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

Authors
Luca Incurvati
University of Amsterdam
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.
Keywords Maximality principles  Set theory  Iterative conception  Reflection principles  Inner model hypothesis  Forcing axioms  Restrictiveness
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DOI 10.1093/philmat/nkw011
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References found in this work BETA

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.
From Mathematics to Philosophy.Hao Wang - 1974 - London and Boston: London.
What is Cantor's Continuum Problem?Kurt Gödel - 1947 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Journal of Symbolic Logic. Oxford University Press. pp. 176--187.

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Citations of this work BETA

In Defense of Countabilism.David Builes & Jessica M. Wilson - forthcoming - Philosophical Studies:1-38.
From Metasemantics to Analyticity.Zeynep Soysal - 2021 - Philosophy and Phenomenological Research 103 (1):57-76.
Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.
Gödelian Platonism and Mathematical Intuition.Wesley Wrigley - 2022 - European Journal of Philosophy 30 (2):578-600.

View all 6 citations / Add more citations

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