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Topic: My final formal answer as to what classes are and what class
membership is!

Replies: 7   Last Post: Apr 7, 2013 4:34 AM

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Posts: 1,635
Registered: 2/27/06
Re: My final formal answer as to what classes are and what class
membership is!

Posted: Apr 7, 2013 12:30 AM
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On Mar 29, 4:30 am, Zuhair <> wrote:
> On Mar 29, 5:30 am, fom <> wrote:

> > It needs work Zuhair.  You are either presenting
> > 4 different definitions that you believe to be
> > equivalent without proof or you are considering
> > 4 different alternatives.  It is very confusing.

> Why do I prefer this definition?

This is EXACTLY what I was just saying that you do, Zuhair. You try
to formalize something before having a clear idea as to what you are
proposing. You try to solve problems by formalizing. Problems are
solved by creative thinking. Then you make the idea crystal clear,
THEN you can formalize it. Here you are formalizing way before then,
to the point where you don't even have the answer yet - so you list 4
possible solutions!

This is like a child handing in his homework late, pages are torn,
parts are missing, he's scribbled on it "I don't know the answer to
this one but I think it's either A, D, E or G."



> The basic issue is that it requires the least assumptions for it to
> work as a definition of class and class membership. I claim that any
> Other definition would work under more restrictive assumptions.
> This method do not require any kind of metaphysics that mounts to
> saying that part-hood of classes and sublcass-hood are equivalent, nor
> does it require any kind of Canonical naming, nor assumptions about
> atom-hood of names or existence or nonexistence of atomless objects,
> etc.. The only things that it require are trivial characterizations of
> part-hood relation which is Generalized Extensional Mereology and also
> it requires discrete(non overlapping) naming with the background of
> first order logic with identity. All those are basic assumptions. What
> might be warranted to think of is contemplating dropping the powerful
> axiom scheme of unrestricted composition and thus be content with just
> EM (Extensional Mereology) + Discrete naming. Which is very trivial.
> This would save us a lot of commitments connected to unrestricted
> composition like the case with having Chimeras and thus reduce our
> Ontological commitment down to a every trivial level. Of course by
> then discussion of those definitions would somehow differ. The idea is
> that further composition would be committed to comprehension axioms
> that would be added over classes and nothing else. And no doubt this
> would be the least background for a definition of classes and their
> membership! However I do hold that Unrestricted Composition (Axiom 5)
> Naturally extends the natural relation of part-hood, anyhow that is a
> debatable ground.
> As regard your question about fusions those are the Mereological
> counterparts of Unions. In Mereological terms fusions are minimal
> Underlaps. The sum(x,y) is just a fusion of x and y.
> The fusion of all phi-ers is THE minimal Underlap of all phi-ers.
> x is a fusion of all phi-ers iff
> (for all y. phi(y) -> y P x) &
> (for all z ((For all q. phi(q) -> q P z) -> x P z))
> Anyhow regarding the fusion of equivalence collections of names,
> (which is not necessarily of
> all equivalence collections) then I already gave the neccesary
> definition.
> Zuhair

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