Ontology

Ontology is the philosophical study of being. More broadly, it studies concepts that directly relate to being, in particular becoming, existence, reality, as well as the basic categories of being and their relations.[1] Traditionally listed as a part of the major branch of philosophy known as metaphysics, ontology often deals with questions concerning what entities exist or may be said to exist and how such entities may be grouped, related within a hierarchy, and subdivided according to similarities and differences.

Parmenides was among the first to propose an ontological characterization of the fundamental nature of reality.

Etymology

The compound word ontology ('study of being') combines

onto- (Greek: ὄν, on; [lower-roman 1] GEN. ὄντος, ontos, 'being' or 'that which is') and
-logia (-λογία, 'logical discourse').[2][3]

While the etymology is Greek, the oldest extant records of the word itself, the New Latin form ontologia appeared

in 1606 in the Ogdoas Scholastica by Jacob Lorhard (Lorhardus), and
in 1613 in the Lexicon philosophicum by Rudolf Göckel (Goclenius).

The first occurrence in English of ontology, as recorded by the Oxford English Dictionary,[4] came in 1664 through Archelogia philosophica nova... by Gideon Harvey[5] The word was first used, in its Latin form, by philosophers, and based on the Latin roots (and in turn on the Greek ones).

Gottfried Wilhelm Leibniz is the only one of the great philosophers of that century to have used the term ontology.[6]

Overview

Some philosophers, notably in the traditions of the Platonic school, contend that all nouns (including abstract nouns) refer to existent entities. Other philosophers contend that nouns do not always name entities, but that some provide a kind of shorthand for reference to a collection either of objects or of events. In this latter view, mind, instead of referring to an entity, refers to a collection of mental events experienced by a person; society refers to a collection of persons with some shared characteristics, and geometry refers to a collection of specific kinds of intellectual activities.[7] Between these poles of realism and nominalism stand a variety of other positions.

Some fundamental questions

Principal questions of ontology include:

  • "What can be said to exist?"
  • "What is a thing?"[8]
  • "Into what categories, if any, can we sort existing things?"
  • "What are the meanings of being?"
  • "What are the various modes of being of entities?"

Various philosophers have provided different answers to these questions. One common approach involves dividing the extant subjects and predicates into groups called categories. Such lists of categories differ widely from one another, and it is through the co-ordination of different categorical schemes that ontology relates to such fields as library science and artificial intelligence. Such an understanding of ontological categories, however, is merely taxonomic, classificatory. Aristotle's categories are the ways in which a being may be addressed simply as a being, such as:[9]

  • what it is (its 'whatness', quiddity, haecceity or essence);
  • how it is (its 'howness' or qualitativeness);
  • how much it is (quantitativeness);
  • where it is (its relatedness to other beings).

Further examples of ontological questions include:

  • What is existence, i.e. what does it mean for a being to be?
  • Is existence a property?
  • Is existence a genus or general class that is simply divided up by specific differences?
  • Which entities, if any, are fundamental?
  • Are all entities objects?
  • How do the properties of an object relate to the object itself?
  • Do physical properties actually exist?
  • What features are the essential, as opposed to merely accidental attributes of a given object?
  • How many levels of existence or ontological levels are there? And what constitutes a "level"?
  • What is a physical object?
  • Can one give an account of what it means to say that a physical object exists?
  • Can one give an account of what it means to say that a non-physical entity exists?
  • What constitutes the identity of an object?
  • When does an object go out of existence, as opposed to merely changing?
  • Do beings exist other than in the modes of objectivity and subjectivity, i.e. is the subject/object split of modern philosophy inevitable?

Concepts

Essential ontological dichotomies include:

Types

Philosophers can classify ontologies in various ways, using criteria such as the degree of abstraction and field of application:[10]

  1. Upper ontology: concepts supporting development of an ontology, meta-ontology.
  2. Domain ontology: concepts relevant to a particular topic, domain of discourse, or area of interest, for example, to information technology or to computer. languages, or to particular branches of science.
  3. Interface ontology: concepts relevant to the juncture of two disciplines.
  4. Process ontology: inputs, outputs, constraints, sequencing information, involved in business or engineering processes.

