[go: up one dir, main page]
Wikipedia

Abstract object theory: Difference between revisions

Browse history interactively
← Previous edit
Content deleted Content added
VisualWikitext
No edit summary
add date of publication
 
(168 intermediate revisions by 47 users not shown)
Line 1:
{{short description|Branch of metaphysics regarding abstract objects}}
{{WIP}}
{{For|the general concept of objecthood in philosophy|Object (philosophy)}}
'''Abstract Object Theory''' is a branch of [[metaphysics]] regarding [[Abstract and concrete|abstract objects]], and studied in hyperdimensional physics. Originally devised by Edward Zalta in 1952,<ref>{{cite web |url= http://mally.stanford.edu/theory.html|title= The Theory of Abstract Objects|last1= |first1= |last2= |first2= |date= February 10th, 1999|work= |publisher= |accessdate=29 March 2013}}</ref> the theory was an expansion of [[Philosophy of mathematics#Contemporary schools of thought#Platonism|mathematical Platonism]].
{{Use mdy dates|date=April 2013}}
[[File:Edward Zalta.jpg|150px|thumb|right|Edward Zalta in 1952]]
'''Abstract object theory''' ('''AOT''') is a branch of [[metaphysics]] regarding [[abstract object]]s.<ref>{{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}}</ref> Originally devised by metaphysician [[Edward Zalta]] in 1981,<ref name=thesis>{{cite thesis|url=https://scholarworks.umass.edu/dissertations_1/2187/|title=An Introduction to a Theory of Abstract Objects (1981)|publisher=ScholarWorks@[[UMass Amherst]]|date=2009|doi=10.7275/f32y-fm90 |access-date=July 21, 2020 |last1=Zalta |first1=Edward N. }}</ref> the theory was an expansion of [[mathematical Platonism]].
==History==
===Mathematical Platonism===
Mathematical Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers. The term Platonism is used because such a view is seen to parallel Plato's Theory of Forms and a "World of Ideas" (Greek: Eidos (εἶδος)) described in Plato's Allegory of the cave: the everyday world can only imperfectly approximate an unchanging, ultimate reality. Both Plato's cave and Platonism have meaningful, not just superficial connections, because Plato's ideas were preceded and probably influenced by the hugely popular Pythagoreans of ancient Greece, who believed that the world was, quite literally, generated by numbers.
[[File:Plato-raphael.jpg|100px|thumb|left|[[Plato]] ]]
===''Theory of Abstract Objects''===
Abstract Objects: An Introduction to Axiomatic Metaphysics is the title of a [[1952]] publication by Edward Zalta that outlines Abstract Object Theory.<ref>Rawls, John. [http://books.google.com/books?id=voCSP6k3FCcC ''Abstract Objects: An Introduction to Axiomatic Metaphysics'']. D. Reidel Publishing Company, 1952</ref>
 
==Overview<!--'Computational metaphysics' and 'Axiomatic metaphysics' redirect here-->==
===''A Paper Regarding the 10th Dimension''===
{{also|Dual copula strategy}}
''A Paper Regarding the 10th Dimension'' is the title of a [[2013]] paper
''Abstract Objects: An Introduction to Axiomatic Metaphysics'' (1983) is the title of a publication by Edward Zalta that outlines abstract object theory.
by Trace Fleeman<ref>{{cite book |last=Fleeman |first=Trace |authorlink= |year=2013 |title= A Paper Regarding the 10th Dimension (as described by Rob Bryanton)|edition=1st |url=http://archive.org/details/apaperregardingthe10thdimension |accessdate=March 31, 2013}}</ref> that first attempted to unify Abstract Object Theory with [[Dimension (mathematics and physics)|Hyperdimensional physics]], using the dimensions as described by [http://www.tenthdimension.com/ Rob Bryanton]. In Rob Bryanton's interpretation, the 10th dimension is point encompassing all [[probability|possibilities]] in all possible [[Multiverse|universes]]<ref>{{cite book |last=Bryanton |first=Rob |authorlink= |year=2006, 2007 |title= Imagining the Tenth Dimension:
 
a new way of thinking about time and space|edition=1st|accessdate=March 31, 2013}}</ref><ref>{{cite web |url= http://thetartan.org/2012/11/12/scitech/ten-dimensions|title= How Things Work: The 10th dimension|author= Brooke Kuei|date= November 12, 2012
AOT is a [[dual predication approach]] (also known as "dual copula strategy") to abstract objects<ref name=SEP>{{cite SEP |url-id=nonexistent-objects |title=Nonexistent Objects |first=Maria |last=Reicher |date=2014 }}</ref><ref name=Jacquette>[[Dale Jacquette]], ''Meinongian Logic: The Semantics of Existence and Nonexistence'', Walter de Gruyter, 1996, p. 17.</ref> influenced by the contributions of [[Alexius Meinong]]<ref>[[Alexius 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.</ref><ref name=:0>Zalta (1983:xi).</ref> and his student [[Ernst Mally]].<ref>[[Ernst Mally]] (1912), ''Gegenstandstheoretische Grundlagen der Logik und Logistik (Object-theoretic Foundations for Logics and Logistics)'', Leipzig: Barth, [https://mally.stanford.edu/mally-book/ObjectTheoreticFoundationsOfLogic2.pdf §§33 and 39].</ref><ref name=:0/> On Zalta's account, there are two modes of [[Predicate (mathematical logic)|predication]]: some objects (the ordinary [[Abstract and concrete|concrete]] ones around us, like tables and chairs) ''exemplify'' properties, while others (abstract objects like numbers, and what others would call "[[nonexistent object]]s", like the [[Round square copula|round square]] and the mountain made entirely of gold) merely ''encode'' them.<ref>Zalta (1983:33).</ref> 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.<ref>Zalta (1983:36).</ref> For every set of properties, there is exactly one object that encodes exactly that set of properties and no others.<ref>Zalta (1983:35).</ref> This allows for a [[Formal system|formalized]] [[ontology]].
|work= |publisher= [[The Tartan]]|accessdate=March 31, 2013}}</ref>. In the paper, he uses Zalta's description of [[Abstract and concrete|abstract objects]] as [[Spacetime|nonspaciotemporal]] substances and unifies it with Bryanton's 10th dimension existing "outside of space and time". It is also the first publication to define [[information]] and [[data]] as abstract objects.
 
