John Edser wrote:

>>JE:-
>>You are welcome. Pay my respects to the
>>white rabbit; he looks unwell...
>>Sets can be supposed to be intersected or not
>>intersected, at will. OK?
> 
> 
> BOH:-
> No!  We've already agreed that intersection has a definition, so sets
> can only be intersected if there are elements that are members of both sets.
> 
> 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:-
>>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!

Indeed.  And it would help if you knew what hte definition was, han then 
applied it to your own theory.

{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?
> 
But this is most certainly not the definition.  I've posted definitions 
3 times on this thread already.

> 
>>JE:-
>>I can make any supposition
>>I like as to the level of intersection as long
>>as the view is incorporated within a testable
>>theory of nature; which it is. OK?
> 
> 
> BOH:-
> OK,
> 
> JE:-
> Thus I am applying set theory within
> a testable theory of biology where I
> can and do, define each fitness element
> to be equivalent within every set, within
> one population. OK?
> 
No, because you're not using set theory.  You're using a different 
definition of set intersection.


> BOH:-
> You're not following the argument:
> 1. You have agreed that elements in an intersection of two sets are
> those which are members of both sets.
> 2. You have defined fitness sets as the offspring produced by a parent.
> 3. You have also agreed that we are not considering sexual species, so
> that each offspring (=fitness element) only has one parent.
>  From this, we can conclude that no fitness element has 2 parents.
> Hence, the intersection is empty.
> 
> JE:-
> Absurd. You cannot *MATHEMATICALLY*
> restrict all fitness set intersections
> as only being valid between parents who
> share the reproduction of the same offspring!
> Nothing in mathematics restricts sets
> of absolute fitnesses being restricted
> this way because mathematics has nothing
> at all to do with the biology. You can
> restrict set intersection this way, within
> however, a contesting theory of biology
> where one of us must refute in favour of
> the other. OK?
> 
Set theory is mathematics, not biology.  If you want to use set theory 
in biological theory, you still have to follow set theory.  You can't 
ignore the rules because then you are not using set theory.  Do you 
understand this - if you're using mathematics to model biology, then you 
must stick within the mathematical logic.



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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