History

Hindu philosophy

Ontology features in the Samkhya school of Hindu philosophy from the first millennium BCE.[11]

Parmenides and monism

In the Greek philosophical tradition, Parmenides was among the first to propose an ontological characterization of the fundamental nature of existence. In the prologue (or proem) to On Nature, he describes two views of existence. Initially, nothing comes from nothing, thus existence is eternal. This posits that existence is what may be conceived of by thought, created, or possessed. Hence, there may be neither void nor vacuum; and true reality neither may come into being nor vanish from existence. Rather, the entirety of creation is eternal, uniform, and immutable, though not infinite (Parmenides characterized its shape as that of a perfect sphere). Parmenides thus posits that change, as perceived in everyday experience, is illusory. Everything that may be apprehended is but one part of a single entity. This idea somewhat anticipates the modern concept of an ultimate theory of everything that finally describes all of existence in terms of one inter-related sub-atomic reality which applies to everything. Most of western philosophy (especially the philosophy of Baruch Spinoza)—including the fundamental concepts of falsifiability—has emerged from this view.

Ontological pluralism

Opposite to the Eleatic monism of Parmenides is the pluralistic conception of being. In the 5th century BC, Anaxagoras and Leucippus replaced[12] the reality of being (unique and unchanging) with that of becoming, therefore by a more fundamental and elementary ontic plurality. This thesis originated in the Hellenic world, stated in two different ways by Anaxagoras and by Leucippus. The first theory dealt with "seeds" (which Aristotle referred to as "homeomeries") of the various substances. The second was the atomistic theory,[13] which dealt with reality as based on the vacuum, the atoms and their intrinsic movement in it.

The materialist atomism proposed by Leucippus was indeterminist, but Democritus (c. 460 – c. 370 BC) subsequently developed it in a deterministic way. Later (4th century BC), Epicurus took the original atomism again as indeterministic. He saw reality as composed of an infinity of indivisible, unchangeable corpuscles or atoms (atomon, lit. 'uncuttable'), but he gives weight to characterize atoms whereas for Leucippus they are characterized by a "figure", an "order" and a "position" in the cosmos.[14] Atoms are, besides, creating the whole with the intrinsic movement in the vacuum, producing the diverse flux of being. Their movement is influenced by the parenklisis (Lucretius names it clinamen) and that is determined by the chance. These ideas foreshadowed the understanding of traditional physics until the advent of 20th-century theories on the nature of atoms.[15]

Plato

Plato developed the distinction between true reality and illusion, in arguing that what is real are eternal and unchanging forms or ideas (a precursor to universals), of which things experienced in sensation are at best merely copies, and real only in so far as they copy ("partake of") such forms. In general, Plato presumes that all nouns (e.g., "beauty") refer to real entities, whether sensible bodies or insensible forms. Hence, in The Sophist, Plato argues that being is a form in which all existent things participate and which they have in common (though it is unclear whether "Being" is intended in the sense of existence, copula, or identity); and argues, against Parmenides, that forms must exist not only of being, but also of Negation and of non-being (or Difference).

Aristotle

In his Categories, Aristotle (384–322 BCE) identifies ten possible kinds of things that may be the subject or the predicate of a proposition. For Aristotle there are four different ontological dimensions:[16]

  1. according to the various categories or ways of addressing a being as such
  2. according to its truth or falsity (e.g. fake gold, counterfeit money)
  3. whether it exists in and of itself or simply 'comes along' by accident
  4. according to its potency, movement (energy) or finished presence (Metaphysics Book Theta).

Avicenna

According to Avicenna (c. 980 – 1037), and in an interpretation of Greek Aristotelian and Platonist ontological doctrines in medieval metaphysics, being is either necessary, contingent qua possible, or impossible. Necessary being is that which cannot but be, since its non-being entails a contradiction. Contingent qua possible being is neither necessary nor impossible for it to be or not to be. It is ontologically neutral, and is brought from potential existing into actual existence by way of a cause that is external to its essence. Its being is borrowed – unlike the necessary existent, which is self-subsisting and is impossible for it not to be. As for the impossible, it necessarily does not exist, and the affirmation of its being is a contradiction.[17]

Other ontological topics

Ontological formations

The concept of ontological formations refers to formations of social relations understood as dominant ways of living. Temporal, spatial, corporeal, epistemological, and performative relations are taken to be central to understanding a dominant formation. That is, a particular ontological formation is based on how ontological categories of time, space, embodiment, knowing and performing are lived—objectively and subjectively. Different ontological formations include the customary (including the tribal), the traditional, the modern, and the postmodern. The concept was first introduced by Paul James in 2006, together with a series of writers including Damian Grenfell and Manfred Steger.[18]

