> MG> Furthermore, this modal logic [G] is not firstorder
>> definable (since the additional axiom requires that the
>> accessibility is wellfounded).
>
> That's fine, if you're concerned about nonwellfounded
> sets. (01)
Michael's point has nothing whatever (inherently, anyway) to do with
nonwellfounded sets, John. A Kripke structure, as you know,
consists of a pair <W,R> such that W is nonempty and R is a binary
relation over W; all Michael is saying is that Loeb's axiom is valid
in a Kripke structure <W,R> only if R is wellfounded, i.e., there
are no infinitely descending Rchains, otherwise put, for every
"proposition" over W (i.e., subset of W) there is an Rleast world in
which it is true. This, again, has nothing at all inherently to do
with wellfounded sets  though in fact it turns out to be quite
fruitful to think of Kripke structures as certain sets of nonwf sets
(where R is the membership relation on those sets), thanks notably to
lovely work by Larry Moss and the late great Jon Barwise. (02)
> CM> I am quite certain that your claim about the number
>> of papers published about S5 is not even close to true,
>> given vast literature on provability logics, temporal
>> logics, logics of belief, and many other applications
>> of modal logic where S5 is inappropriate.
>
> Yes, I was reacting to the significant number of papers
> that try to apply S5 to databases and ontologies. The
> database field, in particular, has practitioners who
> have inflicted many shortsighted disasters on us and
> theoreticians who publish papers that are irrelevant
> to anything that could ever be used in practice.
>
> CM> Yes, of course, because S5 is meant to reflect a
>> context where "law" means something like "logical
>> necessity". It's perfectly appropriate for laws in
>> that sense to be constant across all possible worlds.
>
> Unfortunately, S5 has been applied in fields where the
> "laws" are domaindependent constraints  and that
> makes the applications impossible to generalize.
>
> CM> Which, if true, simply goes to show that S5 is not
>> the right modal logic for modeling DBs.
>
> Or knowledge bases, or ontologies, or.... (03)
I strongly disagree with you there. The relevant necessity in many
ontological contexts is logical necessity, in which case S5 seems
perfectly appropriate. It even seems appropriate for physical
necessity, frankly, i.e., where "[]p" is true at a world w just in
case p is true in all worlds that share w's natural laws. (04)
> What applications can S5 support other than publishing
> papers in the Journal of Tenure and Promotion? (05)
Please, John, that's ridiculous. For one thing, if you were to look,
you'd find that, even in philosophy, a huge amount of work has been
done on logics other than S5, notably, deontic and temporal logics.
And the emphasis on S5 itself has been quite reasonable. The reason
S5 has been popular, once again, is that it is arguably the best
logic for logical necessity. Logical necessity in turn has been
dominant in contemporary metaphysics for the past forty years largely
because of its relevance to issues in the philosophies of logic,
language, mind, and science that were dramatically revitalized not
only by the rise of possible world semantics but also by the so
called "new" theory of reference developed by Kripke, Putnam, and
others. To allude to some sort of Great Academic Conspiracy that is
selectively limiting and controlling the direction of academic
research in modal logic is, frankly, beneath you. There are
excellent reasons for studying S5 in both pure and applied contexts
and excellent reasons for studying other modal logics as well 
research on *both* sides here has been very robust and wellmotivated. (06)
chris (07)
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