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]],<ref>[[Romane Clark]], "Not Every Object of Thought Has Being: A Paradox in Naive Predication Theory", ''Noûs'' '''12'''(2) (1978), pp. 181–188.</ref><ref>[[William J. Rapaport]], "Meinongian Theories and a Russellian Paradox", ''Noûs'' '''12'''(2) (1978), pp. 153–80.</ref><ref>Adriano Palma, ed. (2014). [https://books.google.com/books?id=iYHoBQAAQBAJ&dq= ''Castañeda and His Guises: Essays on the Work of Hector-Neri Castañeda'']. Boston/Berlin: Walter de Gruyter, pp. 67–82, esp. 72.</ref> Alan McMichael's paradox,<ref>Alan McMichael and Edward N. Zalta, [https://link.springer.com/article/10.1007%2FBF00248396 "An Alternative Theory of Nonexistent Objects"], ''Journal of Philosophical Logic'' '''9''' (1980): 297–313, esp. 313 n. 15.</ref> and Daniel Kirchner's paradox)<ref>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.</ref> do not arise within it.<ref>Zalta (2024:253): "Some non-core λ-expressions, such as those leading to the Clark/Boolos, McMichael/Boolos, and Kirchner paradoxes, will be provably empty."</ref> AOT employs [[Range of quantification|restricted]] [[Abstraction#In philosophy|abstraction]] [[Axiom schema|schemata]] to avoid such paradoxes.<ref>Zalta (1983:158).</ref>
 
In 2007, Zalta and [[Branden Fitelson]] introduced the term '''computational metaphysics'''<!--boldface per WP:R#PLA--> to describe the implementation and investigation of formal, '''axiomatic metaphysics'''<!--boldface per WP:R#PLA--> in an [[automated reasoning]] environment.<ref>[[Edward N. Zalta]] and [[Branden Fitelson]], [https://mally.stanford.edu/Papers/computation.pdf "Steps Toward a Computational Metaphysics"], ''Journal of Philosophical Logic'' '''36'''(2) (April 2007): 227–247.</ref><ref>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.</ref>
 
==See Alsoalso==▼
{{cols|colwidth=21em}}
* [[Abstract and concrete]]
* [[Abstractionism (philosophy of mathematics)]]
* [[Algebra of concepts]]
* [[Mathematical universe hypothesis]]
* [[Modal Meinongianism]]
* [[Modal neo-logicism]]
* [[Object of the mind]]
* [[Objective precision]]
{{colend}}
 
==Notes==
{{cols|colwidth=21em}}
{{reflist}}
{{colend}}
 
▲==See Also==
{{Portal|Philosophy}}
{{Portal|Science}}
*[[Philosophy of mathematics#Contemporary schools of thought#Platonism|Mathematical Platonism]]
*[[Philosophy of physics]]
==References==
* [[Edward N. Zalta]], [https://mally.stanford.edu/abstract-objects.pdf ''Abstract Objects: An Introduction to Axiomatic Metaphysics''], Dordrecht: D. Reidel, 1983.
<references />
* Edward N. Zalta, [https://mally.stanford.edu/intensional-logic.pdf ''Intensional Logic and the Metaphysics of Intentionality''], Cambridge, MA: The MIT Press/Bradford Books, 1988.
* Edward N. Zalta, [http://doors.stanford.edu/principia-1999-02-10.pdf ''Principia Metaphysica''], Center for the Study of Language and Information, Stanford University, February 10, 1999.
* Daniel Kirchner, Christoph Benzmüller, Edward N. Zalta, [https://mally.stanford.edu/Papers/mechanizing-principia.pdf "Mechanizing ''Principia Logico-Metaphysica'' in Functional Type Theory"], ''Review of Symbolic Logic'' '''13'''(1) (March 2020): 206–18.
* Edward N. Zalta, [https://mally.stanford.edu/principia.pdf ''Principia Logico-Metaphysica''], Center for the Study of Language and Information, Stanford University, May 22, 2024.
 
==Further reading==
* Daniel Kirchner, [https://d-nb.info/1262308674/34 ''Computer-Verified Foundations of Metaphysics and an Ontology of Natural Numbers in Isabelle/HOL''], PhD thesis, Free University of Berlin, 2021.
* Edward N. Zalta, [https://mally.stanford.edu/Papers/typed-object-theory.pdf "Typed Object Theory"], in José L. Falguera and Concha Martínez-Vidal (eds.), ''Abstract Objects: For and Against'', Springer (Synthese Library), 2020.
 
{{Metaphysics}}
 
[[Category:Abstract object theory| ]]
[[Category:Abstraction]]
[[Category:Analytic philosophy]]
[[Category:Metaphysical theories]]
[[Category:Platonism]]
[[Category:Reality]]
Retrieved from "https://en.wikipedia.org/wiki/Abstract_object_theory"