Abstract object theory
Abstract object theory (AOT) is a branch of
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
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
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
- 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
- ^ 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.
- .
- ^ 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, 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, p. 33.
- ^ Zalta 1983, p. 36.
- ^ Zalta 1983, p. 35.
- JSTOR 2214691.
- ^ Rapaport, William J. (1978). "Meinongian Theories and a Russellian Paradox". Noûs. 12 (2): 153–180.
- ISBN 978-1-61451-663-7.
- ISSN 0022-3611.
- ^ Daniel Kirchner, "Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL", Archive of Formal Proofs, 2017.
- ^ 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."
- ^ Zalta 1983, p. 158.
- 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
- 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: OCLC 1129207159.
