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
Notes
- ^ 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. (2009). An Introduction to a Theory of Abstract Objects (1981) (Thesis). ScholarWorks@ UMass Amherst. doi: 10.7275/f32y-fm90. Retrieved July 21, 2020.
- ^ Reicher, Maria (2014). "Nonexistent Objects". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
- ^ 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.
- ^ a b Zalta (1983:xi).
- ^ Ernst Mally (1912), Gegenstandstheoretische Grundlagen der Logik und Logistik (Object-theoretic Foundations for Logics and Logistics), Leipzig: Barth, §§33 and 39.
- ^ Zalta (1983:33).
- ^ Zalta (1983:36).
- ^ Zalta (1983:35).
- ^ Romane Clark, "Not Every Object of Thought Has Being: A Paradox in Naive Predication Theory", Noûs 12(2) (1978), pp. 181–188.
- ^ William J. Rapaport, "Meinongian Theories and a Russellian Paradox", Noûs 12(2) (1978), pp. 153–80.
- ^ 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.
- ^ Alan McMichael and Edward N. Zalta, "An Alternative Theory of Nonexistent Objects", Journal of Philosophical Logic 9 (1980): 297–313, esp. 313 n. 15.
- ^ Daniel Kirchner, "Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL", Archive of Formal Proofs, 2017.
- ^ Zalta (2024:240): "Some non-core λ-expressions, such as those leading to the Clark/Boolos, McMichael/Boolos, and Kirchner paradoxes, will be provably empty."
- ^ Zalta (1983:158).
- ^ Edward N. Zalta and Branden Fitelson, "Steps Toward a Computational Metaphysics", Journal of Philosophical Logic 36(2) (April 2007): 227–247.
- ^ 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
- Edward N. Zalta, Abstract Objects: An Introduction to Axiomatic Metaphysics, Dordrecht: D. Reidel, 1983.
- Edward N. Zalta, Intensional Logic and the Metaphysics of Intentionality, Cambridge, MA: The MIT Press/Bradford Books, 1988.
- Edward N. Zalta, Principia Metaphysica, Center for the Study of Language and Information, Stanford University, February 10, 1999.
- Daniel Kirchner, Christoph Benzmüller, Edward N. Zalta, "Mechanizing Principia Logico-Metaphysica in Functional Type Theory", Review of Symbolic Logic 13(1) (March 2020): 206–18.
- Edward N. Zalta, Principia Logico-Metaphysica, Center for the Study of Language and Information, Stanford University, February 6, 2024.
Further reading
- Daniel Kirchner, Computer-Verified Foundations of Metaphysics and an Ontology of Natural Numbers in Isabelle/HOL, PhD thesis, Free University of Berlin, 2021.
- Edward N. Zalta, "Typed Object Theory", in José L. Falguera and Concha Martínez-Vidal (eds.), Abstract Objects: For and Against, Springer (Synthese Library), 2020.
