I dont know who came up with this modeling relationship (with the
encoding and decoding arms) first...possibly Rosen....
I will paraphrase what Rosen has written from pages 57-61 (section
3H) of his book LIFE ITSELF.
The modeling relationship connects (in at least one way to apply it)
causal entailments in the natural world to syntactic entailments in
a formal system.
Rosen speaks of "Natural Law" which is basically the belief that we
can know something about nature...and that we can include a
natural system in the modeling relationship. Rosen doesnt prove
that we can know something about nature; its really a matter of
faith. Rosen defines Natural law as the following: (I quote):
" 1. The succession of events or phenomena that we perceive in the
ambiance is not entirely arbitrary or whimsical; there are relations
(e.g., causal relations) manifest in the world of phenomena
2. The relations between phenomena that we have just posited are,
at least in part, capable of being perceived and grasped by the
human mind, i.e, by the cognitive self. "
Rosen claims that a science of the natural world relies on both of
the above statements (assumes they are true).
Statement #1 above (of Natural law) is a statement about nature
independent of human understanding. This statement
gets represented in the modeling relationship by the natural system.
Statement #2 above (of Natural Law) is a statement about ourselves,
about our cognitive self...what can be grasped by our human mind.
In Rosens words "The art of bringing the two into correspondence,
through the establishment of a definite modeling relation between
them, is the articulation of the former within the latter; it is in effect
science itself".
Inside the natural system (N) on the left is causality. Inside the
formal system (F) on the right is inference.
Rosen says "...a comparison of these different kinds of entailment
structures requires the establishment of dictionaries, one for
encoding the phenomena of N into the propositions of F and
another for decoding from propositions of F back into phenomena
in N....The concept of such a dictionary is, of course, precisely
what endows a syntactically defined formalism with external
referents. "
This allows for an "expression of the possibility of using syntactic
truth and semantic truth consistently".
The encoding arrow (arm) is associated with the act of measurement...
an act of abstraction...an act of replacing the thing measured by a
limited set of numbers.
The decoding arrow (arm) represents a de-abstraction, the association
of a phenomenon in N with a proposition in F.
We can now form a diagram (the modeling relationship) with four
arrows (or arms).
(1) the causal events in the natural system
(2) the encoding from phenomena in N to propositions in F
we also use these propositions to from a hypothesis, on
which the inferential machinery of the formal system F
may operate.
(3) the operation of the formal system F on the propositions
(4) the theorems must be decoded back to the phenomena of N.
The theorems thus become predictions about N.
In a successful model, the causal events in the natural system (1) can
also be achieved by following arrows (2) + (3) + (4).
He also notes that the roles of N and F can be reversed...and that
there are some very important consequences of this...
To put some of the recent disussions over the list in perspective,
I was finding issue with Bruce's ussage of the modeling relationship
of not having the natural system included. I think that to start
with the measurements on the left is to have already lost the
essence (the semantic truth) of what Rosen thinks is very important.
--------------------------
Now for other issues...
Don claims that the "complexity" cannot be localized in any one
part (arm) of the modeling relationship...but is a feature of the
whole diagram...I'll go along with this...with thinking on these
lines, perhaps the encoding and decoding arms represents some
semantics (external referents) that are distinct from the syntax
in the fomalism. Perhaps these would represent two distinct ways
of looking at a natural sysetm (semantics and syntax) and therefor
one would call the modeling relationship complex... comments?
Can Natural systems be complex?
What about natural systems that do their own modeling...have
internal predictive models....can we call them complex? or am I
misunderstanding Rosen... It seems to me that if a natural system
has an internal model, then it also must manifest an internal
modeling relationship of its own...and if modeling relationships
can be complex, then it should be at least permissible to consider
that a natural system could be associated with complexity (regardless
of whether the complexity is localized in particular arms or a property
of the whole modeling relationship)...If a whole modeling relationship
could be contained inside a natural system and if that modeling
relationship were complex, wouldn't that be the definition of a
complex system? Or is a modeling relationship exclusively reserved
for models formed by humans....and Natural systems can't have their
own inner models...and therefor, complexity has no meaning for them...
complexity is only present for the way we can look at them. I'm
not offering answers. I'm offering questions.
I have been interpreting (perhaps erroneously) Rosen's chapters in LIFE
ITSELF on relational modeling as being about how a natural system can form
modeling relationships inside themselves...the other
way to view relational modeling (in my opinion) is to view it as the
combination of the encoding, formal system, and decoding arms...that is...
having an augmented "not totally formal" system in which the encoding and
decoding arms arms are contained inside of itself so that it faithfully
represents what is happening (causally) in the natural system.
Wouldn't it be arbitrary which way one looks at it? Wouldn't the only
degeneration be to equate the formal system (not including the encoding and
decoding arms) to the natural system as far as understanding the
causality?
What I am offering for consideration is that on one hand, we can form a
complex modeling relationship by providing the appropriate encoding arm,
decoding arm, and formal system (in respect to a natural sysetm). On the
other hand, a Natural system, too, can form a complex modeling relationship by
having its own encoding arm, internal predictive system, and decoding arm
with respect to itself. And, by understanding the modeling relationship as we
use it, we can understand the modeling relationship as the Natural system uses
it. (and perhaps this is the only way we can understand the modeling
relationship as the natural system uses it...it may not be accessible to us
emperically). This is what I think. I may be wrong. If I am wrong, I want to
know about it.
Jeff Prideaux