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 >
I can see that that should work with what you have done, although I will not take the time to prove it for myself.
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...