In this question: http://mathoverflow.net/questions/19644/what-is-the-definition-of-canonical , people gave interesting "philosophical" takes on what the word "canonical" means. Moreover I percieved an underlying opinion that there was no formal mathematical definition.
Whilst looking for something else entirely, I just ran into Bill Messing's post
on the FOM (Foundations of Mathematics) mailing list. I'll just quote the last paragraph:
"It is my impression that there is very little FOM discussion of either Hilbert's epsilon symbol or of Bourbaki formulation of set theory. In particular the chapitre IV Structures of Bourbaki. For reasons, altogether mysterious to me, the second edition (1970) of this book supressed the appendix of the first edition (1958). This appendix gave what is, as far as I know, the only rigorous mathematical discussion of the definition of the word "canonical". Given the fact that Chevalley was, early in his career, a close friend of Herbrand and also very interested in logic, I have guessed that it was Chevalley who was the author of this appendix. But I have never asked any of the current or past members of Bourbaki whom I know whether this is correct."
It's a 4-day weekend here in the UK and I'm very unlikely to get to a library to find out what this suppressed appendix says. Wouldn't surprise me if someone could find this appendix on the web somewhere though! Is there really a mathematical definition of "canonical"??
NOTE: if anyone has more "philosophical" definitions of the word, they can put them in the other thread. I am hoping for something different here.