[SCL] the relational component of an SCL interpetation

[Chris Menzel]

On Thu, Nov 13, 2003 at 11:52:09AM -0600, Pat Hayes wrote:
> [Robert Kent wrote:]
> >I believe that this is related to endnote 5: "It is possible to
> >model of the members of R extensionally as sets, though this will in 
> >general require non-well-founded set theory, since a relation, qua
> >individual, can be in its own extension." Is this true?
> 
> Yes
> 
> >Is the purpose of R to proscribe self-membership? If so, how exactly
> >does this work? Can we not just simplify as mentioned above and
> >verbally proscribe self-membership?

R is there (among other reasons) precisely to *allow* self-membership
(better, self-predication) without requiring one to adopt a
non-well-founded set theory.

> BUt in fact there is another reason for using this construction, in
> that it allows SCL to axiomatize an intensional theory of relations:
> for example, there can be several distinct universally-false relations
> (several empty classes, in class terminology.) This is a notable
> advantage in many applications.

Right.

-cm