herb z
Posts:
1,187
Registered:
8/26/06


Re: Mathematics as a language
Posted:
Nov 3, 2010 1:52 AM


Aatu Koskensilta wrote: > herbzet writes: > > Bill Taylor wrote: > > > >> Or whether the number 6 really exists. Does it? > > > > It *could* exist  therefore, mathematically, it *does* exist. > > This is a traditional and appealing idea. But just what is meant by > "could" here? What sort of possibility is involved?
For rhetorical punch, I purposely left out the modifier, which is "logical".
What logically could exist  that is, what is not inherently self contradictory  has mathematical existence.
(This may be a traditional idea, but I arrived at it during an exchange of posts with MoeBlee.)
In particular, there appears to be nothing selfcontradictory in the notion of infinite sets  they could exist, therefore, mathematically, they do.
 hz

