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

Luca Incurvati
University of Amsterdam
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
Categories (categorize this paper)
DOI 10.1093/philmat/nkw011
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 70,214
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

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.

View all 82 references / Add more references

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

Similar books and articles

Deflationism, Conservativeness and Maximality.Cezary Cieśliński - 2007 - Journal of Philosophical Logic 36 (6):695 - 705.
A Simple Maximality Principle.Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):527-550.
The Iterative Conception of Set: A (Bi-)Modal Axiomatisation.J. P. Studd - 2013 - Journal of Philosophical Logic 42 (5):1-29.
Combined Maximality Principles Up to Large Cardinals.Gunter Fuchs - 2009 - Journal of Symbolic Logic 74 (3):1015-1046.
Against the Maximality Principle.C. S. Sutton - 2014 - Metaphysica 15 (2):381-390.
The Search for New Axioms.Peter Koellner - 2003 - Dissertation, Massachusetts Institute of Technology
On ◁∗-Maximality.Mirna Džamonja & Saharon Shelah - 2004 - Annals of Pure and Applied Logic 125 (1-3):119-158.
Maximality and Intrinsic Properties.Theodore Sider - 2001 - Philosophy and Phenomenological Research 63 (2):357 - 364.
More on SOP 1 and SOP 2.Saharon Shelah & Alexander Usvyatsov - 2008 - Annals of Pure and Applied Logic 155 (1):16-31.
Maximality and Consciousness.Trenton Merricks - 2003 - Philosophy and Phenomenological Research 66 (1):150-158.


Added to PP index

Total views
166 ( #70,677 of 2,507,555 )

Recent downloads (6 months)
3 ( #209,626 of 2,507,555 )

How can I increase my downloads?


My notes