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

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 Zaljohar@gmail.com Posts: 2,665 Registered: 6/29/07
Re: What are sets? again
Posted: Dec 4, 2012 11:49 PM

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.
>

Correct. However in this theory weak supplementation is provable for
collections of atoms.

> As for no empty set, Zuhair may have seen this axiom in a formulation of
> mereology where the axiom was intended to preclude existence of a null
> part.  This is a standard ontological position among those individuals
> who investigate and reflects a position once taken by Frege in
> criticizing the likes of Hausdorff and Cantor:
>
> "... a forest without trees."
>
> Moreover, Zuhair's construction is similar to Zermelo's 1908 paper on
> set theory.  Heijenoort's translates Zermelo's "Teil" -- that is,
> subsets of nonvoid sets -- as "parts", and, the null set is introduced
> separately.
>
> This is precisely what Zuhair has attempted to do.
>
> <snip>

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