Ray,  (01)
> Out of curiosity, before I diverge too far from ontology, were
> the Bourbaki being intentionally misleading or were they merely
> short on ground truth?  (02) 
They were very serious. But there have been many debates about the
nature of mathematics and the foundations of mathematics from the
late 19th century to the present.  (03)
The Bourbaki strongly believed in a *formalist* approach with set
theory as the foundation. For a strongly favorable view of their
project, see the intro to the following book (which you can read
online from Amazon without spending 20ドル):  (04)
 http://www.amazon.com/Bourbaki-A-Secret-Society-Mathematicians/dp/0821839675  (05)
But that formalist approach led to the so-called "New Math", which
was a disastrous attempt to start teaching set theory in kindergarten.
The Wikipedia article on "New Math" has a brief summary:  (06)
 http://en.wikipedia.org/wiki/New_Math  (07)
Following is a song by Tom Lehrer, as lip synched with graphics:  (08)
 http://www.youtube.com/watch?v=DfCJgC2zezw  (09)
A more serious, but very readable summary of a view I prefer is
the lecture "Mathematics as a Creative Art" by Paul Halmos:  (010)
 http://www-history.mcs.st-and.ac.uk/Extras/Creative_art.html  (011)
The following article has more excerpts by Halmos:  (012)
 http://www.ams.org/notices/200709/tx070901136p.pdf  (013)
John  (014)
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