Date: Mar 30, 2013 8:09 AM
Author: Zaljohar@gmail.com
Subject: Re: My final formal answer as to what classes are and what class<br> membership is!

On Mar 30, 7:33 am, fom <fomJ...@nyms.net> wrote:
> On 3/29/2013 9:37 AM, Zuhair wrote:
>
> <snip>
>
>
>

> > See:http://zaljohar.tripod.com/sets.txt
>
> > Zuhair
>
> I suppose I had been a little harsh
> the other night.  So, I wanted to
> take a moment to apologize.
>

Na, your responses were positive, they stimulated me to write my
definitions in a formal manner as to avoid any ambiguity.

> I know you have been trying to investigate
> set theory in relation to mereology.
>
> But, if you are going to pursue this use
> of a 'name' relation, you should take
> the time to look at some of the web
> pages to which I directed you.  Whether
> or not David Lewis is using a formal
> symbol conveying the sense of a name,
> there is a relevant body of philosophical
> inquiry that applies.


Actually I read some of the links you've supplied, I know about some
of them actually, but thanks a lot for supplying those links, they've
enriched my information. I need to see to what extent such material
would influence what I've been doing. But for the moment, it appears
as if what I'm trying to do is something more trivial than what is
presented in those links, and somehow unrelated. But of course you are
right since I've used the term "name" in my axiomatization. Actually
Randall Holmes use the word "label", also a similar word might be
"token". What I'm referring to as "name" is actually nothing but a
referent object, i.e. an object that refers to a particular object, so
naming here is nothing but a reference relation, it is between objects
and objects and not between symbols and their semantics as with
naming. Perhaps I should have used the term "referent" instead of
name.
so instead of x name of y we can use x refers to y. So "referent" here
is used in the sense of something that refers to and not in the sense
of something that is referred by. so we can say x is a referent of y
to mean actually x refers to y. And also x is a referent iff Exist y.
x refers to y.
Anyhow. What I called as naming relation is actually nothing but
discrete reference which is a very trivial and very circumscribed
concept, unlike the diffuse concept of naming discussed by Russel and
Mill.

I'm recently contemplating some "Local" kinds of trivial sets that
violate the discretness axiom of names that I've presented. A nice
example is to consider every name to be a PART of what it names. In
this context a name is actually a MARKER. Of course the definition of
membership would change into an object whose marker is a part of an
equivalence collections of markers, and of course there must not exist
a marker of any object that have the marker of the member as a part of
it. This will interpret sets in Simple type theory. Also If we add
that all objects are fussions of atoms, the nice thing is that there
would be a finite upper bound on membership for each set, i.e. each
set x with have a maximal bound n(x) such that there exist up to n(x)
iterated singletons of it, i.e. for each x we can only have {x},
{{x}}, {....n(x)times...{x}...}. A somehow strange result. However
this is a local case of sets and no such stipulation can hold for the
general case of membership of sets wide across.

Anyhow I do think that pondering along the lines I've presented
(originally by Lewis) is fruitful.

Zuhair