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.

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 "non-existent 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]