🚀 go-pugleaf

WARNING:

The substantive logic content of this article is extremely low.



If you are looking for meaningful conversation, you have to look elsewhere.



Very well, -- you can't complain now.

In article <1992Nov5.004725.8252@CSD-NewsHost.Stanford.EDU> 
pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:

>In article <1992Nov4.134534.17092@husc3.harvard.edu>
>zeleny@husc10.harvard.edu (Michael Zeleny) writes:

Bill Taylor:
>>>>The slick form of AF, that every nonempty set has a member disjoint from it,

Vaughan Pratt:
>>>Where is this form given?  

MZ:
>>Most everywhere [...]

VP:
>>>	                And why doesn't it rule out Omega = {Omega}?
>>>(Just asking, I'm not expert on this stuff.)

MZ:
>>Neither am I, but that will not prevent me from being charitable
>>enough to let you answer your own question.

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

In a sense, I already do that, but if you should continue asking the
sort of questions exemplified above, I just might have to send them
with a bill to the Stanford School of Continuing Education.

VP:
>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).

Bill's abbreviation was not only reasonably standard, but also well
supported by the context.  I think an unequivocal admission of error
would look better than this craven Reaganite fishing for excuses.

MZ:
>>[...] 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.

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

I use the Principle of Charity.  In any case, as I told you on another
occasion, I do not use the term `wacky' in a pejorative sense.

VP:
>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!).

I was referring to your prattle on the subject of Replacement, as
replicated elsewhere.

MZ:
>>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.

VP:
>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?

Fraenkel and Co have the standard argument replete with additional
references.

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

VP:
>Oh.  Guess that answers my second last question.  :-)

Not to insinuate anything concerning your recent performance on
sci.math, but your own prosaic wackiness hardly *measures* up to 
the rambunctuous rantings of the divine marquis.

>-- 
>Vaughan Pratt				There's no truth in logic, son.

cordially,
mikhail zeleny@husc.harvard.edu
"Un de mes plus grands plaisirs est de jurer Dieu quand je bande."