In the engaged theory approach, ontological formations are seen as layered and intersecting rather than singular formations. They are 'formations of being'. This approach avoids the usual problems of a Great Divide being posited between the modern and the pre-modern. From a philosophical distinction concerning different formations of being, the concept then provides a way of translating into practical understandings concerning how humans might design cities and communities that live creatively across different ontological formations, for example cities that are not completely dominated by modern valences of spatial configuration. Here the work of Tony Fry is important.[19]

Ontology of fictional characters

According to Edward N. Zalta, the ontology of fiction analyses such sentences as: [20]

According to Amie L. Thomasson, fictional discourse can be of four sorts:

  1. Uttered within works of fiction;
  2. Philosophical exercises such as 'Captain Marvel does not exist';
  3. Treating fictional characters as if they were 'real', such as 'Superman can leap tall buildings;' and
  4. Discourse about works of fiction, such as 'Professor Higgins was created by George Bernard Shaw'.[21]

Jeremy Bentham distinguished three kinds of entities:[22]

  1. the real: those that can be perceived, or can be inferred from perception.
  2. the fictitious: abstractions that referred to perceptible things.
  3. the fabulous: those that can be found only in the imagination, where the word 'exist' applies to such only in the sense that they do not really exist.

Francis Herbert Bradley thought that real things exist respectively at particular times and places. He recognised several kinds of entity:[23]

  • the genuinely historical;
  • the fictional;
  • the real;
  • the merely imagined;
  • the existent; and
  • the non-existent.

Alexius Meinong would put fictional entities into the category which he called subsistence.[24] This category contains objects that neither exist spatially or non-spatially. However, they do have properties. The properties are given to these objects in the way they are said to be described. For example, we can talk about the tall unicorn even though the tall unicorn does not exist. We can say the unicorn is in fact tall because this follows from the properties in which the object is characterized.[24]

Ontological and epistemological certainty

René Descartes, with cogito, ergo sum (je pense donc je suis, "I think, therefore I am"), argued that "the self" is something that we can know exists with epistemological certainty. Descartes argued further that this knowledge could lead to a proof of the certainty of the existence of God, using the ontological argument that had been formulated first by Anselm of Canterbury.[25]

Certainty about the existence of "the self" and "the other", however, came under increasing criticism in the 20th century. Sociological theorists, most notably George Herbert Mead and Erving Goffman, saw the Cartesian other as a "Generalized other," the imaginary audience that individuals use when thinking about the self. According to Mead, "we do not assume there is a self to begin with. Self is not presupposed as a stuff out of which the world arises. Rather, the self arises in the world".[26][27] The Cartesian other was also used by Sigmund Freud, who saw the superego as an abstract regulatory force, and Émile Durkheim who viewed this as a psychologically manifested entity which represented God in society at large.

Body and environment, questioning the meaning of being

Schools of subjectivism, objectivism and relativism existed at various times in the 20th century, and the postmodernists and body philosophers tried to reframe all these questions in terms of bodies taking some specific action in an environment. This relied to a great degree on insights derived from scientific research into animals taking instinctive action in natural and artificial settings—as studied by biology, ecology,[28] and cognitive science.

The processes by which bodies related to environments became of great concern, and the idea of being itself became difficult to really define. What did people mean when they said "A is B", "A must be B", "A was B"...? Some linguists advocated dropping the verb "to be" from the English language, leaving "E Prime", supposedly less prone to bad abstractions. Others, mostly philosophers, tried to dig into the word and its usage. Martin Heidegger distinguished human being as existence from the being of things in the world. Heidegger proposes that our way of being human and the way the world is for us are cast historically through a fundamental ontological questioning. These fundamental ontological categories provide the basis for communication in an age: a horizon of unspoken and seemingly unquestionable background meanings, such as human beings understood unquestioningly as subjects and other entities understood unquestioningly as objects. Because these basic ontological meanings both generate and are regenerated in everyday interactions, the locus of our way of being in a historical epoch is the communicative event of language in use.[26] For Heidegger, however, communication in the first place is not among human beings, but language itself shapes up in response to questioning (the inexhaustible meaning of) being.[29] Even the focus of traditional ontology on the 'whatness' or quidditas of beings in their substantial, standing presence can be shifted to pose the question of the 'whoness' of human being itself.[30]

