[SCL] Re: Observation

[Michael Gruninger]

pat hayes wrote:

> BUt the conventional MT for FOL assumes a segregated vocabulary, maps
> relation symbols to relations which are *identified* as sets of
> tuples of members of I, and quantifies over I; and is usually
> interpreted relative to Z_F set theory which has the axiom of
> foundation. So the things in the domain cannot be the relations named
> by the relation symbols, in such a picture. It is this fact plus the
> (false, but widely believed) idea that the axiom of foundation is a
> safety bulwark against paradox, which I strongly suspect is the
> reason for the passionate Horrocks/Patel-Schneider defense of
> conventional FOL semantics.
>
> BTW, all this makes me think that it might be worth stating the MT in
> 'conventional' terms ( ie without an explicit extension mapping) but
> being explicit that we are using Aczel's set theory rather than Z_F:
> what do you think?
>

Hi Pat,
if you are suggesting using non-wellfounded set theory as the basis
for SCL semantics, I would agree. I suggested this long ago, but it
seemed that people were reluctant to leave ZF.

- michael