🚀 go-pugleaf

In article <1992Nov3.041515.27732@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>In article <1992Nov2.205433.21208@tamsun.tamu.edu> cmenzel@tamsun.tamu.edu (Chris Menzel) writes:
>>In article <1992Nov2.040843.4524@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>>>That it [Foundation Axiom] is self-evident to you now seems more
>>>an accident of culture---your training---than of something inherent in
>>>the notion of set....
>>
>>I think that's too strong if, like me, you were introduced to set
>>theory via the iterative hierarchy.  If that's your picture of sets,
>>then the axiom *is* self-evident, and well-foundedness *is* an
>>inherent property of sets.  The question is rather whether the
>>iterative hierarchy encompasses *all* the sets, or whether we've just
>>been looking at a rather limited portion of the universe, as is the
>>case if we take the universe to be nonwellfounded ala Aczel.
>
>The iterative hierarchy is consistent with Z but not with ZF.
>Replacement (F) says in effect that any construction you can iterate
>yields a set.  Hence if the universe is an iterative hierarchy it is a
>set.
>
>Anyone brought up on the iterative hierarchy was told a lie.
>-- 
>Vaughan Pratt			Ain't no truth in logic, son.

This remark is ludicrous.  Constructions iterated on the ordinals do
not necessarily form a set in ZFC, since the ordinals do not form a
set (so Replacement cannot be applied).

-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu