[FOM] A minor issue in modal logic
rgheck at brown.edu
Mon Jul 5 21:23:06 EDT 2010
On 07/05/2010 02:36 PM, Michael Lee Finney wrote:
> I would agree that Np => p does not hold in all modal logics, such as
> denotic or provability logics. However, it does appears to be the
> defining minimal characteristic for logics of necessity. It is the
> basis of the classical system T. There are many other modal logics in
> which this doesn't hold, but they aren't generally regarded as logics
> of necessity.
> It appears to me that you confuse the general idea of modal logics
> with the more specific idea of necessity logics. So if Np => p is not
> validated in all necessity logics, what properties do you see as
> defining the minimal properties of necessity -- as opposed to the
> many other modal logics? You could have Np => Pp as a weaker
> condition (the basis of the classical system D), but that is usually
> considered to be basis of denotic logic (at least when Np => p is not
> also present).
I don't have a general view on this topic, and I'm not sure why I need
to have a view about what characterizes "necessity logics". I'm not even
sure there are "necessity logics", i.e., that there is any natural kind
so characterized. I simply meant to leave it open that someone might
want to deny:
(*) Np |- p
I don't think that's insane. One can of course stipulate that one isn't
dealing with a notion of necessity unless (*) holds, but I'm not sure
what the argument for that would be. Maybe there is one; maybe not.
In any event, as I've said elsewhere, the issue concerned:
NAp |- Np
or more weakly:
NAp |- p
and the remark about (*) was by the way.
More information about the FOM