Abstract Objects

Edited by Sam Cowling (Denison University)
About this topic

Abstract entities such as numbers, propositions, and universals are usually contrasted with concrete entities such as tables, tadpoles, and quasars. While concrete entities are typically held to exist contingently, stand in causal relations, and occupy space and time, abstract entities are usually (though controversially) held to be necessary existents that are causally inert and "outside" of space and time. According to platonists, there are at least some abstract entities, but, given the peculiar metaphysical status of abstract entities, concerns arise about how we might come to know or refer to them. Further controversies surround the nature of the abstract-concrete distinction, the essential features of abstract entities, and the plausibility of nominalism, according to which there are no abstract entities.

Key works The literature on abstract entities is vast and closely connected to debates in the philosophy of mathematics, philosophy of science, philosophy of language, and epistemology. Burgess & Rosen 1997 is the leading survey of nominalist views regarding mathematical entities and includes an excellent survey of the nominalist-platonist debate. Two papers by Paul Benacerraf—Benacerraf 1973 and Benacerraf 1965—are hugely influential. Notable recent work regarding nominalist options in the philosophy of mathematics and other domains include Field 1980, Azzouni 2004, Leng 2010, and Hofweber 2016.  Guides to the specialist literature regarding specific kinds of abstract entities can be found in other entries, but some useful starting points are as follows. On possible worlds, see Divers 2002. On types, see Wetzel 2009. On propositions, see King et al 2014. On fictional entities, see Thomasson 1999.
Introductions Rosen 2008 and Szabó 2003 are useful survey articles of the issues raised by abstract entities. There are also a host of good entries in the Stanford Encyclopedia of Philosophy on topics related to abstract entities. Balaguer 2008, Linnebo 2009, and Rodriguez-Pereyra 2008 are excellent places to start. Armstrong 1989 is a leading introduction to the metaphysics of properties, which are usually held to be abstract entities. MacBride 1999 and MacBride 2003 survey fictionalist and neo-Fregean approaches to abstract mathematical entities. General introductions to metaphysics with useful sections on abstract entities include Jubien 1997 and Loux 1998. Cowling 2017 is a fairly comprehensive and accessible discussion of the metaphysics of abstract entities.
Related categories
Properties* (2,730 | 109)
Ontology of Music* (506 | 324)
Ontology of Mathematics* (2,221 | 304)
Words* (536)
The Nature of Sets* (234 | 96)
Numbers* (343)
See also:

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Material to categorize
  1. Not Necessarily.Raziel Abelson - 1961 - Philosophical Review 70 (1):67-84.
  2. A Defense of Naturalism.Keith Augustine - 2001 - Dissertation, University of Maryland, College Park
    The first part of this essay discusses what naturalism in the philosophy of religion should entail for one's ontology, considers various proposed criteria for categorizing something as natural, uses an analysis of these proposed criteria to develop theoretical criteria for both the natural and nonnatural, and develops a set of criteria for identifying a potentially supernatural event in practice. The second part of the essay presents a persuasive empirical case for naturalism based on the lack of uncontroversial evidence for any (...)
  3. Fisk on Capacities and Natures.Bruce Aune - 1970 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1970:83 - 87.
  4. Why Deflationary Nominalists Shouldn’T Be Agnostics.Jody Azzouni - 2015 - Philosophical Studies 172 (5):1143-1161.
    A feature of agnostic views—views that officially express ignorance about the existence of something —is that they are widely perceived to be epistemically more cautious than views that are committed to the entities in question. This is often seen as giving agnostics a debating advantage: all things being equal, fence-sitters have smaller argumentative burdens. Otávio Bueno argues in this way for what he calls “agnostic nominalism,” the view that we don’t know whether ontologically-independent Platonic objects exist. I show that agnostic (...)
  5. II—Jody Azzouni: Singular Thoughts.Jody Azzouni - 2011 - Aristotelian Society Supplementary Volume 85 (1):45-61.
  6. Between the Concretist and Abstract Concepts of Being.Bogdan Bakies - 1982 - Roczniki Filozoficzne 30 (1):91.
  7. Collapse, Plurals and Sets.Eduardo Alejandro Barrio - 2014 - Principia: An International Journal of Epistemology 18 (3):419.
  8. Realism and Nominalism Revisited.J. D. Bastable - 1955 - Philosophical Studies 5:164-165.
  9. Exemplification Postulates.Robert W. Beard - 1968 - Philosophical Studies 19 (3):33 - 37.
  10. The Epistemology of Abstract Objects.D. A. Bell & W. D. Hart - 1979 - Aristotelian Society Supplementary Volume 53 (1):135-166.
