Re: Extrapolating linear ratios

On Sat, 20 Dec 2008 11:09:18 -0800 (PST) george wrote:


But you really do need to remember that
there ALWAYS WAS, FROM THE BEGINNING,
A DIFFERENT possible resolution of this, namely,
TO DENY THE AXIOM OF FOUNDATION and to declare, from the beginning,
that OF COURSE a set of ALL sets would HAVE to contain itself as a
member.

Right. If we have the _axiom of foundation_ the class of all sets (if we
have such a class in our set/class theory) cannot be a set. Simple as that.
Right. And there might be people who consider it only "natural" that sets
do not contain themselves as elements. (Hence in this case we do not even
need to refer to a "principle of size" for justifying that there's no
universal set in our set/class theory.)


I am NOT defending the course he has ACTUALLY chosen.

Great. Though he already claimed in de.sci.mathematik that you actually DID
that (concerning some other case). You may be sure that he will also use
your present claims for "defending" his views (by quoting them).


Herb
.