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Modal Set Theory

In Otávio Bueno & Scott Shalkowski (eds.), The Routledge Handbook of Modality. London and New York: Routledge (forthcoming)

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  1. Bi-Modal Naïve Set Theory.John Wigglesworth - 2018 - Australasian Journal of Logic 15 (2):139-150.
    This paper describes a modal conception of sets, according to which sets are 'potential' with respect to their members. A modal theory is developed, which invokes a naive comprehension axiom schema, modified by adding `forward looking' and `backward looking' modal operators. We show that this `bi-modal' naive set theory can prove modalized interpretations of several ZFC axioms, including the axiom of infinity. We also show that the theory is consistent by providing an S5 Kripke model. The paper concludes with some (...)
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