fom
Posts:
1,031
Registered:
12/4/12
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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 <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...
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