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distinction of levels of computation is maintained by referring to such struc-
tures as n-th order representors (relators). With these concepts the possi-
bility of introducing “organism” is now open.
7. A living organism is a third order relator which computes the relations
that maintain the organism's integrity.
The full force of recursive expressions is now applied to a recursive defini-
tion of living organisms first proposed by H. R. Maturana 4,5 and further
developed by him and F. Varela in their concept of “autopoiesis” 6 .
As a direct consequence of the formalism and the concepts which were
developed in earlier propositions it is now possible to account for an inter-
action between the internal representation of an organism of himself with
one of another organism. This gives rise to a theory of communication based
on a purely connotative “language.” The surprising property of such a
theory is now described in the eighth proposition.
8. A Formalism necessary and sufficient for a theory of communication must
not contain primary symbols representing communicabilia (e.g., symbols,
words, messages, etc.).
Outrageous as this proposition may look at first glance, on second thought
however it may appear obvious that a theory of communication is guilty
of circular definitions if it assumes communicabilia in order to prove
communication.
The calculus of recursive expressions circumvents this difficulty, and the
power of such expressions is exemplified by the (indefinitely recursive)
reflexive personal pronoun “I.” Of course the semantic magic of such infi-
nite recursions has been known for some time, to wit the utterance “I am
who I am” 7 .
9. Terminal representations (descriptions) made by an organism are mani-
fest in its movements; consequently the logical structure of descriptions arises
from the logical structure of movements.
The two fundamental aspects of the logical structure of descriptions, namely
their sense (affirmation or negation), and their truth value (true or false),
are shown to reside in the logical structure of movement: approach and
withdrawal regarding the former aspect, and functioning or dysfunctioning
of the conditioned reflex regarding the latter.
It is now possible to develop an exact definition for the concept of “infor-
mation” associated with an utterance. “Information” is a relative concept
that assumes meaning only when related to the cognitive structure of the
observer of this utterance (the “recipient”).
10. The information associated with a description depends on an observer's
ability to draw inferences from this description.
Classical logic distinguishes two forms of inference: deductive and inductive 8 .
While it is in principle possible to make infallible deductive inferences
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