"The left-hand side side of
this diagram comprises the sytem being modeled (often called the object
system). The arrow 1 represents the internal entailments that
characterize this object system. The right-hand side of the diagram is a
linguistic system, generally a mathematical one, with its own arrow 3 of
internal, inferential entailment. The crucial ingredients are the arrows 2 and
4, which I have called encoding and decoding, respectively.
(I have discussed the anomolous features of these arrows in more detail
in Life Itself, section 3H.) They do not fit
entirely inside either the object system or the model; they do not represent
entailments, nor are they themselves entailed. They manifest what Einstein
(with Infeld; 1983:33) once called "free creations of the mind", on which he
believed science depends. They introduce an obvious further semantic
element into the model, over and above what semantic (e.g., nonformalizable)
features may already be present in the model. The only condition on them is
that they bring the two entailment structures into congruence - that is, that
they satisfy the commutativity condition, which I have written
as: 1 = 2 +
3 + 4 ." [bold added]
So, the encoding/decoding needs to come from (i.e., be entailed by)
somewhere/something else outside the model per se. As Judith noted:
"Even the "anticipatory model" within the organization of
living systems may only be "active" insofar as it is part of the dynamic
organization of the system itself. "
This issue therefore seems to me highly problematic for the notion of "two
models modeling each other". I cannot envision how one could postulate the verb
"modeling" in that statement without there being 'modelers' of some kind
which are separate from the models themselves and which provide the
encoding/decoding which gives the 'model' a context to actually be a
model of something.
Regards,
Tim