August West  wrote in news:bu7blf$1r8i$1
{at}darwin.ediacara.org:

> 
> AW:
> I think that the first sentence illustrates the misunderstanding. The
> intersection between any two sets is defined by the identities of the
> individual elements that are members of both sets. Because of the
> nature of the definition of a set, the objects in the intersection will
> all share some properties (at least two because each object in the
> intersection will have the property(ies) that make it a member of set A
> AND the property(ies) that make it a member of set B). Let me make that
> clear: if we are considering the intersection of two sets, all members
> of the intersection must share at least TWO properties. In one of JE's
> examples above, the intersection includes all the cats in both sets
> that have red collars. I don't see how that can be: what are the set
> definitions that would lead to this intersection? We could have set A
> being all cats wearing collars and set B as all cats wearing something
> red, but JE seems to be saying that we could define set A as the cats
> living in house A, and set B as the cats living in house B, and then
> get an intersection C that contains all the cats in house A or B that
> have red collars. Cats that have red collars could indeed be a third
> set, but it is not the intersection. The property(ies) that defines the
> intersection is defined by the two original sets; we can't pick any
> other properties once the original sets are defined.


Just a quick clarification  - I don't think you meant to say that all 
members of the intersection must _share_ two properties, but that they 
must _have_ two properties. They only need to share _one_ property, but 
if they don't _have_ at least two properties they can't be in two sets 
and so can't be in an intersection.

As an aside, I have enjoyed your arguments, wit, and style (and cats, 
although I only currently have one). 


Yours,

Bill Morse
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