// Workers AI · dad joke modeWhat did abstract object theory say to its date? You're always on my mind.
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
[edit]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—e.g., numbers, possible worlds,[7] and so-called "nonexistent objects" such as the round square and Meinong's "mountain made 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 significant 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
[edit]Notes
[edit]- ↑ 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.
- ↑ 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.
- ↑ Dale Jacquette, Meinongian Logic: The Semantics of Existence and Nonexistence, Walter de Gruyter, 1996, p. 17.
- ↑ 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.
- 1 2 Zalta 1983, p. xi.
- ↑ Mally, Ernst (1912). Gegenstandstheoretische Grundlagen der Logik und Logistik [Object-theoretic Foundations for Logics and Logistics] (PDF) (in German). Leipzig: Barth. §§33 and 39.
- ↑ Zalta 1983, pp. 78–84.
- ↑ Zalta 1983, p. 33.
- ↑ Zalta 1983, p. 36.
- ↑ Zalta 1983, p. 35.
- ↑ Clark, Romane (1978). "Not Every Object of Thought Has Being: A Paradox in Naive Predication Theory". Noûs. 12 (2): 181–188. JSTOR 2214691.
- ↑ Rapaport, William J. (1978). "Meinongian Theories and a Russellian Paradox". Noûs. 12 (2): 153–180.
- ↑ 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.
- ↑ 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.
- ↑ Daniel Kirchner, "Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL", Archive of Formal Proofs, 2017.
- ↑ Zalta 2026, p. 293: "Some non-core λ-expressions, such as those leading to the Clark/Boolos, McMichael/Boolos, and Kirchner paradoxes, will be provably empty."
- ↑ Zalta 1983, p. 158.
- ↑ 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.
- ↑ 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
[edit]- 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 15, 2026). Principia Logico-Metaphysica (PDF). Center for the Study of Language and Information, Stanford University.
Further reading
[edit]- 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.
External links
[edit]- José L. Falguera and Concha Martínez-Vidal; based on earlier work by Gideon Rosen (August 21, 2025). "Abstract Objects". Stanford Encyclopedia of Philosophy. Retrieved August 23, 2025.
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