RE: SUO: On the supreme supertype
Dear Pat,
>
> Whatever we call it, a more important question is, should it be
> underneath itself?
MW: I presume you mean: "is it a member of itself?"
>
> I can see arguments both ways.
>
> Pro: Everything that has a name must exist. This thing exists;
> therefore, it should be inside the universe of all things that exist.
MW: The way I have it in my head is that thing is a member of class, and
class is a subclass of thing, so thing is a member of thing. What I
understand from this (particularly following Chris M's recent note) is that
this means that Thing is not a set (neither is class) but a proper class.
>
> Con: hierarchies shouldn't have loops in them, because loops are bad.
MW: Being a proper class means I have isolated the "problem" in some sense
(I'm not sure there is one really - but I acknowledge that strict
hierarchies are convenient and useful where we can identify them, I'm just
not convinced that this is sufficient argument for insisting that things are
strict hierarchies even when they aren't).
Regards
Matthew
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Matthew West
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