Ontology and language

Some philosophers suggest that the question of "What is?" is (at least in part) an issue of usage rather than a question about facts.[31] This perspective is conveyed by an analogy made by Donald Davidson: Suppose a person refers to a 'cup' as a 'chair' and makes some comments pertinent to a cup, but uses the word 'chair' consistently throughout instead of 'cup'. One might readily catch on that this person simply calls a 'cup' a 'chair' and the oddity is explained.[32] Analogously, if we find people asserting 'there are' such-and-such, and we do not ourselves think that 'such-and-such' exist, we might conclude that these people are not nuts (Davidson calls this assumption 'charity'), they simply use 'there are' differently than we do. The question of What is? is at least partially a topic in the philosophy of language, and is not entirely about ontology itself.[33] This viewpoint has been expressed by Eli Hirsch.[34][35]

Hirsch interprets Hilary Putnam as asserting that different concepts of "the existence of something" can be correct.[35] This position does not contradict the view that some things do exist, but points out that different 'languages' will have different rules about assigning this property.[35][36] How to determine the 'fitness' of a 'language' to the world then becomes a subject for investigation.

Common to all Indo-European copula languages is the double use of the verb "to be" in both stating that entity X exists ("X is.") as well as stating that X has a property ("X is P"). It is sometimes argued that a third use is also distinct, stating that X is a member of a class ("X is a C"). In other language families these roles may have completely different verbs and are less likely to be confused with one another. For example they might say something like "the car has redness" rather than "the car is red." Hence any discussion of "being" in Indo-European language philosophy may need to make distinctions between these senses.

Ontology and human geography

In human geography there are two types of ontology: small "o" which accounts for the practical orientation, describing functions of being a part of the group, thought to oversimplify and ignore key activities. The other "o", or big "O", systematically, logically, and rationally describes the essential characteristics and universal traits. This concept relates closely to Plato's view that the human mind can only perceive a bigger world if they continue to live within the confines of their "caves". However, in spite of the differences, ontology relies on the symbolic agreements among members. That said, ontology is crucial for the axiomatic language frameworks.[37]

Reality and actuality

According to Alfred N. Whitehead, for ontology, it is useful to distinguish the terms 'reality' and 'actuality'. In this view, an 'actual entity' has a philosophical status of fundamental ontological priority, while a 'real entity' is one which may be actual, or may derive its reality from its logical relation to some actual entity or entities. For example, an occasion in the life of Socrates is an actual entity. But Socrates' being a man does not make 'man' an actual entity, because it refers indeterminately to many actual entities, such as several occasions in the life of Socrates, and also to several occasions in the lives of Alcibiades, and of others. But the notion of man is real; it derives its reality from its reference to those many actual occasions, each of which is an actual entity. An actual occasion is a concrete entity, while terms such as 'man' are abstractions from many concrete relevant entities.

According to Whitehead, an actual entity must earn its philosophical status of fundamental ontological priority by satisfying several philosophical criteria, as follows:

  • There is no going behind an actual entity, to find something more fundamental in fact or in efficacy. This criterion is to be regarded as expressing an axiom, or postulated distinguished doctrine.
  • An actual entity must be completely determinate in the sense that there may be no confusion about its identity that would allow it to be confounded with another actual entity. In this sense an actual entity is completely concrete, with no potential to be something other than itself. It is what it is. It is a source of potentiality for the creation of other actual entities, of which it may be said to be a part cause. Likewise it is the concretion or realization of potentialities of other actual entities which are its partial causes.
  • Causation between actual entities is essential to their actuality. Consequently, for Whitehead, each actual entity has its distinct and definite extension in physical Minkowski space, and so is uniquely identifiable. A description in Minkowski space supports descriptions in time and space for particular observers.
  • It is part of the aim of the philosophy of such an ontology as Whitehead's that the actual entities should be all alike, qua actual entities; they should all satisfy a single definite set of well stated ontological criteria of actuality.

