Date: Mar 23, 2013 6:15 PM
Author: Virgil
Subject: Re: WMytheology � 224

In article 
WM <> wrote:

> I say that there is no finite line that changes the union. So the
> union would be the same if there was no finite line.

That conclusion does not follow from that premise, at least not outside

Given sets {a,b}, {b,c}, and {c,a}, outside Wolkenmuekenheim, one can
omit any one of them from their union without eliminating any element
from that union, so that, by WM's logic, we should be able to eliminate
all of then and sill have that empty union equal to {a,b,c}.

> So the union would be the same if there was no finite line remaining.

Only in Wolkenmuekenheim!

> Your, no, we cannot remove all lines, amounts to: There must remain
> some finite line in order not to change the union.

True. But one line , while necessary is not not sufficient to keep that
original union. Nothing less that an infinite set of lines is sufficient.

Which anyone brighter than a rock would know.

WM presumes, contrary to fact, and knowing it to be contrary to fact,
that one line can always do what any set of lines can do.

For instance, for each original line to be a subset of some line in a
set of lines, one needs an infinite set of lines.

Similarly, for every natural to be a member of some line in a set of
lines, no set less of than infinitely many lines is sufficient, so the
infiniteness of such a set is necessary.

Every infinite set of lines does this but no finite set of lines can do

Which DISproves WM's presumption, and DISproves his argument above.

So WM is