On 2/7/2013 7:54 AM, WM wrote: > On 7 Feb., 09:10, William Hughes <wpihug...@gmail.com> wrote: >> On Feb 7, 9:00 am, WM <mueck...@rz.fh-augsburg.de> wrote: >> <snip> >> >>> What does that mean for the set of accessible numbers? >> >> That this potentially infinite set is not listable. > > Here we stand firm on the grounds of set theory. > > Once upon a time there used to be a logocal identity: The expression > "Set X is countable" used to be equivalent to "Set X can be listed".
Cantor understood that for a collection to be a set, there was an underlying canonical well-ordered form.
That includes every transfinite number about which any competent set theorist dreamed.
The only meaningful sense in which sets are "listed" includes the discernible multitude of infinities you invoke with every attempt at denial.