[FOM] 1. Re: foundations meeting/FOMUS/discussion (martdowd at aol.com)

[John Corcoran]

Bruno Bentzen writes: It turns out that in practice mathematicians often
identify two structures whenever they are isomorphic.
Martin Dowd replied: This is only partly true.  Dedekind's and Cantor's
construction of the real numbers yield isomorphic structures (although the
isomorphism itself is a mathematically interesting object; also, the
definition of isomorphism is set-theoretic).  On the other hand, the
definition of a Galois group involves distinguishing isomorphic but unequal
structures.
MY COMMENTS AND QUESTIONS.
(1) Dowd gives the impression that he is objecting to Bentzen but his reply
is a non-sequitur: nothing he said suggests any correction to Bentzen's
innocuous truism. Am I missing something?
(2) Does everyone agree on what it means to identify two structures?
(3) Why should anyone identify two structures? What is achieved?
JOHN CORCORAN