hammick. Woodbridge, CT: Ox Bow, 1990.

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    A translation of Les atomes (Paris: Librairie Félix Alcan, 1913). A summary of the work of Jean Perrin, and others, that scientifically established the existence of atoms.

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  • Psillos, Stathis. Scientific Realism: How Science Tracks Truth. London: Routledge, 1999.

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    An excellent textbook survey of the issue of realism in philosophy of science, along with a discussion of some historical examples.

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  • van Fraassen, Bas C. The Scientific Image. Oxford: Clarendon, 1980.

    DOI: 10.1093/0198244274.001.0001Save Citation »Export Citation » Share Citation »

    An influential attempt, called “constructive empiricism,” to sustain the claim that scientists need only ontologically commit themselves to observable entities. Van Fraassen separates his characterization of observable entities from the earlier positivistic commitments, such as the distinction between observational and theoretical language.

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  • Van Fraassen, Bas C. “The Perils of Perrin, in the Hands of Philosophers.” Philosophical Studies 143.1 (2009): 5–24.

    DOI: 10.1007/s11098-008-9319-9Save Citation »Export Citation » Share Citation »

    Attempts to show that the Perrin case, contrary to realist assumptions, is compatible with constructive empiricism, an irrealist position about atoms.

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Philosophy of Perception

Debates about nonexistents arise most directly in philosophy of perception with respect to hallucinations. Ayer 1956 suggests there is a common use of the word “see” according to which someone having a hallucination can be said not to see anything at all. Austin 1970 is a keen analysis of ordinary ways of talking about what we see, including how we talk about hallucinations; it is very critical of Ayer’s earlier work. Cartwright 1987 worries about the logical form of statements like Macbeth’s “Is this a dagger which I see before me?” Perception of nonexistents (during hallucinations) is rich in content, and yet the descriptions of such content seems necessarily object-directed. Evans 1982 faces this problem directly, and attempts to handle it by invoking pretense. Smith 2002 is a masterful discussion of the problem of hallucination that criticizes earlier approaches, including that of Evans 1982, and argues that only the positing of Meinongian objects as what is perceived during hallucinatory events can do justice both to the phenomenology and to our ways of speaking about that phenomenology. Azzouni 2010 attempts both to characterize the phenomenology of, and to talk about, hallucinations using empty singular terms and neutralism with respect to the quantifiers; it is critical of earlier work, such as Evans 1982 and Smith 2002.

  • Austin, J. L. Sense and Sensibilia. London: Oxford University Press, 1970.

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    Keen analysis from the perspective of ordinary language of our ways of talking about what we see. Contains an influential and important discussion of the argument from hallucination.

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  • Ayer, A. J. The Problem of Knowledge. Harmondsworth, UK: Penguin, 1956.

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    Ayer suggests that there is a common use of the word “see” according to which someone having an hallucination can be said not to see anything at all.

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  • Azzouni, Jody. Talking about Nothing: Numbers, Hallucinations and Fictions. Oxford: Oxford University Press, 2010.

    DOI: 10.1093/acprof:oso/9780199738946.001.0001Save Citation »Export Citation » Share Citation »

    Discusses hallucinatory experience and talk, arguing that this can be handled by neutral quantifiers and empty singular terms. Criticizes previous approaches, especially Evans 1982 and Smith 2002.

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  • Cartwright, Richard. “Macbeth’s Dagger.” In Philosophical Essays. By Richard Cartwright, 13–20. Cambridge, MA: MIT Press, 1987.

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    Worries about the logical form of statements like Macbeth’s “Is this a dagger which I see before me?” Paper originally presented 1957.

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  • Evans, Gareth. The Varieties of Reference. Edited by John McDowell. Oxford: Oxford University Press, 1982.

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    Contains a substantial discussion of hallucinatory talk. Sophisticated attempt to characterize all such talk in terms of pretense.

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  • Smith, A. D. The Problem of Perception. Cambridge, MA: Harvard University Press, 2002.

