John Edser wrote:

>>JE:-
>>Sets CAN be intersected even if they do not have
>>equivalent elements. In this case the intersection
>>is empty. In my case, ALL parental set elements are
>>_defined_ as _equivalent_ units of fitness so they
>>can be 100% intersected. I CAN define them this way
>>if the definition was included within a testable theory
>>of nature, which it was. OK?!?
> 
> 
> JE:-
> PLEASE ANSWER THE QUESTION
> 
There is no question.  Unless you meant the prvious question, which I 
did answer.

> 
>>>JE:-
>>>My proposition re: natural selection supposes
>>>they are always 100% intersected within the
>>>same population.
>>
> 
>>BOH:-
>>But this can only come about if the offspring are
>>products of all the parents, by the definition of
>>an intersection.
> 
> 
>>JE:-
>>Nonsense. "The offspring" do not
>>have to be "products of all the parents
>>by the definition of an intersection".
>>A set intersection is defined in mathematics
>>not biology!
> 
> 
> BOH:-
> Indeed.
> 
> JE:-
> Can we now take it that you retract your
> crazy insistence that the offspring must be
> "products of all the parents, by the
> definition of an intersection" because
> mathematics _cannot_ define when parental
> fitness set elements are the same allowing
> a non empty intersection between parental
> set of fitness, only a science of biology, can!
> All mathematics can do here, is define
> the condition under which the set intersection
> is not empty. This is when the fitness set
> elements are defined by a science of biology
> to be the same type of fitness elements,
> i.e. equivalent fitness elements. Within
> Darwinian theory all fitness elements have
> exactly the same worth to natural selection,
> i.e. they are all defined as mathematically equivalent.
> Do you agree or disagree? Please answer the question.
> 
You snipped the rest of my reply, from which it should have been obvious 
that I don't agree with your "definition" of intesection, so that hte 
answer to this should have been obvious.

Put simply, biology tells you the properties of the elements.  If 
several elements have the same property, they are in the same set (note 
that elements can be in several sets).  Once you have used the biology 
to tell you what properties an element has, then the mathematics takes 
over, and tells you, for example, which elements are in the intersection 
between two sets (i.e. the elements that have the properties that define 
both sets).


> If you agree:

I don't.

> then all total parental fitness sets can be 100%
> intersected within one population producing all
> the orders of natural selection within that
> population.
> 
> 
>>JE:-
>>{at}# The mathematical rule is: as
>>long as the sets are defined to have equivalent
>>units they CAN be validly intersected, period.
>>They are so defined, so they can be intersected.
>>OK?
> 
> 
> BOH:-
> But this is most certainly not the definition.  I've posted definitions
> 3 times on this thread already.
> 
> JE:-
> Please answer the questions above
> and stop trying to evade these issues.
> 
My answr (as should have been clear) is "no".

> What I wrote above does not contradict
> these definitions. Please say why you
> think it does.
> 
How many times do we have to go over this?  You give conditions under 
which they CAN be intersected, but have said nothing about the 
conditions under which they ARE intersected - i.e. you have said 
absolutely NOTHING about how to tell whether any element is in an 
intersection.  In othe words, you have not defined the operation of 
intersection of sets at all, only given one initial condition.

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/
---
þ RIMEGate(tm)/RGXPost V1.14 at BBSWORLD * Info{at}bbsworld.com

---
 * RIMEGate(tm)V10.2áÿ* RelayNet(tm) NNTP Gateway * MoonDog BBS
 * RgateImp.MoonDog.BBS at 1/9/04 6:13:09 AM