Dear Friends,
Within the context of my membership of the Autopoiesis-Dialogue list I
received the following posts. I would like to cross post it here in order
that the discussion that Joel Issacson and Hugo Urrestazu are having can be
considered by the Members as I believe that it is very relevant to the
current thread on Causation that we have ongoing. While I have some
technical issues with Hugo's point about the problem of infinite regress in
formal systems, his statements are unusually clear and crisp and deserve
consideration.
Onward!
Stephen
-----Original Message-----
From: Hugo Urrestarazu
Sent: Wednesday, November 17, 2010 6:24 AM
To: autopoiesis-dialog...@yahoogroups.com
Subject: [autopoiesis-dialognet] Re:Autopoietic Recursion Re-Examined
Hi Joel
I would like to react to your post about the "Recursive Distinctioning (RD"
There you state, concerning the notion of Recursion:
". It turned out that the notion of "recursion", invoked repeatedly by
Maturana in many of his writings and teachings, is a bit ambiguous.
Only in the mid-1990 Maturana became more specific in this regard.
This state of affairs seems to have caused some confusion among avid
Maturana followers, and thus it is fairly common to see people
entangle circularity and recursion in a way that suggests that
recursion is the outcome of some natural circularity in the biology
of cognition (rather than the other way around)."
And below, you say also:
". Either repetition or recursion may generate in an observer a
perception of circularity; but, in principle, when circularity is
observed one cannot tell whether it is a by-product
of repetition or recursion. Which obviously means that one needs to
be circumspect when observing circularity and refrain from positing
circularity as the ultimate 'engine' of perception; for it is rather
Recursive Distinctioning.."
I was a student of Maturana, back in the 70's in Santiago. In our
discussions I never encounter ambiguous references concerning the notion of
recursion. As a physicist I was quite satisfied with his account of the
phenomenological explanation of how recursiveness manifests itself in
biological (and hence, cognitive) phenomena.
At the time we concluded that all operations of distinction made by
observers and explained to other observers, can be stated in general for any
observable phenomenal domain, provided that the formal relations used in the
languaging domain in order to describe the relations between the dynamic
entities existing in the observed phenomenal domain express causal
interactions, whatever the causation mechanism may be. This applies also to
the distinction of the phenomenon of recursion as a natural observable
process (note that I talk about an observable phenomenon and not about a
"notion" or abstract concept).
This distinction is essential to avoid a common theoretical snare when
appealing to abstract reasoning. The snare consists of confusing the
phenomenal relationships that an observer can establish on observational
grounds with logical inferences resulting from theoretical formalisms meant
to model an observed phenomenology.
Entailment (meaning strict, logical, or analytical implication, as between
two statements so that one can be deduced from the other on purely logical
grounds) is a cognitive operation involving logical statements of the sort:
"if A is true then B is true" (A entails B), which leads to the definition
of a relation Re (A,B);
whereas causation is a description of observed phenomena involving
statements such as:
"I observe that whenever X happens, then Y happens consecutively within a
finite time interval" (X causes Y), which leads to the definition of a
relation Rc (X,Y).
Both previous statements can be used to define mathematical abstract
relations like Re (A,B) (for entailment) and Rc (X,Y) (for causation), but
the meaning of the word 'then' is quite different in each case.
In the first case it expresses an inference that has significance only in
formal terms with respect to rules, axioms or theorems expressed within a
formal mathematical system with a timeless logical validity.
In the latter case, the word 'then' can be replaced by the expression 'it
happens that', which refers to an observed fact totally unrelated to any
observer's cognitive operation other than the act of observing and its
validity is circumstantial and time dependant.
This distinction between entailment relations and causation relations
becomes crucial when describing reflexive and reciprocal relations between
dynamical entities, because in the first case reflexivity or reciprocity
relations are interpreted as timeless 'recursive' functional applications
leading to infinite regress, whereas in the second case, as the causation
propagation time is explicitly taken into account, reflexive and reciprocal
relations may be interpreted as succession of causation events with a
restricted time dependant phenomenal validity, in which unbounded recursive
causation loops lead to changes and transformations, but never to the kind
of infinite regress or contradiction prone results that pure logical
entailments may produce in our mathematical formalisms.
Causation flow refers to the notions of events occurring in time, of
successions of such events and of observed regularities in those successions
of events. The notion of causal relationship linking objects arisen in our
experience as observers refers to the observation of repeated regularities
in the successions of events concerning those entities, so that we are
allowed to claim that we can distinguish relations that link those entities
together in our perception of their dynamic activity. This is the case (more
or less trivial) of the molecular activity which is the basis of biological
processes, but it is also the case of other higher order phenomena where we
can distinguish dynamical entities interacting together, like the neural
activity patterns in the brain leading to the observation of high level
cognitive phenomena, for example.
