Abstract object theory

{{short description|Branch of metaphysics regarding abstract objects}}

{{For|the general concept of objecthood in philosophy|Object (philosophy)}}

Abstract object theory (AOT) is a branch of metaphysics regarding abstract objects.{{cite web | url=http://mally.stanford.edu/theory.html | title=The Theory of Abstract Objects | last1=Zalta | first1=Edward N. | date=2004 | publisher=The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University | access-date=July 18, 2020}} Originally devised by metaphysician Edward Zalta in 1981,{{cite thesis | last1=Zalta | first1=Edward N. | date=1981 | title=An Introduction to a Theory of Abstract Objects | publisher=UMass Amherst | hdl=20.500.14394/12282 | hdl-access=free | doi=10.7275/f32y-fm90 | doi-access=free | url=https://scholarworks.umass.edu/bitstreams/d2a3ed8c-6f57-43b0-a55e-ba91ae0dc839/download}} 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 objectsDale Jacquette, Meinongian Logic: The Semantics of Existence and Nonexistence, Walter de Gruyter, 1996, p. 17. influenced by the contributions of Alexius MeinongAlexius Meinong, "Über Gegenstandstheorie" ("The Theory of Objects"), in Alexius Meinong, ed. (1904). [https://archive.org/details/untersuchungenzu00mein Untersuchungen zur Gegenstandstheorie und Psychologie] (Investigations in Theory of Objects and Psychology), Leipzig: Barth, pp. 1–51.{{sfn|Zalta|1983|p=xi}} and his student Ernst Mally.{{cite book | first=Ernst | last=Mally | date=1912 | title=Gegenstandstheoretische Grundlagen der Logik und Logistik | language=de | trans-title=Object-theoretic Foundations for Logics and Logistics | publication-place=Leipzig | publisher=Barth | url=https://mally.stanford.edu/mally-book/ObjectTheoreticFoundationsOfLogic2.pdf | at=§§33 and 39}}{{sfn|Zalta|1983|p=xi}} 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 "nonexistent objects", like the round square and the mountain made entirely of gold) merely encode them.{{sfn|Zalta|1983|p=33}} 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.{{sfn|Zalta|1983|p=36}} For every set of properties, there is exactly one object that encodes exactly that set of properties and no others.{{sfn|Zalta|1983|p=35}} 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,{{cite journal | author-link=Romane Clark | last=Clark | first=Romane | title=Not Every Object of Thought Has Being: A Paradox in Naive Predication Theory | work=Noûs | volume=12 | number=2 | date=1978 | pages=181–188 | jstor=2214691}}{{cite journal | author-link=William J. Rapaport | last=Rapaport | first=William J. | title=Meinongian Theories and a Russellian Paradox | work=Noûs | volume=12 | number=2 | date=1978 | pages=153–180}}* {{cite book | editor-last=Palma | editor-first=Adriano | title=Castañeda and his guises: Essays on the work of Hector-Neri Castañeda | publisher=De Gruyter | series=Philosophische Analyse / Philosophical Analysis | year=2014 | isbn=978-1-61451-663-7 | url=https://books.google.com/books?id=iYHoBQAAQBAJ&pg=PA72 | language=br | publication-place=Boston/Berlin | pages=67–82, esp. 72}} Alan McMichael's paradox,{{cite journal | last=McMichael | first=Alan | last2=Zalta | first2=Edward N. | title=An alternative theory of nonexistent objects | journal=Journal of Philosophical Logic | volume=9 | issue=3 | date=1980 | issn=0022-3611 | doi=10.1007/BF00248396 | pages=297–313, esp. p. 313 n. 15}} and Daniel Kirchner's paradox)Daniel Kirchner, [http://isa-afp.org/entries/PLM.html "Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL"], Archive of Formal Proofs, 2017. do not arise within it.{{sfnq|Zalta|2024|p=253|q=Some non-core λ-expressions, such as those leading to the Clark/Boolos, McMichael/Boolos, and Kirchner paradoxes, will be provably empty.}} AOT employs restricted abstraction schemata to avoid such paradoxes.{{sfn|Zalta|1983|p=158}}

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.{{cite journal | last=Fitelson | first=Branden | last2=Zalta | first2=Edward N. | title=Steps toward a computational metaphysics | journal=Journal of Philosophical Logic | volume=36 | issue=2 | date=14 March 2007 | issn=0022-3611 | doi=10.1007/s10992-006-9038-7 | doi-access=free | pages=227–247 | url=https://mally.stanford.edu/Papers/computation.pdf}}Jesse Alama, Paul E. Oppenheimer, Edward N. Zalta, [https://mally.stanford.edu/Papers/cade.pdf "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

{{cite book | last=Zalta | first=Edward N. | url=https://mally.stanford.edu/abstract-objects.pdf | title=Abstract Objects: An Introduction to Axiomatic Metaphysics | publication-place=Dordrecht | publisher=D. Reidel | date=1983}}
{{cite book | last=Zalta | first=Edward N. | url=https://mally.stanford.edu/intensional-logic.pdf | title=Intensional Logic and the Metaphysics of Intentionality | publication-place=Cambridge, MA | publisher=The MIT Press/Bradford Books | date=1988}}
{{cite book | last=Zalta | first=Edward N. | url=http://doors.stanford.edu/principia-1999-02-10.pdf | title=Principia Metaphysica | publisher=Center for the Study of Language and Information, Stanford University | date=February 10, 1999}}
{{cite journal | first1=Daniel | last1=Kirchner | first2=Christoph | last2=Benzmüller | first3=Edward N. | last3=Zalta | url=https://mally.stanford.edu/Papers/mechanizing-principia.pdf | title=Mechanizing Principia Logico-Metaphysica in Functional Type Theory | work=Review of Symbolic Logic | volume=13 | number=1 | date=March 2020 | pages=206–218}}
{{cite book | last=Zalta | first=Edward N. | url=https://mally.stanford.edu/principia.pdf | title=Principia Logico-Metaphysica | publisher=Center for the Study of Language and Information, Stanford University | date=May 22, 2024}}

Abstract object theory

Overview

See also

Notes

References

Further reading