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

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 fom Posts: 1,968 Registered: 12/4/12
Re: What are sets? again
Posted: Dec 5, 2012 3:08 AM

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.

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...

Date Subject Author
11/30/12 Zaljohar@gmail.com
12/1/12 William Elliot
12/1/12 Zaljohar@gmail.com
12/2/12 William Elliot
12/2/12 Graham Cooper
12/2/12 Zaljohar@gmail.com
12/2/12 William Elliot
12/2/12 ross.finlayson@gmail.com
12/3/12 William Elliot
12/4/12 fom
12/9/12 Charlie-Boo
12/4/12 fom
12/2/12 Charlie-Boo
12/3/12 Graham Cooper
12/3/12 William Elliot
12/4/12 fom
12/4/12 Zaljohar@gmail.com
12/5/12 fom
12/5/12 Zaljohar@gmail.com
12/4/12 Zaljohar@gmail.com
12/5/12 Zaljohar@gmail.com
12/5/12 Zaljohar@gmail.com