[FOM] FOM: ISOMORPHISM, EQUALITY, AND IDENTITY
John Corcoran
corcoran at buffalo.edu
Mon Mar 28 14:34:49 EDT 2016
FOM: ISOMORPHISM, EQUALITY, AND IDENTITY
On Sat, Mar 26, 2016 at 08:01:24PM +0300, Arnon Avron wrote:
I cannot quite understand the claim that in mathematics "isomorphic" means
"equal".
JOHN CORCORAN TRIES TO HELP.
There are two preliminary points.
(1) I have known a few mathematicians who said things such as "isomorphic
models of Peano arithmetic are equal", where 'equal' meant identical, i.e.
one and the same model. In fact, some said in print that isomorphic systems
differ only notationally.
See page 190 in:
https://www.academia.edu/19651797/1980._Categoricity_History_and_Philosophy_
of_Logic_1_187_207._MR82j_03034
(2) I have known a few mathematicians who said things such as "isomorphic
models of Peano arithmetic are equal", where by 'equal' they did not mean
identical, i.e. one and the same model. They were respecting the tradition
of using 'equals' for a relation that could hold between different objects.
DISCUSSION:
https://www.academia.edu/s/dd9dc8569f?source=link
ABSTRACT:
https://www.academia.edu/13451441/Equality_and_identity._Bulletin_of_Symboli
c_Logic._19_2013_255-6._Coauthor_Anthony_Ramnauth_
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