Abstract object theory

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Not to be confused with Object theory.
For the general concept of objecthood in philosophy, see Object (philosophy).

Abstract object theory (AOT) is a branch of metaphysics regarding abstract objects.[1] Originally devised by metaphysician Edward Zalta in 1981,[2] the theory was an expansion of mathematical Platonism.

Overview[]

See also: Dual copula strategy

Abstract Objects: An Introduction to Axiomatic Metaphysics (1983) is the title of a publication by Edward Zalta that outlines abstract object theory.

AOT is a dual predication approach (also known as "dual copula strategy") to abstract objects[3][4] influenced by the contributions of Alexius Meinong[5][6] and his student Ernst Mally.[7][6] On Zalta's account, there are two modes of predication: some objects (the ordinary concrete ones around us, like tables and chairs) exemplify properties, while others (abstract objects like numbers, and what others would call "non-existent objects", like the round square, and the mountain made entirely of gold) merely encode them.[8] While the objects that exemplify properties are discovered through traditional empirical means, a simple set of axioms allows us to know about objects that encode properties.[9] For every set of properties, there is exactly one object that encodes exactly that set of properties and no others.[10] This allows for a formalized ontology.

A notable feature of AOT is that several notable paradoxes in naive predication theory (namely Romane Clark's paradox undermining the earliest version of Héctor-Neri Castañeda's guise theory,[11][12][13] Alan McMichael's paradox,[14] and Daniel Kirchner's paradox)[15] do not arise within it.[16] AOT employs restricted abstraction schemata to avoid such paradoxes.[17]

In 2007, Zalta and Branden Fitelson introduced the term computational metaphysics to describe the implementation and investigation of formal, axiomatic metaphysics in an automated reasoning environment.[18][19]

See also[]

Notes[]

  1. ^ Zalta, Edward N. (2004). "The Theory of Abstract Objects". The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University. Retrieved July 18, 2020.
  2. ^ "An Introduction to a Theory of Abstract Objects (1981)". ScholarWorks@UMass Amherst. 2009. Retrieved July 21, 2020.
  3. ^ Reicher, Maria (2014). "Nonexistent Objects". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
  4. ^ Dale Jacquette, Meinongian Logic: The Semantics of Existence and Nonexistence, Walter de Gruyter, 1996, p. 17.
  5. ^ Alexius Meinong, "Über Gegenstandstheorie" ("The Theory of Objects"), in Alexius Meinong, ed. (1904). Untersuchungen zur Gegenstandstheorie und Psychologie (Investigations in Theory of Objects and Psychology), Leipzig: Barth, pp. 1–51.
  6. ^ a b Zalta (1983:xi).
  7. ^ Ernst Mally (1912), Gegenstandstheoretische Grundlagen der Logik und Logistik (Object-theoretic Foundations for Logics and Logistics), Leipzig: Barth, §§33 and 39.
  8. ^ Zalta (1983:33).
  9. ^ Zalta (1983:36).
  10. ^ Zalta (1983:35).
  11. ^ Romane Clark, "Not Every Object of Thought has Being: A Paradox in Naive Predication Theory", Noûs 12(2) (1978), pp. 181–188.
  12. ^ William J. Rapaport, "Meinongian Theories and a Russellian Paradox", Noûs 12(2) (1978), pp. 153–80.
  13. ^ Adriano Palma, ed. (2014). Castañeda and his Guises: Essays on the Work of Hector-Neri Castañeda. Boston/Berlin: Walter de Gruyter, pp. 67–82, esp. 72.
  14. ^ Alan McMichael and Edward N. Zalta, "An Alternative Theory of Nonexistent Objects", Journal of Philosophical Logic 9 (1980): 297–313, esp. 313 n. 15.
  15. ^ Daniel Kirchner, "Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL", Archive of Formal Proofs, 2020[2017].
  16. ^ Zalta (2021:238): "some λ-expressions ... such as those leading to the Clark/Boolos, McMichael/Boolos, and Kirchner paradoxes, are provably empty."
  17. ^ Zalta (1983:158).
  18. ^ Edward N. Zalta and Branden Fitelson, "Steps Toward a Computational Metaphysics", Journal of Philosophical Logic 36(2) (April 2007): 227–247.
  19. ^ Jesse Alama, Paul E. Oppenheimer, Edward N. Zalta, "Automating Leibniz's Theory of Concepts", in A. Felty and A. Middeldorp (eds.), Automated Deduction – CADE 25: Proceedings of the 25th International Conference on Automated Deduction (Lecture Notes in Artificial Intelligence: Volume 9195), Berlin: Springer, 2015, pp. 73–97.

References[]

Further reading[]

  • Edward N. Zalta, "Typed Object Theory", in José L. Falguera and Concha Martínez-Vidal (eds.), Abstract Objects: For and Against, Springer (Synthese Library), 2020.
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