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

Luca Incurvati
University of Amsterdam
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
Keywords Non-well-founded set theory  Anti-foundation axiom  Iterative conception
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Reprint years 2014
DOI 10.1007/s10992-012-9259-x
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Logic, Logic and Logic.George Boolos - 1998 - Harvard University Press.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.

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