The Graph Conception of Set

Journal of Philosophical Logic 43 (1):181-208 (2014)
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Abstract

The non-well-founded set theories described by Aczel (1988) have received attention from category theorists and computer scientists, but have been largely ignored by philosophers. At the root of this neglect might lie the impression that these theories do not embody a conception of set, but are rather of mere technical interest. This paper attempts to dispel this impression. I present a conception of set which may be taken as lying behind a non-well-founded set theory. I argue that the axiom AFA is justified on the conception, which provides, contra Rieger (Mind 109:241–253, 2000), a rationale for restricting attention to the system based on this axiom. By making use of formal and informal considerations, I then make a case that most of the other axioms of this system are also justified on the conception. I conclude by commenting on the significance of the conception for the debate about the justification of the Axiom of Foundation

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Luca Incurvati
University of Amsterdam

Citations of this work

Observation and Intuition.Justin Clarke-Doane & Avner Ash - forthcoming - In Carolin Antos, Neil Barton & Venturi Giorgio (eds.), Palgrave Companion to the Philosophy of Set Theory.
Identity and Extensionality in Boffa Set Theory.Nuno Maia & Matteo Nizzardo - 2024 - Philosophia Mathematica 32 (1):115-123.
Non-wellfounded set theory.Lawrence S. Moss - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

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Philosophical papers.Frank Plumpton Ramsey - 1925 - New York: Cambridge University Press. Edited by D. H. Mellor.
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The iterative conception of set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
Russell's Mathematical Logic.Kurt Gödel - 1946 - In Paul Arthur Schilpp (ed.), The Philosophy of Bertrand Russell, 2nd edition. Evanston, IL: The Library of Living Philosophers, Inc.. pp. 123-154.

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