FOM: Axiom of Extensionality

[Kanovei]

>From: "Dean Buckner" <Dean.Buckner at btopenworld.com>
>Date: Fri, 17 May 2002 18:46:20 +0100

>Or take the set {Alice, Bob, Carol}.  Does this continue to exist even if
>they cease to? 

To answer this question one has to carry out one simple 
thing: give a precise unambiguous definition what each 
term means, for instance, what is Alice. 
This can be a thing in the physical universe or a concept 
of some science like "the number $\pi$" or a recognizable 
object of another kind, no matter what but unambiguously 
specified. 

For instance, U="the set of all unicorns", to understand this 
one has to specify what is going to be a unicorn. 
Any educated one would say that this is a certain concept 
in ancient naturphilosophy, a name of a nonexistent animal. 
In this sense, U ={u} is a (non-empty) singleton, where u is 
the concept as described. 
If on the contrary one means, by unicorn, an extant animal 
roaming somewhere on the Earth, 
which satisfies the concept in all major detail (including 
myphical) then the set U becomes empty.  

As soon as one is going to be precise enough rather than 
trying to capitalize on intentionally vague and ambiguous 
setup, questions like the above get a simple resolution. 

V.Kanovei