Whitehead proposed that his notion of an occasion of experience satisfies the criteria for its status as the philosophically preferred definition of an actual entity. From a purely logical point of view, each occasion of experience has in full measure the characters of both objective and subjective reality. Subjectivity and objectivity refer to different aspects of an occasion of experience, and in no way do they exclude each other.[38]

Examples of other philosophical proposals or candidates as actual entities, in this view, are Aristotle's 'substances', Leibniz' monads, and Descartes ′res verae' , and the more modern 'states of affairs'. Aristotle's substances, such as Socrates, have behind them as more fundamental the 'primary substances', and in this sense do not satisfy Whitehead's criteria. Whitehead is not happy with Leibniz' monads as actual entities because they are "windowless" and do not cause each other. 'States of affairs' are often not closely defined, often without specific mention of extension in physical Minkowski space; they are therefore not necessarily processes of becoming, but may be as their name suggests, simply static states in some sense. States of affairs are contingent on particulars, and therefore have something behind them.[39] One summary of the Whiteheadian actual entity is that it is a process of becoming. Another summary, referring to its causal linkage to other actual entities, is that it is "all window", in contrast with Leibniz' windowless monads.

This view allows philosophical entities other than actual entities to really exist, but not as fundamentally and primarily factual or causally efficacious; they have existence as abstractions, with reality only derived from their reference to actual entities. A Whiteheadian actual entity has a unique and completely definite place and time. Whiteheadian abstractions are not so tightly defined in time and place, and in the extreme, some are timeless and placeless, or 'eternal' entities. All abstractions have logical or conceptual rather than efficacious existence; their lack of definite time does not make them unreal if they refer to actual entities. Whitehead calls this 'the ontological principle'.

Microcosmic ontology

There is an established and long philosophical history of the concept of atoms as microscopic physical objects. They are far too small to be visible to the naked eye. It was as recent as the nineteenth century that precise estimates of the sizes of putative physical atoms began to become plausible. Almost direct empirical observation of atomic effects was due to the theoretical investigation of Brownian motion by Albert Einstein in the very early twentieth century. But even then, the real existence of atoms was debated by some. Such debate might be labeled 'microcosmic ontology'. Here the word 'microcosm' is used to indicate a physical world of small entities, such as for example atoms.

Subatomic particles are usually considered to be much smaller than atoms. Their real or actual existence may be very difficult to demonstrate empirically.[40] A distinction is sometimes drawn between actual and virtual subatomic particles. Reasonably, one may ask, in what sense, if any, do virtual particles exist as physical entities? For atomic and subatomic particles, difficult questions arise, such as do they possess a precise position, or a precise momentum? A question that continues to be controversial is 'to what kind of physical thing, if any, does the quantum mechanical wave function refer?'.[8]

Ontological argument

In the Western Christian tradition, in his 1078 work Proslogion, Anselm of Canterbury proposed what is known as 'the ontological argument' for the existence of God.[lower-roman 2] Anselm defined God as "that than which nothing greater can be thought", and argued that this being must exist in the mind, even in the mind of the person who denies the existence of God. He suggested that, if the greatest possible being exists in the mind, it must also exist in reality. If it only exists in the mind, then an even greater being must be possible—one which exists both in the mind and in reality. Therefore, this greatest possible being must exist in reality. Seventeenth century French philosopher René Descartes deployed a similar argument. Descartes published several variations of his argument, each of which centred on the idea that God's existence is immediately inferable from a "clear and distinct" idea of a supremely perfect being. In the early eighteenth century, Gottfried Leibniz augmented Descartes' ideas in an attempt to prove that a "supremely perfect" being is a coherent concept. Norman Malcolm revived the ontological argument in 1960 when he located a second, stronger ontological argument in Anselm's work; Alvin Plantinga challenged this argument and proposed an alternative, based on modal logic. Attempts have also been made to validate Anselm's proof using an automated theorem prover.

More recently, Kurt Gödel proposed a formal argument for God's existence. Other arguments for God's existence have been advanced, including those made by Islamic philosophers Mulla Sadra and Allama Tabatabai.

Hintikka's locution for existence

Jaakko Hintikka puts the view that a useful explication of the notion of existence is in the words "one can find," implicitly in some world or universe of discourse.[41]

Prominent ontologists

gollark: <@139395104455524352> the max length?
gollark: ¡¿...?!
gollark: Why?
gollark: At best you can sell low-priced stuff to the owners of megashops.
gollark: It's hard due to sheer inequality.

