From: rusin@vesuvius.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Re: Sets, classes, contradictions, etc. (Practical application!)
Date: 4 Nov 1996 15:33:22 GMT

In article <E0Bw2C.E9D@spcuna.spc.edu>,
David K. Davis <davis_d@spcunb.spc.edu> wrote:
>Kralor (ms-drake@students.uiuc.edu) wrote:
>: Please try not to bruise me...I'm just a naive college student who's 
>: curious.  I recently started reading about set theory and all the 
>: contrivances that are used to eliminate paradoxes such as Russell's.  I 
>: was just wondering if the entire situation could be resolved by an axiom 
>: which doesn't allow sets to be members of themselves, or does this lead 
>: to other problems?  Thanks for any help--
>
>I'll just say that this is not enough. You also get in trouble if a set is
>a member of a member of itself and so on. So you need a stronger axiom
>to prevent that. But let someone else say what axiom - it's been too long.

In my youth I wasted time playing the computer game Adventure. ("You
are in a maze of twisty little passages, all different.") Being the
mathematically perverse kind of person I am, I instructed the machine
"put sack in sack". It was clever enough to say "You can't do that."
Unsatisfied, I tried
	put sack in bottle
		OK
	put bottle in sack
		OK
All future attempts to retrieve either item met with "You can't get at it".

Clearly programmers should be forced to take axiomatic set theory to
learn what needs to be done...

dave