  11. Comments on Maddy and Tymoczko.Paul Benacerraf - 1984 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:476 - 485.
  12. Mathematics and Poetry.Ermanno Bencivenga - 2006 - Inquiry: An Interdisciplinary Journal of Philosophy 49 (2):158 – 169.
    Since Descartes, mathematics has been dominated by a reductionist tendency, whose success would seem to promise greater certainty: the fewer basic objects mathematics can be understood as dealing with, and the fewer principles one is forced to assume about these objects, the easier it will be to establish a secure foundation for it. But this tendency has had the effect of sharply limiting the expressive power of mathematics, in a way that is made especially apparent by its disappointing applications to (...)
  13. Universals as Sortals in the Categories.Hugh H. Benson - 1988 - Pacific Philosophical Quarterly 69 (4):282-306.
  14. Frege's Hidden Nominalism.Gustav Bergmann - 1958 - Philosophical Review 67 (4):437-459.
  15. The Notion of Structure.S. Bernard Lonergan - 1996 - Method 14 (2):117-132.
  16. Solution of a Mathematical Problem in the Theory of Heredity.S. N. Bernshtein - 1976 - Social Science Information 15 (4-5):797-821.
  17. Readymades, Monochromes, Etc.: Nominalism and the Paradox of Modernism.J. M. Bernstein - 2002 - Diacritics 32 (1):83-100.
  18. Abstract.Alexander U. Bertland - 1996 - New Vico Studies 14:96-99.
  19. Nominalism and Inner Experience.Peter Bieri - 1982 - The Monist 65 (January):68-87.
  20. The Reality of Numbers.John Bigelow - 1988 - Mind 100 (2):283-287.
  21. Semantic Nominalism.John Bigelow - 1981 - Australasian Journal of Philosophy 59 (4):403 – 421.
  22. Resemblance Nominalism and Counterparts.A. Bird - 2003 - Analysis 63 (3):221-228.
  23. Otto Heyn Als Nominalist Dissertation.Katharina Biske - 1930 - Druckerei-Genossenschaft.
  24. The Theory of Semantic Categories and the Problem of the Typology of Universals.Bogdan Bjankov - 1983 - der 16. Weltkongress Für Philosophie 2:398-405.
    According to the basic idea of the theory of semantic categories the huge variety of expressions could be reduced to three basic classes, called basic semantic categories: names, statements, and functors. On this basis abstract objects or universale can be reduced also to three basic typest abstract objects-terms, abstract objects-statements, and abstract objects-operators. The so-called auxilliary signs, in particular brackets in formalized languages, fulfil a certain, structural function and, on this ground, can be numbered to the type of abstract objects-operators (...)
  25. 3 Mathematical Objects and Identity.Patricia Blanchette - 2007 - In Michael O'Rourke Corey Washington (ed.), Situating Semantics: Essays on the Philosophy of John Perry. pp. 73.
  26. Medieval Currencies : Nominalism and Art.C. D. Blanton - 2010 - In Andrew Cole & D. Vance Smith (eds.), The Legitimacy of the Middle Ages: On the Unwritten History of Theory. Duke University Press.
  27. The Nominalist Argument of the New Essays.Martha Brandt Bolton - 1996 - The Leibniz Review 6:1-24.
  28. Mathematics and Metalogic.Daniel Bonevac - 1984 - The Monist 67 (1):56-71.
    In this paper I shall attempt to outline a nominalistic theory of mathematical truth. I call my theory nominalistic because it avoids a real (see [4]) ontological commitment to abstract entities. Traditionally, nominalists have found it difficult to justify any reference to infinite collections in mathematics. Even those who have tried to do so have typically restricted themselves to predicative and, thus, denumerable realms. I Indeed, many have linked impredicative definitions to platonism; nominalists have tended to agree with Weyl that (...)
  29. Frege's Theorem and the Peano Postulates.George Boolos - 1995 - Bulletin of Symbolic Logic 1 (3):317-326.
  30. Whence the Contradiction?George Boolos - 1993 - Aristotelian Society Supplementary Volume 67:211--233.
  31. P. 54-72.(1985)'Nominalist Platonism'.Reprinted Boolos - 1998 - Philosophical Review 94:327-44.
  32. Generale E Particolare.Andrea Borghini - unknown
    Is it true that some entities are general, while others are particular? Ramsey famously challenged this distinction, and more recently Fraser McBride has revived the challenge. In this paper I argue that there are at least five substantial distinctions among entities, and that the distinction between general and particular entities should be made to correspond to one or more of those substantial distinctions.
