Abstract object theory (AOT) is a branch of

metaphysics Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of ...

regarding

abstract object In philosophy and the arts, a fundamental distinction exists between abstract and concrete entities. While there is no universally accepted definition, common examples illustrate the difference: numbers, sets, and ideas are typically classif ...

s. Originally devised by metaphysician

Edward Zalta Edward Nouri Zalta (; born March 16, 1952) is an American philosopher who is a senior research scholar at the Center for the Study of Language and Information at Stanford University. He received his Bachelor of Arts, BA from Rice University in 1 ...

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 and his student Ernst Mally. On Zalta's account, there are two modes of predication: some objects (the ordinary

concrete Concrete is a composite material composed of aggregate bound together with a fluid cement that cures to a solid over time. It is the second-most-used substance (after water), the most–widely used building material, and the most-manufactur ...

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. 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 Ontology is the philosophical study of existence, being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of realit ...

. 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 Guise ( , ; ) is a commune in the Aisne department in Hauts-de-France in northern France. The city was the birthplace of the noble family of Guise, Dukes of Guise, who later became Princes of Joinville. Population Sights The remains of t ...

, Alan McMichael's paradox, and Daniel Kirchner's paradox) do not arise within it. AOT employs restricted

abstraction Abstraction is a process where general rules and concepts are derived from the use and classifying of specific examples, literal (reality, real or Abstract and concrete, concrete) signifiers, first principles, or other methods. "An abstraction" ...

schemata to avoid such paradoxes. In 2007, Zalta and

Branden Fitelson Branden Fitelson (; born August 17, 1969) is an American philosopher and Distinguished Professor of Philosophy at Northeastern University. He is known for his expertise on formal epistemology and philosophy of science Philosophy of science ...

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.

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Overview

See also

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Further reading