The potential hierarchy of sets

Review of Symbolic Logic 6 (2):205-228 (2013)
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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.

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Author's Profile

Øystein Linnebo
University of Oslo

Citations of this work

Modal Science.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):453-492.
Classicism.Andrew Bacon & Cian Dorr - forthcoming - In Peter Fritz & Nicholas K. Jones (eds.), Higher-order Metaphysics. Oxford University Press.
Varieties of Indefinite Extensibility.Gabriel Uzquiano - 2015 - Notre Dame Journal of Formal Logic 56 (1):147-166.

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References found in this work

Pluralities and Sets.Øystein Linnebo - 2010 - Journal of Philosophy 107 (3):144-164.
Mathematics Without Foundations.Hilary Putnam - 1967 - Journal of Philosophy 64 (1):5-22.
The Iterative Conception of Set: A (Bi-)Modal Axiomatisation.J. P. Studd - 2013 - Journal of Philosophical Logic 42 (5):1-29.
Our Knowledge of Mathematical Objects.Kit Fine - 2005 - In T. Z. Gendler & J. Hawthorne (eds.), Oxford Studies in Epistemology. Clarendon Press. pp. 89-109.
Philosophy of mathematics, selected readings.Paul Benacerraf & Hilary Putnam - 1966 - Revue Philosophique de la France Et de l'Etranger 156:501-502.

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