🚀 go-pugleaf

In article <1992Nov4.134534.17092@husc3.harvard.edu> zeleny@husc10.harvard.edu (Michael Zeleny) writes:
>
>Taylor:
>>>The slick form of AF, that every nonempty set has a member disjoint from it,
>
>Pratt:
>>Where is this form given?  
>
>Most everywhere [...]
>
>>Pratt:                And why doesn't it rule out Omega = {Omega}?
>>(Just asking, I'm not expert on this stuff.)
>
>Neither am I, but that will not prevent me from being charitable
>enough to let you answer your own question.

Why, do you turn in all your Usenet posts along with your tax return?

Actually it's just me being dense (and Bill being nonstandard).  I took
Bill's AF to mean AntiFoundation when he meant Axiom of Foundation
(whence he *meant* to rule out Omega={Omega}).  I should have figured
that out sooner (broken enough eggs in the past two days to start an
omelette parlor).

>[...] e.g. in Drake (_Set Theory_), whose pithy comments on
>the Axiom of Replacement (a.k.a. the `F' in `ZFC') will go a long way
>toward disabusing you of your wacky revisionist notions.

Thank god.  I've been posting wacky messages for weeks and no one seems
to have noticed till now.  How do you do it?

But let's get our facts straight on what I'm proposing to revise.  I
haven't lifted a finger against Replacement, in fact I need it to make
money with it by 2012 (come on, Replacement, come on, be strong for
me!).

>Some _philosophical_ reservations concerning Replacement can be made
>from a generic Limitation of Size standpoint, -- right now I do not
>have the references, but they are likely to be found in Maddy's JSL
>expository articles on the ZFC axioms.  However, from the more refined
>standpoint of the cumulative hierarchy, Drake more or less has the
>last word.

Again, I'm not in the market to be talked out of Replacement, or talk
anyone out of it.  Foundation on the other hand seems as pointless as
the cumulative hierarchy: each needs the other and neither seems to be
much use to the rest of mathematics.  Now who can you point me at with
a convincing pitch for Foundation?

>Always looking for
>logico-philosophical esoterica, Italian motorcycle parts, Swiss
>firearms, or XVIIIth century French smut.

Oh.  Guess that answers my second last question.  :-)
-- 
Vaughan Pratt				There's no truth in logic, son.