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Topic: What are sets? again
Replies: 21   Last Post: Dec 9, 2012 10:12 AM

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Posts: 1,968
Registered: 12/4/12
Re: What are sets? again
Posted: Dec 5, 2012 3:08 AM
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On 12/4/2012 10:02 PM, Zuhair wrote:
> On Dec 5, 5:06 am, fom <> 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...

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