See also

References

Notes

  1. ὄν is the present-tense participle of the verb εἰμί (eimí, 'to be' or 'I am').
  2. "There are three main periods in the history of ontological arguments. The first was in 11th century, when St. Anselm of Canterbury came up with the first ontological argument." Szatkowski, Miroslaw, ed. 2012. Ontological Proofs Today. Ontos Verlag. p. 22.

Citations

  1. Ontology.” Merriam-Webster Dictionary. Retrieved 3 May 2020.
  2. "ontology". Online Etymology Dictionary.
  3. εἰμί. Liddell, Henry George; Scott, Robert; A Greek–English Lexicon at the Perseus Project
  4. "ontology." Oxford Advanced Learner's Dictionary. Oxford Dictionaries (2008)
  5. Harvey, Gideon. 1663. Archelogia philosophica nova, or, New Principles of Philosophy. Containing Philosophy in General, Metaphysicks or Ontology, Dynamilogy or a Discourse of Power, Religio Philosophi or Natural Theology, Physicks or Natural philosophy. London: J.H.
  6. Devaux, Michaël, and Marco Lamanna. 2009. "The Rise and Early History of the Term Ontology (1606–1730)." Quaestio 9:173–208. pp. 197–98.
  7. Griswold, Charles L. (2001). Platonic Writings/Platonic Readings. Penn State Press. p. 237. ISBN 978-0-271-02137-9.
  8. Isham, C. J. 1995. Lectures on Quantum Theory: Mathematical and Structural Foundations. London: Imperial College Press. ISBN 1-86094-000-5. pp. 63–7.
  9. Cook, H. P., trans. 1983. Categories Vol. 1, by Aristotle. Loeb Classical Library. Cambridge, MA: Harvard University Press.
  10. Vesselin Petrov (2011). "Chapter VI: Process ontology in the context of applied philosophy". In Vesselin Petrov (ed.). Ontological Landscapes: Recent Thought on Conceptual Interfaces Between Science and Philosophy. Ontos Verlag. pp. 137ff. ISBN 978-3-86838-107-8.
  11. Larson, G. J., R. S. Bhattacharya, and K. Potter, eds. 2014. "Samkhya." Pp. 3–11 in The Encyclopedia of Indian Philosophies 4. Princeton University Press. ISBN 978-0-691-60441-1.
  12. Graham, Daniel W. 2006. Explaining the Cosmos: The Ionian Tradition of Scientific Philosophy. Princeton: Princeton University Press. ISBN 9780691125404. Lay summary.
  13. "Ancient Atomism (Stanford Encyclopedia of Philosophy)". Plato.stanford.edu. Retrieved 2010-02-21.
  14. Aristotle, Metaphysics, I, 4, 985
  15. Lawson, Clive; Latsis, John Spiro; Martins, Nuno, eds. (2007). Contributions to Social Ontology. Routledge Studies in Critical Realism. London: Routledge (published 2013). ISBN 9781136016066. Retrieved 3 Mar 2019.
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  20. Zalta, Edward N. 2009. "Fictional truth, objects, and characters." Pp. 267–69 in A Companion to Metaphysics (2nd ed.), edited by J. Kim G. S. Rosenkrantz, and E. Sosa. Chichester, UK: Wiley–Blackwell. ISBN 9781405152983. p. 267.
  21. Thomasson, Amie L. (2009). "Fictional Entities" (PDF). In Kim, Jaegwon; Sosa, Ernest; Rosenkrantz, Gary S. (eds.). A Companion to Metaphysics (Second ed.). Wiley-Blackwell.
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  23. Stock, G. (2009). Francis Herbert Bradley, pp. 155–158 in A Companion to Metaphysics, ed. Kim, J., Rosenkrantz, G.S., Sosa, E., Wiley–Blackwell, Chichester UK, 2nd edition, ISBN 9781405152983, p. 157.
  24. Kroon, Fred; Voltolini, Alberto (2018). "Fictional Entities". In Zalta, Edward N. (ed.). The Stanford Encyclopedia of Philosophy.
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  35. Hirsch, Eli. 2011. "Quantifier variance and realism." Pp. 68–95 in Quantifier Variance and Realism: Essays in Metaontology. New York: Oxford University Press. ISBN 978-0-19-973211-1. First published as "Quantifier variance and realism."
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