Date: Dec 5, 2012 3:02 PM
Author: Zaljohar@gmail.com
Subject: Re: What are sets? again

On Dec 5, 11:08 am, fom <fomJ...@nyms.net> wrote:
> On 12/4/2012 10:02 PM, Zuhair wrote:
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> > 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.
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> >> You have made an incorrect step here.
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> >> 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.

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> >> 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.

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> > 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...