In my opinion, most of the fuzz about the problem of "Recursive
Distinctioning (RD)" arises when we discover as observers that our
biological activity involved in distinguishing observable phenomena where
recursion occurs as a phenomenon, is an observable phenomenon in itself in
which recursion also takes place. It is difficult to express this in the
languaging domain, but confusion arises only when we assimilate abstract
notions, concepts and mathematical constructs to the phenomena that we are
trying to observe-distinguish-explain. This kind of intellectual exercises
are breathtaking indeed, but if you keep to a strict phenomenological
approach within the ontology of observing, all conundrums and theoretical
artefacts of logical reasoning may be avoided at the price of some effort.
Hugo Urrestarazu
-----Original Message-----
From: joelisaacson2001
Sent: Sunday, November 14, 2010 8:26 PM
To: autopoiesis-dialog...@yahoogroups.com
Subject: [autopoiesis-dialognet] Autopoietic Recursion Re-Examined
Hi all,
During the past 30 days there was a burst of activity on a discussion
list called CYBCOM that is associated with the American Society for
Cybernetics.
It was triggered by the unlikely issue of cybernetics as a capitalist
tool that had been raised by by radical thinkers some 10 years ago in
a French publication named Tiqqun. A series of articles attacking
cybernetics appeared in a volume titled "The Cybernetic Hypothesis."
The CYBCOM discussion soon veered into wide ranging topics relating
to basic ideas of cybernetics. A central concept discussed was
"Recursive Distinctioning," which led to close examination of the
notions of recursion, circularity, and the relationship between the
two.
What is Recursive Distinctioning (RD)?
The act of distinguishing, or distinction-making, and its import in
cognition is long understood within cybernetic circles. Many
thinkers, including Bateson and Maturana went as far as talking about
distinctions-of-distinctions (or "difference that makes a
difference") and sometimes even suggested further recursion of
distinction-making operations of distinctions upon distinctions.
In RD, recursion of distinction-making is taken to be indefinite, and
the consequences of such indefinite recursion are observed in great
detail. It can be shown, thru rigorous mathematical means, that RD
will always converge on a closed cycle.
It usually starts as a linear transforming process, but eventually
ends up in circularity. So, in RD, recursion and circularity seem to
be entangled, where the latter is a by-product of the former.
What is Recursion?
It turned out that the notion of "recursion", invoked repeatedly by
Maturana in many of his writings and teachings, is a bit ambiguous.
Only in the mid-1990 Maturana became more specific in this regard.
This state of affairs seems to have caused some confusion among avid
Maturana followers, and thus it is fairly common to see people
entangle circularity and recursion in a way that suggests that
recursion is the outcome of some natural circularity in the biology
of cognition (rather than the other way around).
Recursion has numerous meanings across many disciplines. So, simply
reading a Wikipedia article on the matter may serve more to confuse
than enlighten.
The specific type of recursion that applies in Recursive
Distinctioning is the same that applies in Cellular Automata,
fractals, and (for a specific example) the Mandelbrot Set.
This form of recursion is straightforward:
An initial pattern is selected or given; a certain transformative
operation is applied to the initial pattern, which generates a
second, new pattern; the same transformative operation is applied to
the second pattern, which produces a third pattern... and so on and
on... indefinitely. Typically, very complex set of patterns
emerges, some cyclical and some not, some symmetrical, and some
self-similar, etc. Generally, there is no way to predict in advance
what a given initial pattern will generate globally under what
transformative operation. In RD, the particular transformative
operation is distinction-making, such that each new pattern is the
result of distinction-making within the prior pattern. Thus, we have
a realization of angoing process of distinctions-of-distinction-of-
distinctions- .... indefinitely, in a formal automaton whose
properties can be studied in great technical detail.
A side discussion in CYBCOM also differentiated between mere
repetition and recursion.
Either repetition or recursion may generate in an observer a
perception of circularity; but, in principle, when circularity is
observed one cannot tell whether it is a by-product
of repetition or recursion. Which obviously means that one needs to
be circumspect when observing circularity and refrain from positing
circularity as the ultimate 'engine' of perception; for it is rather
Recursive Distinctioning.
I hope that this is relevant to this group and would welcome comments
and further discussion.
Best,
-- Joel
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