"Paul Lutus" <nospam@nosite.zzz> wrote in message news://izXO7.107540$YD.8811261@news2.aus1.giganews.com... > "The Scarlet Manuka" <sacha@maths.uwa.edu.au> wrote in message > news://a6934a10.0112031920.1314297a@posting.google.com... > > > > A default > > > definition is, ipso facto, a single definition. > > > > Only if it is to be universally applied. I see no reason why > > a default may not have limited scope. > > This begs the question of the meaning of "default definition," in a way > calculated to generate heat, not light.
Why? As I've said many times now, it's quite reasonable to give a default number system for a particular subject. Then "default definition" resolves to a context-dependent number system. This poses no problems, unless you want to know what the default is without specifying a context - in which case the answer is obviously that there is none.
> > Let's restore some context. "Such a number system" refers to > > the specific phrase, "the number system that permits ordinary > > arithmetic operations". My claim is that there are many such > > number systems, and therefore one cannot speak of "the number > > system that permits ordinary arithmetic operations", as if > > there was only one, any more than one can speak of "the positive > > integer less than 10", because that does not specify a single > > integer. > No default. End of story.
Set a default integer, say 2. We still can't speak of "the positive integer less than 10". As I said in the bit you discarded, if you have a non-singleton set, making one of its elements the default doesn't change the set to a singleton.
