Re: Set Nesting and Set Intersection Within Evolutionary Theory

[This is a resend. The original sent Fri 20/10/2006 9:16 AM appears not to
have been posted]

Guy A Hoelzer hoelzer@xxxxxxx wrote:-

JE:-
I would like to thank Guy for this clear response. I think we differ
as to
exactly what type of subset sexual selection constitutes. A nested
subset is
not equivalent to an intersecting subset. From Guy's previous
responses I
will assume that he means an intersecting sub set and not a nested sub
set.
Is this correct?

No. In fact, I take the word "subset" to be inconsistent with
"intersecting
sets."

JE:-
Ok. You are NOT assuming a set intersection between sexual selection and
natural selection? Please confirm.

I see sexual selection as completely, 100% nested within the concept of
natural selection. No aspect of sexual selection strays outside the
scope
of natural selection. I don't think that I have ever been ambiguous on
this stand.

JE:-
I take it that you do not repudiate the use of set intersection within all
models of evolutionary theory just in this particular case?

In set theory it is possible for A to entirely intersect with B such that
all of A becomes a subset of B. This remains mathematically
indistinguishable from A nested within B but only because mathematics
ignores set nesting. Mathematics is only concerned with the number of the
most primary set elements which remains the same in either case. OTOH the
sciences must distinguish between "A nested within B" and any case of just
"A intersected with B" because they remain _empirically_ different. My point
was: If you take the Darwinian proposition (which you appear to agree with)
that sexual selection was and always has been a nested subset of natural
selection and then proceed to oversimplify this allowing sexual selection to
just intersect with natural selection, then such an oversimplified model can
now allow a contradiction _excluded_ by the theory. This means via such a
reduction the model can now contradict the theory it was oversimplified from
allowing cause and effect within just an oversimplified model to become
entirely reversed! As an example, Neo Darwinists originally assumed set
intersection and not set nesting between sexual selection and natural
selection in their attempts to explain the extinction of the Irish Elk by
allowing the demise of this species to be caused by sexual selection and not
natural selection.


http://en.wikipedia.org/wiki/Irish_Elk



The sexually selected trait of antler size became larger and larger. The Neo
Darwinian argument that sexual selection can validly contest and win against
natural selection resulting in the extinction of the Irish Elk species was
invalid. Sexual selection can only contest and win against natural section
if it is proposed that they only intersect, which you agree remains
prohibited.

The reduction of nested sets to become just intersecting sets within Neo
Darwinism remains common, e.g. the proposal of independently and not
dependently selected meiotic drive genes. Gene centric Neo Darwinists have
proposed using their popular gene centric "selfish" gene model to explain
how meiotic drive genes become selected in nature. They assume that these
genes only form intersecting and not nested sets with non selfish genes
allowing them to independently compete against each other. A modeling
reduction of set nesting to just set intersection has allowed genes driven
by a non random form of meiosis to contest and win against their more common
non driven counterparts for the selection of exactly the _same_ body when
such an event is possible. This is because genetic selection, like sexual
section, remains a nested set and not just an intersecting set with
Darwinian natural selection which empirically and refutably restricts the
most outer nested set to just the fertile organism level of selection.

Evolutionary theory (no matter what you predicate it on) requires an
assumption of fitness. You argue that fitness is just reproduction *AND*
survival but I argue that it is reproduction *OR* survival. IOW your
conjunction of reproduction with survival represents yet another set
intersection whereas mine remains a nested set proposition (proven by the
use of OR). Since the testability of evolutionary theory depends almost
entirely on defining fitness, using your conjunction "AND" does not allow a
test to refutation to exist reducing evolutionary theory to just a dictate.
OTOH using "OR" does provide a refutation as the simple reverse of the
proposed set nesting: the prohibited set nesting of reproduction within
survival for an objective measure of fitness. It can be empirically shown
that survival limits reproduction in the same way that sexual selection
limits natural selection proving them to be _one way_ set nested
assumptions. The proof is simple. In either case only one CAN be assumed to
be maximized. Natural selection is maximized and never sexual selection just
as reproduction is maximized and never survival. In general, only the most
outer nested set can be maximized in any nested set proposition whereas all
intersecting sets can be.


