"The inherent self-referential paradox in replication was noticed by Rosen
("On a logical paradox implicit in the notion of a self-reproducing automaton"
Bull. Math. Biophys. 21: 387-394[1959]), ......An intended refutation of the
paradox by Guttman (1966) operated with the idea of probabalistic (and hence
imperfect) replication; it completely misses the point, however. ........
........Think of an automaton as a function f: A--->B. Since we did not
specify what B as a set stands for, it can be, for instance, a machine that
synthesizes other automata. Self-reproduction of f would then mean a situation
when f is in B. However, in usual mathematics, functions are used for
computation, and to compute B we need to define f: it is defined however, only
if B is defined, but f is a part of B.........
(The probabalistic argument) assumes that to produce a slightly different f'
instead of f solves the problem. That a probabalistic setting actually does
not help is visible from our exposition, and was first pointed out by Loefgren
("An Axiomatic Explanation of Complete Self-Reproduction", Bull. Math. Biophys.
30, 415-425 [1968])."
This seems to have bearing on Goertzel's claim that "stochastic computing"
is the way to overcome any failure of "normal" Turing machines by replacing
them by random machines.
7.6.3 Autopoiesis [p 387]
"Autopoiesis should be praised for being a first clear formulation of ideas
on self-maintainance processes. In this sense the theory of autopoieses is a
forerunner of our own theories. .....
....Let us start to examine the main statement of Maturana and Varela,
namely, that autopoiesis involves a distinct mode of existence and a new type
of logic. In the self-producing circle there is no first element and the
beginning presupposes the end. Hence, according to autopoiesis, the linear
cause-effect logic of causal systems is no more applicable. This standpoint
is easily understandable if we consider how referentiality and
self-referentiality are related. If we understand self-reference as the
situation in which a function f is applied to itself ( as f(f) = . or
f(.) = f etc.), then the basic form of what we may call a REFERENTIAL
RELATION is simply the function f. Such functions are interpretable as
expressions of causality if applied to processes, as we know: it follows that
self-reference would correspond to SELF-CAUSALITY, in the most straightforward
interpretation( this is discusssed by Hart 1987)."
skipping forward....." The self-referential, autonomous units concieved in the
autopoiesis theory are ultimately closed to themselves. They are examples for
the Kantian Ding an sich. If self-reference and autonomy are complete, there
is no window left in the system through which we can peep. more importantly,
there is no possibility to define or modify the system from the outside.
It is very logical that Maturana and Varela go on to explain evolution as a
random drift process."
finally.....he compares this approach to evolution to its counterpart in
cognitive science....then
"Autopoiesis is in line with these efforts [the neutralist alternative to
the selectionist position and the emphasis on internal organization in the mind]
And yet, i think its conclusions are wrong. They come from the rigid,
closed-to itself construction. Evolution need not be random if it is not
selectional; the mind need not be closed if it is not commanded from outside."
Thus, the ideas of Rosen, as developed by Kampis, are able to cature the
thrust of the autopoietic goal without its shortcomings, it seems. Being
closed to efficient cause ids distinctly more flexible than being
"organizationally" closed, yet retains all the good stuff it seems.
Please help me see my error if I am misrepresenting any part of this.
Best wishes,
Don Mikulecky
Mikulecky@gems.vcu.edu