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The potential hierarchy of sets
Review of Symbolic Logic 6 (2):205-228 (2013)
Abstract
Some reasons to regard the cumulative hierarchy of sets as potential rather than actual are discussed. Motivated by this, a modal set theory is developed which encapsulates this potentialist conception. The resulting theory is equi-interpretable with Zermelo Fraenkel set theory but sheds new light on the set-theoretic paradoxes and the foundations of set theory.Author's Profile
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Citations of this work
Classicism.Andrew Bacon & Cian Dorr - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press. pp. 109-190.
The modal logic of set-theoretic potentialism and the potentialist maximality principles.Joel David Hamkins & Øystein Linnebo - 2022 - Review of Symbolic Logic 15 (1):1-35.
The Many and the One: A Philosophical Study of Plural Logic.Salvatore Florio & Øystein Linnebo - 2021 - Oxford, England: Oxford University Press.
References found in this work
Philosophy of mathematics, selected readings.Paul Benacerraf & Hilary Putnam - 1966 - Revue Philosophique de la France Et de l'Etranger 156:501-502.
The Iterative Conception of Set: a (Bi-)Modal Axiomatisation.J. P. Studd - 2013 - Journal of Philosophical Logic 42 (5):1-29.
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