Abstract object theory
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 to abstract objects.[3][4] 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 "non-existent objects", like the round square, and the mountain made entirely of gold) merely encode them.[5] 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.[6] For every set of properties, there is exactly one object that encodes exactly that set of properties and no others.[7] This allows for a formalized ontology.
A notable feature of AOT is that Romane Clark's paradox (a paradox in naive predication theory undermining the earliest version of Héctor-Neri Castañeda's guise theory)[8][9][10] and Alan McMichael's paradox (another paradox in naive predication theory)[11] do not arise within it (AOT employs restricted abstraction schemata to avoid these paradoxes).[12]
In 2007, Zalta and Branden Fitelson have introduced the term computational metaphysics to describe the implementation and investigation of formal, axiomatic metaphysics in an automated reasoning environment.[13]
See also
Precursors
Related concepts
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.
- ^ "An Introduction to a Theory of Abstract Objects (1981)". ScholarWorks@UMass Amherst. 2009. 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.
- ^ 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.
- ^ Zalta (1983:158).
- ^ Edward N. Zalta and Branden Fitelson, "Steps Toward a Computational Metaphysics",Journal of Philosophical Logic 36(2) (April 2007): 227–247.
- ^ a b Zalta (1983:xi).
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, 1996.
Further reading
- Edward N. Zalta, "Typed Object Theory", in José L. Falguera and Concha Martínez-Vidal (eds.), Abstract Objects: For and Against, Springer (Synthese Library), 2020.
- Daniel Kirchner, Christoph Benzmüller, Edward N. Zalta, "Mechanizing Principia Logica-Metaphysica in Functional Type Theory", Review of Symbolic Logic 13(1) (March 2020): 206–18.
