Synthese 197 (2):623-649 (2017)

Authors
Abstract
Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism and actualism face complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Reprint years 2020
DOI 10.1007/s11229-017-1336-9
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
Through your library

References found in this work BETA

Add more references

Citations of this work BETA

Universism and Extensions of V.Carolin Antos, Neil Barton & Sy-David Friedman - forthcoming - Review of Symbolic Logic:1-50.

Add more citations

Similar books and articles

Maximality Principles in Set Theory.Luca Incurvati - 2017 - Philosophia Mathematica 25 (2):159-193.
Closed Maximality Principles and Generalized Baire Spaces.Philipp Lücke - 2019 - Notre Dame Journal of Formal Logic 60 (2):253-282.
The Iterative Conception of Set: A (Bi-)Modal Axiomatisation.J. P. Studd - 2013 - Journal of Philosophical Logic 42 (5):1-29.
A Simple Maximality Principle.Joel Hamkins - 2003 - Journal of Symbolic Logic 68 (2):527-550.
A Simple Maximality Principle.Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):527-550.
On a Class of Maximality Principles.Daisuke Ikegami & Nam Trang - 2018 - Archive for Mathematical Logic 57 (5-6):713-725.
Maximality, Function, and the Many.Robert Francescotti - 2019 - Metaphysica 20 (2):175-193.
Against the Maximality Principle.C. S. Sutton - 2014 - Metaphysica 15 (2):381-390.
Modified Numerals and Maximality.Brian Buccola & Benjamin Spector - 2016 - Linguistics and Philosophy 39 (3):151-199.
Deflationism, Conservativeness and Maximality.Cezary Cieśliński - 2007 - Journal of Philosophical Logic 36 (6):695 - 705.

Analytics

Added to PP index
2017-03-06

Total views
84 ( #138,496 of 2,506,489 )

Recent downloads (6 months)
11 ( #68,237 of 2,506,489 )

How can I increase my downloads?

Downloads

My notes