  33. O Conceito de Descobrimento.Gerd A. Bornheim - 1998
  34. Against Angles and the Fregean-Cantorian Theory of Number.Andrew Boucher - unknown
    How-many numbers, such as 2 and 1000, relate or are capable of expressing the size of a group or set. Both Cantor and Frege analyzed how-many number in terms of one-to-one correspondence between two sets. That is to say, one arrived at numbers by either abstracting from the concept of correspondence, in the case of Cantor, or by using it to provide an out-and-out definition, in the case of Frege.
  35. Structural, Electronic, Optical and Elastic Properties of the Complex K2PtCl6-Structure hydridesARuH6: First-Principles Study. [REVIEW]O. Boudrifa, A. Bouhemadou, Ş Uğur, R. Khenata, S. Bin-Omran & Y. Al-Douri - forthcoming - Philosophical Magazine:1-34.
  36. On Zalta's Notion of Encoding in Conceivability Contexts.Sacha Bourgeois-Gironde - 2004 - Metaphysica.
    Zalta's notion of encoding which lies at the core of his theory of abstract objects is refined so that it can capture cognitive dynamic phenomena such as multiple object-tracking in particular intentional contexts; namely hypothetical stipulation concerning abstract objects and counter-essential conceivability about ordinary ones. Zalta's Modal Axiom of Encoding is weakened and the notion of 'quasi-encoding' is spelt out.
  37. Did Plato Believe in Immanent Universals?George Mcmillan Bowles - 1970 - Dissertation, Stanford University
  38. Wessel Gansfort Between Albertism and Nominalism.Hag Braakhuis - 1993 - In Fokke Akkerman, Gerda C. Huisman & Arie Johan Vanderjagt (eds.), Wessel Gansfort (1419-1489) and Northern Humanism. E.J. Brill. pp. 40--30.
  39. Nonlinearities in the Undercooled Properties of Ti39.5Zr39.5Ni21.R. C. Bradshaw, A. D. Arsenault, R. W. Hyers, J. R. Rogers, T. J. Rathz, G. W. Lee‖, A. K. Gangopadhyay & K. F. Kelton - 2006 - Philosophical Magazine 86 (3-5):341-347.
  40. The Languages of Realism and Nominalism.Richard B. Brandt - 1956 - Philosophy and Phenomenological Research 17 (4):516-535.
  41. Exemplification of Predicates.Ann Ferguson Brentlinger - 1970 - Noûs 4 (3):285-293.
  42. The Stoic View on Universals.Ada Bronowski - 2007 - Documenti E Studi Sulla Tradizione Filosofica Medievale 18:71-87.
  43. Abstract Objects Bob Hale Oxford: Blackwell, 1987. Pp. 282. $75.00. [REVIEW]James Robert Brown - 1988 - Dialogue 27 (4):729-.
  44. Bob Hale, "Abstract Objects". [REVIEW]James Robert Brown - 1988 - Dialogue 27 (4):729.
  45. Frege on Knowing the Foundation.Tyler Burge - 1998 - Mind 107 (426):305-347.
    The paper scrutinizes Frege's Euclideanism - his view of arithmetic and geometry as resting on a small number of self-evident axioms from which non-self-evident theorems can be proved. Frege's notions of self-evidence and axiom are discussed in some detail. Elements in Frege's position that are in apparent tension with his Euclideanism are considered - his introduction of axioms in The Basic Laws of Arithmetic through argument, his fallibilism about mathematical understanding, and his view that understanding is closely associated with inferential (...)
  46. Abstract Objects.John P. Burgess & Bob Hale - 1992 - Philosophical Review 101 (2):414.
  47. Attaining to the Abstract.Edmund C. Burke - 1929 - Modern Schoolman 6 (1):8-9.
  48. The Adequacy of Resemblance Nominalism About Perfect Naturalness.Ralf Busse - 2016 - Philosophy and Phenomenological Research:443-469.
    Resemblance Nominalism About Perfect Naturalness is the view that perfect naturalness of classes is best defined by a conceptual primitive of resemblance between particulars. The adequacy of RNPN is defended by outlining nominalism as the strictly anti-constitutive view that the particulars’ being the fundamental ways they are is not constituted by anything further, supplying a doubly plural contrastive and graded resemblance predicate that allows for a definition of perfect naturalness on an actualist basis, and proving a representation and a uniqueness (...)
  49. Resemblance and Identity: An Examination of the Problem of Universals.Panayot Butchvarov - 1968 - Philosophical Review 77 (3):386-389.
  50. The Uses of Argument. [REVIEW]L. C. - 1958 - Review of Metaphysics 11 (4):697-697.
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