On Dec 5, 11:08 am, fom <fomJ...@nyms.net> wrote: > On 12/4/2012 10:02 PM, Zuhair wrote: > > > > > > > > > > > On Dec 5, 5:06 am, fom <fomJ...@nyms.net> wrote: > >> On 12/2/2012 11:20 PM, William Elliot wrote: > > >>> On Fri, 30 Nov 2012, Zuhair wrote: > > >> <snip> > > >>>> ll. Supplementation: x P y & ~ y P x -> Exist z. z P y & ~ x P z. > > >>> x subset y, y not subset x -> some z subset y with x not subset z. > >>> x proper subset y -> some z subset y with x not subset z > >>> x proper subset y -> y\x subset y, x not subset y\x > > >>> Oh my, no empty set. > > >> You have made an incorrect step here. > > >> In mereology there is no reason to take y\x as substantive. > > >> Supplementation is supposed to enforce existence of a proper part of y > >> in y\x. > > >> In this case, z could be a proper part of x. Then zPy and -xPz is > >> satisfied. > > >> This is not a supplementation axiom in the classical sense. > > > I'm really sorry that I didn't have the chance to look at all of your > > responses. I'd do once I have time. > > Anyhow for now, it is sufficient to note that my theory does prove > > Weak supplementation for collections of atoms that is if x is a proper > > part of y and y is a collection of atoms then there exist a part of y > > that do not overlap with x. > > > Zuhair > > Yes. > > I can see that that should work with what you have done, although > I will not take the time to prove it for myself.
hmmm..., I see that I might have been wrong really. You seem to be right.
What is needed is actually Weak supplementation, which is:
ll. Supplementation: x PP y -> Exist z. z P y & ~ z O x.
where z O x <-> Exist v. v P z & v P x
Zuhair > > Then, of course, your null atom is simply a distinguished atom > in a theory that respects no empty class. > > Don't worry to much about my responses. In part, I was rewriting > your sentences as part of an attempt to understand what you were > doing relative to my own meager knowledge. > > Anyway, George will begin flaming me soon enough...