Notions of Invariance for Abstraction Principles

Philosophia Mathematica 18 (3):276-292 (2010)
  Copy   BIBTEX

Abstract

The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character—permutation invariance—has not received a lot of attention in this debate. This paper aims to fill this gap. After characterizing abstraction principles as particular mappings from the subsets of a domain into that domain and exploring some of their properties, the paper introduces several distinct notions of permutation invariance for such principles, assessing the philosophical significance of each

Categories

Keywords

Reprint years

DOI

10.1093/philmat/nkq010

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 100,619

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Abstraction and Four Kinds of Invariance.Roy T. Cook - 2017 - Philosophia Mathematica 25 (1):3–25.
The Undergeneration of Permutation Invariance as a Criterion for Logicality.Catarina Dutilh Novaes - 2014 - Erkenntnis 79 (1):81-97.
Relative categoricity and abstraction principles.Sean Walsh & Sean Ebels-Duggan - 2015 - Review of Symbolic Logic 8 (3):572-606.
Invariance Principles as Regulative Ideals: From Wigner to Hilbert: Thomas Ryckman.Thomas Ryckman - 2008 - Royal Institute of Philosophy Supplement 63:63-80.
Logicality and Invariance.Denis Bonnay - 2006 - Bulletin of Symbolic Logic 14 (1):29-68.
Logical Indefinites.Jack Woods - 2014 - Logique Et Analyse -- Special Issue Edited by Julien Murzi and Massimiliano Carrara 227: 277-307.
Structural-Abstraction Principles.Graham Leach-Krouse - 2015 - Philosophia Mathematica:nkv033.
Care and Abstract Principles.Ornaith O'Dowd - 2012 - Hypatia 27 (2):407-422.
Introduction to Special Issue: Abstraction Principles.Salvatore Florio - 2017 - Philosophia Mathematica 25 (1):1-2.
‘Neo-logicist‘ logic is not epistemically innocent.Stewart Shapiro & Alan Weir - 2000 - Philosophia Mathematica 8 (2):160--189.

Analytics

Added to PP
2010-08-11

Downloads
180 (#132,316)

6 months
17 (#165,540)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

G. Aldo Antonelli
University of California, Davis

Citations of this work

Collective Abstraction.Jon Erling Litland - 2022 - Philosophical Review 131 (4):453-497.
Structuralist Neologicism†.Francesca Boccuni & Jack Woods - 2020 - Philosophia Mathematica 28 (3):296-316.
Logical Indefinites.Jack Woods - 2014 - Logique Et Analyse -- Special Issue Edited by Julien Murzi and Massimiliano Carrara 227: 277-307.
Relative categoricity and abstraction principles.Sean Walsh & Sean Ebels-Duggan - 2015 - Review of Symbolic Logic 8 (3):572-606.

View all 22 citations / Add more citations

References found in this work

Logic, semantics, metamathematics.Alfred Tarski - 1956 - Oxford,: Clarendon Press. Edited by John Corcoran & J. H. Woodger.
What are logical notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
The limits of abstraction.Kit Fine - 2002 - New York: Oxford University Press. Edited by Matthias Schirn.
Logicism and the ontological commitments of arithmetic.Harold T. Hodes - 1984 - Journal of Philosophy 81 (3):123-149.
Abstract Objects.Gideon Rosen - 2012 - In Ed Zalta (ed.), Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.

View all 22 references / Add more references