John Edser wrote:

>>>>>BOH:-
>>>>
>>>>>From the first site:
>>>>
>>>>>"Given two sets A and B, the intersection of A and
B, written A INT B,
>>>>>is the set C of all elements that are in both A and B."
>>>>
>>>>>From the second site:
>>>>
>>>>>"A INT B: A intersection B is the set of all
elements that are in both
>>>>>sets A and B."
>>>>
>>>>>From the third site:
>>>>
>>>>>"Intersection - Denotes the set of elements that
are members of all the
>>>>>sets under consideration."
>>>>>(I've written INT for the intersection symbol, as it
doesn't appear in
>>>>>ASCII).
> 
> 
>>>>>JE:-
>>>>>Only _equivalent_ set elements are in n set
>>>>>intersections and not "the same" set element.
> 
> 
>>>>BOH:-
>>>>Having given you the quotes, I was hoping you would
actually comment on
>>>>them, rather than continue on about equivalence.  It's simply not a
>>>>matter of whether elements are equivalent - it's whether a matter of
>>>>which sets that are members of.\
> 
> 
> 
> 
>>>>JE:-
>>>>I have commented on the quotes, in detail.
>>>>For example, "set C of all elements that
>>>>are in both A and B" means that all the
>>>>set elements in the intersection C are strictly
>>>>_equivalent_ elements and not just elements
>>>
>>>>from one set, i.e not "the same" elements.
> 
> 
>>>BOH:-
>>>This is opaque to me.  Are you saying that the elements in the
>>>intersection C are not also in sets A and B?
> 
> 
>>>JE:-
>>>The concept of equivalence is simple.
>>>Two things may be defined equivalent.
>>>This does not make them the one, same,
>>>thing, but it does mean either of them
>>>can represent the other. All I am saying
>>>is that the elements in intersection C are equivalent
>>>set elements to the set elements in set A and B.
> 
> 
>>BOH:-
>>Now can you answer my question - are you saying that the elements in the
>>intersection C are not also in sets A and B?
>>JE:-
>>All the elements in the intersection C are also in sets
>>A and B.
> 
> 
> BOH:-
> Thank you.  After many months, you finally say this.
> 
> JE:-
> Rubbish.
> I have never disagreed that "All the elements in the
> intersection C are also in sets A and B" as a "how"
> proposition. Please provide a quote of myself where I
> have stated, either implicitly or explicitly that "All the
> elements in the  intersection C are NOT also in sets
> A and B"!
> 

 From the 3rd of September this year:


Totol set intersection does NOT mean the
same 4 offspring are being reproduced
by more than one parent, it means that 4 offspring were
reproduced by one parent and another, different, 4
offspring were reproduced by another, non related parent
within the intersection. Neither of these
2 parents were sexual partners. When you intersect
6 with 4 the intersection contains 4 offspring
from TWO SETS not just one set, producing a total
8, with 2 offspring not intersected. The total remains
10 offspring (6+4 = 10). You have to count the 4
in the intersection _twice_ not just once because 2
sets are being intersected.

You seem not to understand that the intersection
contains a _mixture_ of ALL the reproductions of
every parent in one population. You seem to think
that a mixture of parental fitness elements must
be an invalid category; it isn't. It is simply
the category of fitness comparison.


The second paragraph clearly states that the intersection contains the 
elements of all parents - i.e. each individual in it must be the 
offspring of every parent.  Some orgy!


> We disagree re: a "why" proposition, i.e. why and
> not how, "All the elements in the intersection C are also
> in sets A and B". I stated explicitly that WHY set elements
> within any intersection are also in the intersecting
> sets is simply because that were EQUIVALENT set elements and
> not  the SAME set elements. 

But then you are depaerting from the definitions of intersection. 
Elements are in the intersection precisely because they are members of 
both sets.

Do you/can you, logically
> discriminate within a why proposition, as to _why_
> "All the elements in the intersection C are also in
> sets A and B"?
> 
Err, yes.  because of the definition of an intersection.

> BOH:-
>  Just to check,
> does this means that you do agree with the following definitions of
> intersection (copied from a few days ago):
>   "Given two sets A and B, the intersection of A and B, written A INT B,
> is the set C of all elements that are in both A and B."
>   From the second site:
> "A INT B: A intersection B is the set of all elements that are in both
> sets A and B."
>   From the third site:
> "Intersection - Denotes the set of elements that are members of all the
> sets under consideration."
> (I've written INT for the intersection symbol, as it doesn't appear in
> ASCII).
> 
> JE:-
> Yes, as "how" propositions. The "why" proposition
> has not been dealt with, in the above.
> 
> 
>>JE:-
>>Because all the set elements within the intersection
>>are defined equivalent nobody knows, and nobody is required to
>>know, where the set elements represented within the intersection
>>originated from.
>>You refuse to make any shift from abstract set elements
>>to set elements that are defined as biological entities.
> 
> 
> BOH:-
> Because I had to make sure we both meant the same thing - there's no
> point in talking about the biology if we're using different mathematical
> languages.
> 
> JE:-
> Do you agree that all fitness set elements are equivalent
> but are _not_ just the one, same, fitness element?
> 
I want to nail down the concept of intersection first, before I get onto 
anything else - and we've been on that since June.

Bob

-- 
Bob O'Hara

Rolf Nevanlinna Institute
P.O. Box 4 (Yliopistonkatu 5)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 23743
Mobile: +358 50 599 0540
Fax:  +358-9-191 22 779
WWW:  http://www.RNI.Helsinki.FI/~boh/
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