Australasian Journal of Logic 15 (2):139-150 (2018)

John Wigglesworth
University of York
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 discussion of the nature of the modalities involved, drawing comparisons with noneism, the view that there are some non-existent objects.
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DOI 10.26686/ajl.v15i2.4859
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References found in this work BETA

The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Towards Non-Being: The Logic and Metaphysics of Intentionality.Graham Priest - 2005 - Oxford, England: Oxford University Press.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.

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