Abstract object theory

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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

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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] influenced by the contributions of Alexius Meinong[4][5] and his student Ernst Mally.[6][5] 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.[7] 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.[8] For every set of properties, there is exactly one object that encodes exactly that set of properties and no others.[9] 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,[10][11][12] Alan McMichael's paradox,[13] and Daniel Kirchner's paradox)[14] do not arise within it.[15] AOT employs restricted abstraction schemata to avoid such paradoxes.[16]

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.[17][18]

See also

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Notes

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  3. ^ Dale Jacquette, Meinongian Logic: The Semantics of Existence and Nonexistence, Walter de Gruyter, 1996, p. 17.
  4. ^ 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.
  5. ^ a b Zalta 1983, p. xi.
  6. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  7. ^ Zalta 1983, p. 33.
  8. ^ Zalta 1983, p. 36.
  9. ^ Zalta 1983, p. 35.
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  14. ^ Daniel Kirchner, "Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL", Archive of Formal Proofs, 2017.
  15. ^ Zalta 2025, p. 258: "Some non-core λ-expressions, such as those leading to the Clark/Boolos, McMichael/Boolos, and Kirchner paradoxes, will be provably empty."
  16. ^ Zalta 1983, p. 158.
  17. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  18. ^ 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

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Further reading

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  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
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  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
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