Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: My final formal answer as to what classes are and what class membership is!
Posted:
Mar 30, 2013 8:09 AM


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



