Abstract object theory explained

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

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 "nonexistent 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

References

Further reading

Notes and References

  1. Web site: The Theory of Abstract Objects . Zalta . Edward N. . 2004 . The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University. July 18, 2020.
  2. An Introduction to a Theory of Abstract Objects (1981). ScholarWorks@UMass Amherst. 2009. 10.7275/f32y-fm90 . July 21, 2020 . Zalta . Edward N. .
  3. nonexistent-objects . Nonexistent Objects . Maria . Reicher . 2014 .
  4. [Dale Jacquette]
  5. [Alexius Meinong]
  6. Zalta (1983:xi).
  7. [Ernst Mally]
  8. Zalta (1983:33).
  9. Zalta (1983:36).
  10. Zalta (1983:35).
  11. [Romane Clark]
  12. [William J. Rapaport]
  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, 2017.
  16. Zalta (2024:253): "Some non-core λ-expressions, such as those leading to the Clark/Boolos, McMichael/Boolos, and Kirchner paradoxes, will be provably empty."
  17. Zalta (1983:158).
  18. [Edward N. Zalta]
  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.

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