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A note on Isomorphism and Identity

Angere, Staffan LU (2014) In Preprint without journal information
Abstract
This note argues that, insofar as contemporary mathematics is concerned, there is overwhelming evidence that if mathematical objects are structures, then isomorphism should not be taken as their identity condition. This goes against a common version of structuralism in the philosophical literature. Four areas are presented in which identifying isomorphic structures or objects leads to contradiction or inadequacy. This is followed by a philosophical discussion on possible ways to approach the distinction, and a section on the possibility of proceeding intensionally, as is done in e.g.\ the Univalent Foundations program.
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author
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
in
Preprint without journal information
publisher
Manne Siegbahn Institute
ISSN
0348-7911
language
English
LU publication?
yes
id
96d0cb01-5d2b-466b-a378-36b0e9508eb4 (old id 4393841)
date added to LUP
2014-04-28 12:06:11
date last changed
2016-04-16 10:55:58
@article{96d0cb01-5d2b-466b-a378-36b0e9508eb4,
  abstract     = {This note argues that, insofar as contemporary mathematics is concerned, there is overwhelming evidence that if mathematical objects are structures, then isomorphism should not be taken as their identity condition. This goes against a common version of structuralism in the philosophical literature. Four areas are presented in which identifying isomorphic structures or objects leads to contradiction or inadequacy. This is followed by a philosophical discussion on possible ways to approach the distinction, and a section on the possibility of proceeding intensionally, as is done in e.g.\ the Univalent Foundations program.},
  author       = {Angere, Staffan},
  issn         = {0348-7911},
  language     = {eng},
  publisher    = {Manne Siegbahn Institute},
  series       = {Preprint without journal information},
  title        = {A note on Isomorphism and Identity},
  year         = {2014},
}