All subsets are nested entirely within the full set.

JE:-
They can be either IRREVERSIBLY or just IRREVERSIBLY assumed to be
so...[snip]

This is not an option in the way I am using the concept of nestedness
here,
because I do not take the concepts of natural and sexual selection as
dynamic ones.

JE:-
Dynamic or not, the nested set assumption always describes an irreversible
proposition whereas intersecting sets remain reversible. In general: B
nested in A excludes A nested in B whereas B intersecting with A does not
exclude A intersecting B. The difference between them is _enormous_.

Mathematically oversimplified Neo Darwinistic models can reduce set nesting
to become just a set intersection allowing a contradictory proposition which
remains _excluded_ by the parent theory to the model. In the case of sexual
selection any reduction of its relationship to natural selection as a set
intersection allows sexual selection and natural selection to act
independently. This is absolutely required to allow one to be able to
contest and win over the other. However, the set nesting structure of the
theory the model was oversimplified from entirely prohibits any such thing.
This is because the reverse set nesting of any nested set proposition
represents a refutation of the original proposition. If it is proposed that
A is nested in B but it becomes discovered that B remains empirically nested
within A then this verification refutes the original proposition. This is
not the case for set intersection. If it is proposed that A intersects B but
it is discovered that B intersects A then the original proposition remains
verified.


Reversibility requires change (dynamics), which simply do
not
exist in this context.

JE:-
This depends on what you mean by "change". In the set nesting context this
can only mean one thing: a prohibited reverse of the original set nesting
proposition which is B nested in A OR A nested in B. OTOH set intersection
allows both, i.e. B intersected with A AND A intersected with B.
The conjunction "and" means something very different to "or". Only set
intersection allows additive (via the use of "and") and therefore set
independence. OTOH "OR" provides non additive set nesting with set
dependence (the smaller nested set remains dependent on the larger).


These concepts cannot be reversed or changed in any
way that would permit a relationship other than one in which sexual
selection is a subset of natural selection.


Natural selection is a process
that applies to any heritable variant in a population of reproducing
entities that influences fitness (a function of both survival and
reproduction), while sexual selection is a form of natural selection that
emerges when heritable variants in such a population specifically
influence
reproductive success through social interactions. So, sexual selection is
more narrowly defined in such a way that it occupies a portion of the
landscape existing under the definition of natural selection. Natural
selection includes all of sexual selection without exception.

JE:-
But Neo Darwinistic oversimplified models commonly assume what you say must
remain excluded: just a reversible intersection of sexual selection with
natural selection. As I have outlined in some detail, this is not the only
case of a deliberate reduction of set nesting to just set intersection in
order to construct a Neo Darwinian model. The use of such reduction always
constitutes a misuse when it allows the reverse nested set proposition of
the parent theory. The term "misuse" can be defined in an entirely objective
and testable way: any oversimplified model which has been allowed to contest
and replace the theory it was oversimplified from.

Regards,

John Edser
Independent Researcher

edser@xxxxxxxxxxxxxx


.

Relevant Pages

  • Re: Set Nesting and Set Intersection Within Evolutionary Theory
    ... You are NOT assuming a set intersection between sexual selection and ... natural selection. ... I take it that you do not repudiate the use of set intersection within all ... most outer nested set to just the fertile organism level of selection. ...
    (sci.bio.evolution)
  • Re: Total Darwinian Fitness as a FALSIFIABLE FITNESS MAXIMAND
    ... bioepistemic evolution as a multirank selection system in which the ... I did did discuss "Nested Sets of Fitness" with Dr Bob O'Hara a few ... organisms reproduced with three genes in each is NOT equivalent to a TDF ... Any set intersection requires shared elements to have something defined ...
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    ... I did did discuss "Nested Sets of Fitness" with Dr Bob O'Hara a few ... the unit of selection problem within evolutionary theory because only ... organisms reproduced with three genes in each is NOT equivalent to a TDF ... Any set intersection requires shared elements to have something defined ...
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