Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Background Theory
Replies: 4   Last Post: Dec 8, 2012 6:13 AM

 Messages: [ Previous | Next ]
 Zaljohar@gmail.com Posts: 2,665 Registered: 6/29/07
Re: Background Theory
Posted: Dec 8, 2012 2:23 AM

On Dec 7, 7:21 pm, fom <fomJ...@nyms.net> wrote:
> On 12/7/2012 8:46 AM, Zuhair wrote:
>

> > One might wonder if it is easier to see matters in the opposite way
> > round, i.e. interpret the above theory in set theory? the answer is
> > yes it can be done but it is not the easier direction, nor does it
> > have the same natural flavor of the above,
> > it is just a technical formal piece of work having no natural
> > motivation. Thus I can say with confidence that the case is that Set
> > Theory is conceptually reducible to Representation Mereology and not
> > the converse!

>
> I have no doubt that you are correct.  In another post
> in your thread I summarized the work of Lesniewski which
> uses the part relation to characterize classes.  His
> method was specifically designed to circumvent the
> grammatical form that leads to Russell's paradox.
>

Yes, this is clearly resolved here. A set would be an element of
itself iff
it represents a collection of atoms having it among them, this is not
that difficult
to ponder about since indeed a representative of a group can be among
that
group like in for example a father representing his family. Now the
collection of all
sets that do not represent collections of atoms of which they are a
part (i.e.
sets that are not elements of themselves) can be easily composed in
this
theory but also this theory easily prove that such a collection cannot
have
a representative atom. Set-hood is not about collections of atoms per
se,
it is about uniquely representing those by atoms. So as you see above
what seems to be a counter-intuitive result i.e. the non existence of
the set
of all sets that are not elements of themselves, is actually rendered
a quite
natural and intuitive result by the above line of thinking, that's why
I say that
the real benefit of background theory is that it makes one see the
whole picture
behind set theory, it reveals the whole background Ontology that is
usually hidden
from the customary presentation of standard set\class theories.
This background theory enable one to understand NAIVELY things that
otherwise
would be very difficult to grasp, like non well founded sets, non
definable sets,
non extensional objects, the interplay between classes and sets, the
etc... so to me it aids a lot in understanding those matters.

Zuhair

Date Subject Author
12/7/12 Zaljohar@gmail.com
12/7/12 fom
12/8/12 Zaljohar@gmail.com
12/8/12 fom
12/8/12 Zaljohar@gmail.com