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    Proposes Meinongian objects as the targets of hallucinatory experience and talk about hallucinations. Critical of previous approaches to hallucination and the argument from hallucination, as in Evans 1982 and Austin 1970.

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Philosophy of Fiction

Discourse about fictional genres, characters, their properties, and so on has long been recognized to be problematic, both for metaphysics and for philosophy of language. The original problem of nonexistents has most cleanly emerged in discussions of fictional discourse. Anthologies on the nonexistent, like Everett and Hofweber 2000, are mostly concerned with literary fiction, less so with other areas where prima facie discourse about nonexistents takes place. Kroon and Voltolini 2016 is a recent online guide to the philosophical topic of fiction. Thomasson 1999 is a book-length study of the metaphysics and language of fictional discourse that argues for a realist approach to fictional entities. Van Inwagen 2001 also argues for a realist construal of fictional entities, based on the indispensable need for inferences that quantify over fictional entities. Friend 2007 evaluates realist and anti-realist approaches to fictional discourse and argues that, in either case, pretense must play a major role.

  • Everett, Anthony, and Thomas Hofweber, eds. Empty Names, Fiction and the Puzzles of Non-Existence. Stanford, CA: CSLI, 2000.

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    A good anthology focused primarily on pretense approaches to avoiding ontological commitment to fictional entities. Focused primarily on literary fiction as a problematical discourse.

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  • Friend, Stacie. “Fictional Characters.” Philosophy Compass 2.2 (2007): 141–156.

    DOI: 10.1111/j.1747-9991.2007.00059.xSave Citation »Export Citation » Share Citation »

    Evaluates realist and anti-realist approaches to fictional discourse. Argues that pretense, in either case, must play a major role.

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  • Kroon, Fred, and Alberto Voltolini. “Fiction.” In The Stanford Encyclopedia of Philosophy. Edited by Edward M. Zalta. Stanford, CA: Stanford University, 2016.

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    A recent online guide to philosophical issues surrounding fiction, with extensive bibliography. Especially good on Meinongian and neo-Meinongian approaches to the topic.

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  • Thomasson, Amie L. Fiction and Metaphysics. Cambridge, UK: Cambridge University Press, 1999.

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    A book-length presentation of a theory of fictional objects, with substantial sensitivity to fictional practice.

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  • van Inwagen, Peter. “Creatures of Fiction.” In Ontology, Identity, and Modality: Essays in Metaphysics. By Peter van Inwagen, 37–56. Cambridge, UK: Cambridge University Press, 2001.

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    Uses an indispensability argument to argue for a realist view of fictional entities.

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Philosophy of Language

A commitment to propositions seems to be a necessary component of semantic theories. (See McGrath 2018 for a general introduction to propositions and for a bibliography.) And yet they are problematic in various ways that invite the suggestion that they don’t exist. Moore 1999 brings Benacerraf-style objections to bear against propositions. Armour-Garb and Woodbridge 2012 describes reasons for doubting that propositions exist, and in this way motivates a semantic-pretense approach to proposition-talk; the authors criticize the pragmatic-pretense approach to propositions. A different pretense approach to propositions can be found in Balaguer 1998. Schiffer 2003 is a book-length presentation of a pleonastic approach to the metaphysics of propositions, treating them as genuine mind-independent entities that nevertheless are introduced by “something-from-nothing” transformations.

Metaphysics

Possible worlds semantics seems to be demanded in order to make sense of counterfactual discourse. Lewis 1986 is an influential book-length argument in favor of a realist approach to possible worlds, one that takes possible worlds to be concrete. Lewis criticizes other approaches, such as “Ersatzism,” which tries to use abstracta to play the roles that he thinks concrete possible worlds are needed for. Rosen 1990 is a recent attempt to show that possible worlds themselves are not needed; a fictionalizing operator suitably placed in front of discourse can do the job instead. Rosen’s article has generated a small industry of responses and counter-responses. Nolan 2016 is an excellent survey of this material.

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