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Re: My final formal answer as to what classes are and what class membership is!
Posted:
Apr 2, 2013 9:17 PM


On Mar 30, 8:09 am, Zuhair <zaljo...@gmail.com> wrote: > 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.
The title of your thread is "My Formal Answer . . ." so you're already formal and it is obvious that you are trying to be formal in the use of nonEnglish syntax.
Zuhair, this happens every time you try to define a formal system. There is so much that is missing or illdefined. I always tell you to do things like give an informal description and use a more appropriate language. But you seem to always brush aside any comments and say you immediately fixed it or you knew about it and it isn't actually a problem because you really meant something else, even though the other party is quoting you directly.
I have formally axiomatized at least 5 branches of math/logic/cs and know exactly what you need to do. And my various principles such as not having complex primitives are well grounded in practical use.
Don't you think you could make better use of this space if you just listened to what people say instead of just adding even more and saying you fixed the first mistake by adding more syntax on top of that?
CB
> > 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



