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Non-wellfounded set theory

Stanford Encyclopedia of Philosophy (2008)

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  1. A Yabloesque Paradox in Epistemic Game Theory.Can Başkent - 2018 - Synthese 195 (1):441-464.
    The Brandenburger–Keisler paradox is a self-referential paradox in epistemic game theory which can be viewed as a two-person version of Russell’s Paradox. Yablo’s Paradox, according to its author, is a non-self referential paradox, which created a significant impact. This paper gives a Yabloesque, non-self-referential paradox for infinitary players within the context of epistemic game theory. The new paradox advances both the Brandenburger–Keisler and Yablo results. Additionally, the paper constructs a paraconsistent model satisfying the paradoxical statement.
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  • The Graph Conception of Set.Luca Incurvati - 2014 - Journal of Philosophical Logic 43 (1):181-208.
    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 (...)
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  • Some Non-Classical Approaches to the Brandenburger–Keisler Paradox.Can Başkent - 2015 - Logic Journal of the IGPL 23 (4):533-552.