Abstract object theory

Abstract object theory (AOT) is a branch of metaphysics regarding abstract objects. Originally devised by metaphysician Edward Zalta in 1981, 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 influenced by the contributions of Alexius Meinong and his student Ernst Mally. 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. 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. For every set of properties, there is exactly one object that encodes exactly that set of properties and no others. 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, Alan McMichael's paradox, and Daniel Kirchner's paradox) do not arise within it. AOT employs restricted abstraction schemata to avoid such paradoxes.

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.

See also

• Abstract and concrete
• Abstractionism (philosophy of mathematics)
• Algebra of concepts
• Mathematical universe hypothesis
• Modal Meinongianism
• Modal neo-logicism
• Object of the mind
• Objective precision

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. Zalta, Edward N. (1981). An Introduction to a Theory of Abstract Objects (Thesis). UMass Amherst. doi:10.7275/f32y-fm90. hdl:20.500.14394/12282.
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. Zalta 1983, p. xi.
6. Mally, Ernst (1912). Gegenstandstheoretische Grundlagen der Logik und Logistik [Object-theoretic Foundations for Logics and Logistics] (PDF) (in German). Leipzig: Barth. §§33 and 39.
7. Zalta 1983, p. 33.
8. Zalta 1983, p. 36.
9. Zalta 1983, p. 35.
10. Clark, Romane (1978). "Not Every Object of Thought Has Being: A Paradox in Naive Predication Theory". Noûs. 12 (2): 181–188. JSTOR 2214691.
11. Rapaport, William J. (1978). "Meinongian Theories and a Russellian Paradox". Noûs. 12 (2): 153–180.
12. * Palma, Adriano, ed. (2014). Castañeda and his guises: Essays on the work of Hector-Neri Castañeda. Philosophische Analyse / Philosophical Analysis (in Breton). Boston/Berlin: De Gruyter. pp. 67–82, esp. 72. ISBN 978-1-61451-663-7.
13. McMichael, Alan; Zalta, Edward N. (1980). "An alternative theory of nonexistent objects". Journal of Philosophical Logic. 9 (3): 297–313, esp. p. 313 n. 15. doi:10.1007/BF00248396. ISSN 0022-3611.
14. Daniel Kirchner, "Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL", Archive of Formal Proofs, 2017.
15. Zalta 2024, p. 253: "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. Fitelson, Branden; Zalta, Edward N. (March 14, 2007). "Steps toward a computational metaphysics" (PDF). Journal of Philosophical Logic. 36 (2): 227–247. doi:10.1007/s10992-006-9038-7. ISSN 0022-3611.
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

• Zalta, Edward N. (1983). Abstract Objects: An Introduction to Axiomatic Metaphysics (PDF). Dordrecht: D. Reidel.
• Zalta, Edward N. (1988). Intensional Logic and the Metaphysics of Intentionality (PDF). Cambridge, MA: The MIT Press/Bradford Books.
• Zalta, Edward N. (February 10, 1999). Principia Metaphysica (PDF). Center for the Study of Language and Information, Stanford University.
• Kirchner, Daniel; Benzmüller, Christoph; Zalta, Edward N. (March 2020). "Mechanizing Principia Logico-Metaphysica in Functional Type Theory" (PDF). Review of Symbolic Logic. 13 (1): 206–218.
• Zalta, Edward N. (May 22, 2024). Principia Logico-Metaphysica (PDF). Center for the Study of Language and Information, Stanford University.

Further reading

• Kirchner, Daniel (2021). Computer-Verified Foundations of Metaphysics and an Ontology of Natural Numbers in Isabelle/HOL (PhD thesis). Free University of Berlin.
• Zalta, Edward N. (May 2020). "Typed object theory" (PDF). In Falguera López, José Luis; Martínez-Vidal, Concha (eds.). Abstract objects: For and against. Synthese library: Studies in epistemology, logic, methodology, and philosophy of science. Vol. 422. Cham, Switzerland: Springer Nature. pp. 59–88. doi:10.1007/978-3-030-38242-1_4. ISBN 978-3-030-38241-4. OCLC 1129207159.