Roy,  
  
Well, you are the expert on this, but  
I would submit that there is an underlying  
principle common to at least the Bourbaki  
and Hilbert programs as well as the Euclid  
program.  That underlying program is best  
described as being Occam's Razor, a kind  
of intellectual optimization: how do we  
prove the useful results we want to have  
proven with the smallest set of assumptions/  
axioms.  You are right, although you did not  
quite state it this way, that for many of  
these folks, especially the Bourbakists, this  
optimization goal was probably more important  
than the absolute reality or lack thereof of  
the axioms.  
      
Euclid may not have formulated in precisely   
these terms, as Hilbert pretty clear did (even  
if he did not specifically cite Occam [or Ockham]),  
but having a heuristic goal would tend to lead  
one to such a simplification.  Perhaps we might  
think of Euclid as having been a satisficer in  
this realm, with wanting to have as few axioms  
as possible, but with the constraint that they  
appeal to common sense and at least appear to  
be true.  
  
Barkley Rosser