Abstract object theory (AOT) is a branch of

metaphysics Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...

regarding

abstract object In metaphysics, the distinction between abstract and concrete refers to a divide between two types of entities. Many philosophers hold that this difference has fundamental metaphysical significance. Examples of concrete objects include plants, hum ...

s. 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 Dale Jacquette, ''Meinongian Logic: The Semantics of Existence and Nonexistence'', Walter de Gruyter, 1996, p. 17. influenced by the contributions of

Alexius Meinong Alexius Meinong Ritter von Handschuchsheim (17 July 1853 – 27 November 1920) was an Austrian philosopher, a realist known for his unique ontology. He also made contributions to philosophy of mind and theory of value. Life Alexius Meinon ...

Zalta (1983:xi). and his student Ernst Mally. On Zalta's account, there are two modes of

predication Predicate or predication may refer to: * Predicate (grammar), in linguistics * Predication (philosophy) * several closely related uses in mathematics and formal logic: ** Predicate (mathematical logic) ** Propositional function ** Finitary relatio ...

: some objects (the ordinary

concrete Concrete is a composite material composed of fine and coarse aggregate bonded together with a fluid cement (cement paste) that hardens (cures) over time. Concrete is the second-most-used substance in the world after water, and is the most ...

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 Round Square is an international network of schools, based on the educational concepts of Kurt Hahn, and named after a distinctive building at Gordonstoun. Founded by a group of seven schools in the late 1960s, by 1996 it had grown to 20 membe ...

, 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 In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality. Ontology addresses questions like how entities are grouped into categories and which of these entities ...

. 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 Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or " concrete") signifiers, first principles, or other methods. "An a ...

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 In computer science, in particular in knowledge representation and reasoning and metalogic, the area of automated reasoning is dedicated to understanding different aspects of reasoning. The study of automated reasoning helps produce computer progr ...

environment.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.

Notes

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, September 6, 2022.

Overview

See also

Notes

References

Further reading