Identity, indiscernibility, and Ante Rem structuralism: The tale of I and –I

Philosophia Mathematica 16 (3):285-309 (2008)
Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true of the other. I suggest that ‘i’ functions like a parameter in natural deduction systems. I gave an early version of this paper at a workshop on structuralism in mathematics and science, held in the Autumn of 2006, at Bristol University. Thanks to the organizers, particularly Hannes Leitgeb, James Ladyman, and Øystein Linnebo, to my commentator Richard Pettigrew, and to the audience there. The paper also benefited considerably from a preliminary session at the Arché Research Centre at the University of St Andrews. I am indebted to my colleagues Craige Roberts, for help with the linguistics literature, and Ben Caplan and Gabriel Uzquiano, for help with the metaphysics. Thanks also to Hannes Leitgeb and Jeffrey Ketland for reading an earlier version of the manuscript and making helpful suggestions. I also benefited from conversations with Richard Heck, John Mayberry, Kevin Scharp, and Jason Stanley. CiteULike    Connotea    What's this?
Keywords structuralism   identity
Categories (categorize this paper)
DOI 10.1093/philmat/nkm042
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 24,411
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
Irene Heim (1990). E-Type Pronouns and Donkey Anaphora. Linguistics and Philosophy 13 (2):137--77.
Craige Roberts (2003). Uniqueness in Definite Noun Phrases. Linguistics and Philosophy 26 (3):287-350.

View all 15 references / Add more references

Citations of this work BETA
Jeffrey Ketland (2011). Identity and Indiscernibility. Review of Symbolic Logic 4 (2):171-185.

View all 21 citations / Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

135 ( #32,226 of 1,924,738 )

Recent downloads (6 months)

21 ( #24,803 of 1,924,738 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.