🚀 go-pugleaf

Mike Oliver <oliver@math.ucla.edu> wrote in message news:<3D81259B.ED8BF3C7@math.ucla.edu>...
> John wrote:
> > Mike Oliver <oliver@math.ucla.edu> wrote in message
> > news:<3BF949CB.340F494@math.ucla.edu>
> >> I can't figure out what you're worried about.  Suppose you give
> >> us an example of two essentially different "axioms of extensionality
> >> restricted to sets".
> > 
> > Here's the extensionality principle with which you are familiar.
> > 
> > N4 AxAy[Az(z in x <-> z in y) -> x = y] Classical Extensionality
> > 
> > And here's the extensionality principle you asked that I give.
> > 
> > C4 AxAy[Az(z in x <-> z in y) -> {Et(x in t & y in t) <-> xIy}] Correy
> > Extensionality
> > 
> >> I don't think you can; there's no remotely
> >> plausible way of doing so.  Therefore the phrase is not ambiguous.
> > 
> > Well, what about it?  Do you still hold that the phrase
> > "extensionality restricted to sets" is unambiguous?
> 
> This discussion is from almost a year ago; I looked back at
> it in groups.google.com and can't figure out why I was ever
> interested enough to contribute an article to it.  I also don't
> know whether you're making a distinction between this predicate "I"
> and the equals sign.  But then it's not like I really care.
> 
> I'll admit in principle that it's possible to make a distinction
> based on whether what's "restricted to sets" is the x,y,z or
> just the x,y.

I don't understand what you mean by, 

"...it's possible to make a distinction based on whether
what's "restricted to sets" is the x,y,z or just the x,y."

Nor can I imagine why you would say such a
distinction is "possible in principle", when staring you
in the face is an axiom that makes it.

Finally, when you said, "Suppose you give US an example"
(emphasis added), who (besides yourself) did "us" refer to,
and who did it exclude?

--John