When I use the term "model" I am referring to a relationship between two
things (two objects). These two things can be two natural systems, two
formal systems, or a natural system and a formal system. A Natural system
is something that is actually out there in nature. A formal system is something
that performs computations...something that is always expressible by an
algorithm...a synthetic structure...built up from parts...reducible...something
we use as a tool to understand something else. The Natural system may or
may not be reducible. The encoding arm would include such "causal structure"
as deciding what to measure (from the system on the left), taking the
measurement, and coming up with (or choosing the system on the right). The
"causal structure" in the decoding arm would include knowing how to interpret
the results from the system on the right (that is, attach the appropriate
meaning), and performing a realization of the meaning. So the encoding and
decoding arms include a little of us (subjectivity). We want the things to the
left and right to be totally objective.
In the modeling relation (as Im developing it here) there are two different
possible paths. The first path is from something with meaning (A) through the
system on the left to something else with meaning (B). The second path is from
that same something with meaning (A) through the encoding arm which measures the
natural system and creates the formal system. The formal system then operates
on the data producing results. The decoding arms then actually perform a
realization of what the results mean.
Consider the following little example. The natural system on the left is an
electrical circuit with an input and output. The input has 10 volts across it.
The output has 5 volts across it. You would like to form a model that connects
an appropriate formal system to this natural system. Your formal system is to
divide by 2. The encoding arm measures the input to the electrical circuit
getting the symbol "10V", creates the formal system, strips off the "V" and then
enters "10" into the formal system. The formal system then performs its
calculation ending up with the symbol "5". The decoding arm then takes this
symbol "5", attaches the "V" symbol to it, knows what "5V" means and then
actually creates the voltage.
The two paths through the modeling relation are as follows:
1) Going from actually having 10 volts at the input of the electrical circuit
to actually having 5 volts at the output of the electrical circuit.
2) With the 10 volts present, remove the electrical circuit and proceed through
the encoding arm, the formal system and through the decoding arm. This path
will result in actually having 5 volts at the end of the decoding arm.
Bruce writes:
>From my viewpoint the natural system does not appear at all! The
>more natural side (the experimental data, recorded observations
>etc.) are already models (not necessarily formal in the wider sense
>but definitely non-natural). The modeller then comes up with a
>(usually more formal) model of this 'data-model'.
With the above (Bruces) viewpoint, one may want to describe my little example
as follows: The natural system on the left is the measurement that was made
at the input and output of the electrical circuit (the symbols "10V" and "5V"
respectively). The encoding arm strips off the "V" from the "10V" and puts
the "10" into the formal system (which was created also by the encoding arm).
The formal system then performs its computation coming up with the symbol
"5". The decoding arm then appends a "V" on the "5" ending up with the
symbol "5V".
There are two paths through this modeling relation:
1) going from the "10V" symbol to the "5V" symbol that constituted the system
on the left.
2) Starting with the "10V" symbol and proceeding through the encoding arms,
formal system, and decoding arms to get the symbol "5V".
One may wonder "what is the point to this distinction of these two examples?".
(The importance of the distinction isnt apparent from the above examples).
One has to consider a system with some kind of self-reference. [Im struggling
with this concept so my following example probably needs some work :-( ].
Consider, for instance, that the natural system (to the left) is actually the
whole modeling relationship. We now have (I think) an inpredicativity, vicious
circle, or some infinite regress in the works... (something we usually try to
avoid). Remember, the encoding and decoding arms have a little of us in them
(subjectivity). Now if the natural system to the left is actually the whole
modeling relation, it also has a little of us in it....therefor it isnt
completely objective as we usually like to think of the term.
We thus have two choices.
1) Expand our idea of "objectivity" to include such impredicativities,
self-references, vicious circles, and the like.... Allow them to be an
"objective" entity to study.... a part of science. (this is radical)
2) make sure (through personal discipline) that we never actually consider a
natural system (on the left) that is actually the whole modeling
relationship. Therefor, we avoid the issue. We maintain "objectivity" as
we have been using it. (this is conventional)
I think that having the system on the left (of the modeling relationship) as
being the measurements from a Natural system (not the property of the
natural system itself) is one way (and a good way) of insuring choice #2 above.
But if you do want to be able to consider self-references and the like (for
example, if you think they might be of some importance in biological systems)
then a modeling relationship that only has measurements on the left will not
allow you access to studying this property (self-reference).
I know this all may sound a bit confusing...Im in the process of sorting out my
thoughts... Ill write more later (when I have time).
Ill also spend more time (later) examining the translation from your language
into the one I have adopted. I think that is a very useful process!!!
Jeff Prideaux