August West  wrote in
news:bukvps$1694$1{at}darwin.ediacara.org: 

> When I wrote the paragraph, I DID mean to say that all members of the
> intersection must share two properties. On further reflection, I think
> I still mean that. Perhaps I'm missing something here. My thinking
> runs as follows. The members of set A all share the properties that
> define set A (for simplicity, let's say that set A is defined by one
> property, so all members share that property). Similarly, the members
> of set B all share the property (again, assuming one property for the
> present discussion) that defines set B, and this property is different
> from that defining set A (else sets A & B would be the same). Any
> member in the intersection of A & B (call it set C) must manifest the
> property that defines set A AND the property that defines set B, thus
> all members of C share the two properties that defined the original
> sets. Of course, set C has a defining property - namely, the
> combination of the set A & B definitions - and all set C members share
> that property, so perhaps this is the sense in which you meant that
> they all share ONE property.

No, I was just being stupid. The set of red cats and the set of red dogs 
share the property of being red, but the intersection is null.  You did 
correctly point out the source of my error - I was visualizing an 
intersection, and seeing the intersection as having a geographic location - 
but the intersection needs to share two properties. Maybe that's why I have 
so much trouble trying to use set definitions when I work with databases 
:-)

 
> As an aside, it seems to me that this is where JE's mistake lies. The
> properties that define set C, the intersection, are determined by the
> set A & B definitions. We are not allowed to look for further
> similarities that are not in the definitions of set A & B. That is,
> given the definitions of set A & B above, I cannot go on to say "Hey,
> wait a minute, all the cats in set A & set B have two ears, therefore
> because there are fewer cats in set A, set A is a subset of set B".
> This is exactly what JE does in his examples. He argues that we can
> define sets A & B, and then look for other common properties OUTSIDE
> of these definitions to determine the intersection. In reality, the
> property defining the intersection is fixed by the the two initial set
> definitions. Thus if set A is offspring of parent A and set B is
> offspring of parent B, the intersection is now AUTOMATICALLY defined
> as "offspring of parent A AND parent B".

I wish I could understand where John Edser is coming from in his sets of 
offspring. I have sometimes thought I understood him, but then when I try 
to put that understanding down on paper, it makes no sense.


Yours,

Bill Morse
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