Maximality Principles in Set Theory

Philosophia Mathematica 25 (2):159-193 (2017)
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Abstract

In set theory, a maximality principle is a principle that asserts some maximality property of the universe of sets or some part thereof. Set theorists have formulated a variety of maximality principles in order to settle statements left undecided by current standard set theory. In addition, philosophers of mathematics have explored maximality principles whilst attempting to prove categoricity theorems for set theory or providing criteria for selecting foundational theories. This article reviews recent work concerned with the formulation, investigation and justification of maximality principles.

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Luca Incurvati
University of Amsterdam

Citations of this work

In defense of Countabilism.David Builes & Jessica M. Wilson - 2022 - Philosophical Studies 179 (7):2199-2236.
From metasemantics to analyticity.Zeynep Soysal - 2020 - Philosophy and Phenomenological Research 103 (1):57-76.
Are Large Cardinal Axioms Restrictive?Neil Barton - 2023 - Philosophia Mathematica 31 (3):372-407.
Maddy On The Multiverse.Claudio Ternullo - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 43-78.

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References found in this work

Second Philosophy: A Naturalistic Method.Penelope Maddy - 2007 - Oxford, England and New York, NY, USA: Oxford University Press.
The potential hierarchy of sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.
What is Cantor's Continuum Problem?Kurt Gödel - 1947 - The American Mathematical Monthly 54 (9):515--525.
The set-theoretic multiverse.Joel David Hamkins - 2012 - Review of Symbolic Logic 5 (3):416-449.

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