Re: Total Darwinian Fitness as a FALSIFIABLE FITNESS MAXIMAND
- From: johnhewitt22@xxxxxxxxx
- Date: Tue, 17 Mar 2009 11:35:28 -0500 (EST)
Dear John,
May I begin by saying that, even though he uses a silly name, I agree
with one observer, "sam the centipede," that you should probably put
your ideas together into one place. I disagree with most of the rest
of his comments.
Your comments about nested sets bring to mind my views on evolution.
As you may know, I think it is incorrect to regard evolution as
fundamentally a genetic process; instead, I hold that evolution should
be regarded as fundamentally a data process and therefore best
described in terms of data systems. I call the evolutionary ideas that
emerge from that perception bioepistemic evolution. As you will also
know, data systems can be arranged in ranks of super-systems, systems,
subsystems and sub-subsystems etc. ad infinitum. That led me construct
bioepistemic evolution as a multirank selection system in which the
different ranks have this kind of hierarchical, systems - subsystem
relationship to one another. (Bioepistemic evolution is an example of
what many people call multilevel selection but it is constructed in a
less arbitrary way than some of the approaches found in the scientific
literature.)
It seems to me possible that your nested sets are, in some sense,
linked or related to these different ranks of evolving systems but I
do not understand your ideas sufficiently well to grasp the possible
connection between them. Can you clarify what you are saying about
nested sets or refer me to a more extended discussion?
Sincerely
John Hewitt
On Mar 16, 5:47=A0pm, John Edser <ed...@xxxxxxxxxxxxxx> wrote:
JE:-
Hi cccccccccc,
I did did discuss "Nested Sets of Fitness" with Dr Bob O'Hara a few
years ago ago and I thank him for his input. The concept was new to me
so I am sure I made some mistakes. One of the important points with
regard to internet group discussion is to introduce newer concepts of
which the author is not so sure.
Here is a summery of my updated view. Of course, I greatly appreciate
your rational criticism of it. What I contribute to sbe remains
falsifiable which I consider to be just a basic requirement. I will
start an outline with a discussion of proper (nested) sets which are NOT
equivalent to intersecting sets.
Non mathematical propositions require NON reversible proper subsets
(nested, Russian Doll set types). These form the A,E,I,O logical
relationships which remain the basis of ANY proposition (including those
of mathematics). In turn these A,E,I,O propositional sets can be
associated to form The Traditional Square of Opposition which provides a
key for understanding the difference between a non verification and a
falsification. To the left of each corner of the square can be found a
non verification while diagonally opposite a critical falsification. A
verification can be located to the right of each corner. This square
represents the cornerstone of any argument which can be proposed to be
reasonable.
As an example Popper's proposition of "all swans are white" nests the
subject "swan" (S) in the proposed predicate (P) "white" excluding the
reverse. The nested set reversal "all white (things) are swans"falsifies
the original. A reverse set nesting of "white" within "swans" excludes
"all swans are white" because the same meaning cannot be preserved
within any set nested reversal. A tautology (any self referential
proposition) is composed of a simple equality proposed to exist between
S and P =A0e.g. in Poppers proposal "white" would now have to be
equivalent to a "swan" allowing S=3DP and P=3DS. Nested associations are
strictly NON reversible and NON additive. Multiplication using Russian
Doll sets is not the same as multiplication within mathematics because
the commutative law does not now apply. For example, two books
containing three stamps each is not equivalent to three books containing
two stamps even though both describe six stamps in total. What the
commutative law does is delete the "book" level as an
oversimplification. This critical deletion has direct implications for
the unit of selection problem within evolutionary theory because only
each book can be naturally selected within Darwinism, i.e. _not each
stamp_. This is because the fitness of each set of stamps remain 100% at
their book level and not the reverse. To select any stamp you must
firstly select one whole book. Thus a parental TDF of two fertile
organisms reproduced with three genes in each is NOT equivalent to a TDF
total of three organisms reproduced with two genes each _even if the
total number of genes replicated remains the same_. IOW, using today's
popular Neo Darwinian gene level of selection (which was and remains
just an uncorrected mathematical model within which the fitness
epistatic organism level has been deleted for convenience) these fitness
remain the same.
Mathematics can only employ entirely reversible (intersecting) set
associations otherwise the commutative law would have to be deleted
destroying mathematics. This is because everything in mathematics has to
remain reversible across "=3D", ">" ands "<" signs. Intersecting sets are
alone, 100% reversible as in: if A intersects B then B intersects A.
OTOH nested sets remain 100% NON reversible: if B is proposed to be a
nested subset of A then A cannot possibly be a nested subset of B. In
short what is meant by "additive" within evolutionary theory is any set
intersection and what is meant by "non additive" is any nested set in
which the commutative law does NOT apply. It should be noted that the
nested situation remains EMPIRICALLY basic. IOW, mathematics is based on
an oversimplification of empirically based reason. In short, mathematics
is based on science, science is not based on mathematics.
Any set intersection requires shared elements to have something defined
in common. For example the intersection of the sets "tables" and "wood"
constitutes all the tables made from wood. Thus the intersection of 100
tables of which just 5 are wooden with 100 wooden other things leaves 5
in the intersection and 95 outside in each case. If every table was made
of wood then as far as the table set goes, 100 are in the intersection
and nothing outside of it. In this case the table set remains non empty,
just 100% intersected. At any time this intersection can be reversed
without any change being applied to any intersected set element. This is
not the case for nested (proper) sets.
Since every TDF total represents a falsifiable, Darwinian Fitness
constant per parent per population, then every TDF can validly be
intersected with every other _in the same population_. I contend that
this automatically calculates a natural selective result for any
population where only the largest TDF can be naturally selected FOR.
The winning reproductive total constitutes a TDF with some set elements
which are NOT intersected, i.e. a selected for TDF must display non
shared set elements. Quite clearly, intersecting sets of TDF totals
within which every reproduced fertile adult constitutes a single set
element (which is independently additive and and not dependently non
additive) is just a default process, i.e. no more complex system is
required to make it. Any INDEPENDENT fitness count, i.e. the TDF tally
of a proposed INDEPENDENT IN FITNESS unit of selection must remain 100%
additively associated with every other TDF in one same population.
Things added (reversibly intersected) have absolutely no impact on each
other allowing each element to remain fitness independent_. Natural
selection occurs via the simple default of the intersection of every set
element within each TDF tally per population of just fertile
individuals. The net result is that ONLY each set element (each fertile
form) can possibly be selected and only populations of these can
possibly evolve. Individuals cannot evolve and populations cannot be
selected. If populations could be selected (as was originally proposed
by Wallace) then the contradiction arises that selected populations are
proposed to be fitness nested AND intersected when they cannot be both.
Populations are empirically, just additive in fitness whereas the
fitness of each part of each fertile adult which constitutes one TDF
fitness set element remains non additive. This critical difference
remains empirically based, i.e. is not just proposition of mathematics
but _a falsifiable proposition of evolutionary science_.
=A0>snip<
Regards,
John Edser
Independent Researcher
ed...@xxxxxxxxxxxxxx
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