Abstract

Chapter 2 is an investigation of non-well-founded set theories. The standard set theory, Zermelo–Fraenkel (ZFC), and the associated iterative conception of sets, is well suited for Metaphysical Foundationalism: there is a base class of basic entities (the empty set and individuals) from which all other sets are built. Various non-well-founded set theories are examined, and a particular non-well-founded set theory, Boffa set theory, is argued for. This set theory allows for both infinite regress and circularity in chains of set membership. Such a theory, it is argued, results in infinite regresses and circles of ontological dependence, and thus this set theory motivates Metaphysical Infinitism and Holism.

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