Review of Symbolic Logic 10 (4):651-662 (2017)

Authors
Sam Roberts
Universität Konstanz
Abstract
This article introduces a new reflection principle. It is based on the idea that whatever is true in all entities of some kind is also true in a set-sized collection of them. Unlike standard reflection principles, it does not re-interpret parameters or predicates. This allows it to be both consistent in all higher-order languages and remarkably strong. For example, I show that in the language of second-order set theory with predicates for a satisfaction relation, it is consistent relative to the existence of a 2-extendible cardinal (Theorem 7.12) and implies the existence of a proper class of 1-extendible cardinals (Theorem 7.9).
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1017/S1755020317000223
Options
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: 72,634
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

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Iteration Again.George Boolos - 1989 - Philosophical Topics 17 (2):5-21.
E Pluribus Unum: Plural Logic and Set Theory.John P. Burgess - 2004 - Philosophia Mathematica 12 (3):193-221.
Plural Quantification and Classes.Gabriel Uzquiano - 2003 - Philosophia Mathematica 11 (1):67-81.

View all 10 references / Add more references

Citations of this work BETA

Modal Structuralism and Reflection.Sam Roberts - 2019 - Review of Symbolic Logic 12 (4):823-860.
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.
Global Reflection Principles.P. D. Welch - 2017 - In I. Niiniluoto, H. Leitgeb, P. Seppälä & E. Sober (eds.), Logic, Methodology and Philosophy of Science - Proceedings of the 15th International Congress, 2015. College Publications.
Proving Theorems From Reflection.Philip Welch - 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. 79-97.

View all 8 citations / Add more citations

Similar books and articles

Semistationary and Stationary Reflection.Hiroshi Sakai - 2008 - Journal of Symbolic Logic 73 (1):181-192.
Rescuing Reflection.Ilho Park - 2012 - Philosophy of Science 79 (4):473-489.
Generic Compactness Reformulated.Bernhard König - 2004 - Archive for Mathematical Logic 43 (3):311-326.
Square and Non-Reflection in the Context of Pκλ.Greg Piper - 2006 - Annals of Pure and Applied Logic 142 (1):76-97.
Global Reflection Principles.P. D. Welch - 2017 - In I. Niiniluoto, H. Leitgeb, P. Seppälä & E. Sober (eds.), Logic, Methodology and Philosophy of Science - Proceedings of the 15th International Congress, 2015. College Publications.
Conditionalization, Reflection, and Self-Knowledge.Jonathan Weisberg - 2007 - Philosophical Studies 135 (2):179-197.
Distorted Reflection.Rachael Briggs - 2009 - Philosophical Review 118 (1):59-85.
Deference, Respect and Intensionality.Anna Mahtani - 2016 - Philosophical Studies:1-21.

Analytics

Added to PP index
2017-11-02

Total views
52 ( #221,848 of 2,533,818 )

Recent downloads (6 months)
1 ( #388,784 of 2,533,818 )

How can I increase my downloads?

Downloads

My notes