HOME

TheInfoList



OR:

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 consci ...
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 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 BA at Rice University in 1975 and his PhD fr ...
in 1981, the theory was an expansion of
mathematical Platonism The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people' ...
.


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 Meinong ...
Zalta (1983:xi). and his student
Ernst Mally Ernst Mally (; ; 11 October 1879 – 8 March 1944) was an Austrian analytic philosopher, initially affiliated with Alexius Meinong's Graz School of object theory. Mally was one of the founders of deontic logic and is mainly known for his contr ...
. 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 object An object of the mind is an object that exists in the imagination, but which, in the real world, can only be represented or modeled. Some such objects are abstractions, literary concepts, or fictional scenarios. Closely related are intentional ob ...
s", 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 member ...
, 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 ex ...
. 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 Héctor-Neri Castañeda (December 13, 1924 – September 7, 1991) was a Guatemalan- American philosopher and founder of the journal ''Noûs''. Biography Born in San Vicente, Zacapa, Guatemala, he emigrated to the United States in 1948 and studied ...
's
guise theory Guise (; nl, Wieze) 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 ...
, 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 abst ...
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. Bibliography * Edward ...
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 prog ...
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.


See also

*
Abstract and concrete 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 ...
*
Abstractionism (philosophy of mathematics) Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structur ...
*
Algebra of concepts Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathema ...
*
Mathematical universe hypothesis In physics and cosmology, the mathematical universe hypothesis (MUH), also known as the ultimate ensemble theory and struogony (from mathematical structure, Latin: struō), is a speculative " theory of everything" (TOE) proposed by cosmologist Ma ...
*
Modal Meinongianism Noneism, also known as modal Meinongianism (named after Alexius Meinong), is a theory in logic and metaphysics. It holds that some things do not exist. It was first coined by Richard Routley in 1980 and appropriated again in 2005 by Graham Priest. ...
*
Modal neo-logicism In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that — for some coherent meaning of 'logic' — mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or al ...
*
Object of the mind An object of the mind is an object that exists in the imagination, but which, in the real world, can only be represented or modeled. Some such objects are abstractions, literary concepts, or fictional scenarios. Closely related are intentional o ...


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.


Further reading

* Daniel Kirchner
''Computer-Verified Foundations of Metaphysics and an Ontology of Natural Numbers in Isabelle/HOL''
PhD thesis, Free University of Berlin, 2021. * Edward N. Zalta
"Typed Object Theory"
in José L. Falguera and Concha Martínez-Vidal (eds.), ''Abstract Objects: For and Against'', Springer (Synthese Library), 2020. {{Metaphysics Abstraction Metaphysical theories Platonism Reality