Date: Mar 18, 2013 1:09 PM
Subject: Re: Matheology § 224
On 3/18/2013 7:29 AM, WM wrote:
> Every list yields another diagonal.
> And every diagonal can be included in another list.
> Both these facts are the two sides of infinity.
What these facts correspond with is the
structure of a directed set.
Directed sets are, indeed, infinite.
Absolute infinity cannot be treated as
That does not mean one cannot have a
> With same right he could have argued that there are more even than odd
> non-negative integers, because 0 is even and after every odd integer
> there follwos an even one, just overlooking that after every even
> integer there follows an odd one.
But, Cantor understood the strict reasoning inherent
to the nature of class-based logical construction.
What he could have done if he were of lesser skill
is not what he did do -- because he knew better.