Don:
You know I've always thought and said that the use of the notion and
word "complex" with respect to the relationship between models and
reality was arbitrary and generally off base. In more precise terms,
here is why:
First of all, most people use the word complex to mean the opposite of
simple. And most assume there is little or no room for any middle
ground between the simple and the complex. This, in my book, is a
classic example of the use of "or" logic or what you might call a formal
model.
Correct me if I'm wrong, but your model of the modeling relation is, a
formal model. To me, this is the same as the Cretan who said that all
Cretans are liars. Because he is a Cretan, there is no way to tell
whether he is telling the truth or lying. So there is no way to
decipher this self referencing statement about statements. Whenever you
get this kind of circular reasoning, it is called an error or confusion
of logical types.
In other words, this seems to be a formal statement that is assumed to
be either true or false about whether all formal statements, or all
statements for that matter are true or false. One major problem with
this line of reasoning is that there is an excluded middle in the
statement about statements that says all statements with an excluded
middle are false.
In this proposition, we must take it as a given truth that all simple
models are false. But if they are false, then this model about simple
statements may also be false. As a result, there is no way to make sense
of this simple model that says that, in effect, all models are simple
and all simple models are false, including this one.
So to my way of thinking, this notion that all simple models are false
is a classic confusion of logical typing. It is also an "or" logic
statement about statements that is patently confusing on its face.
The only justification for using such a ruse is that to anyone that
thinks it through, it tends to confirm Godel's notion that there is no
way to get the uncertainty out of our models. And I think we agree that
all our models have limits and uncertainties that we should always keep
in mind.
However, I don't think this should be taken to mean that all our models
are, of necessity, simple approximations of marginal or no value.
Further, there is nothing in anything you have said that convinces me
that we humans are incapable of modeling both the physical and non
physical aspects of our being. And just because our models are less
than perfect, we should no abandon our efforts to understand beyond what
we perceive to be the limits of our understanding.
Again, correct me if I'm wrong, but I interpret the dichotomy you
advocate to mean that all human models are simple and therefore none of
our models can ever hope to come close to improving any aspect of our
human understanding. I guess the implications of this latter point are
the ones that bothers me most. The apparent absoluteness of your
proposition could easily lead to a fatalistic and hopeless attitude that
could, in turn, lead us to give up trying to learn more about our
selves, each other and the universe we are a part of. If there is one
thing of which I am certain in all this, it is that such a fatalistic
attitude is not what you intend to foster.
Norm
"Donald C. Mikulecky" wrote:
>
> Let me try it another way. There is a true dichotomy here. "Complex is the
> *real* world. The *only* "simple" things arise in our models of that world..
> Don
>
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Posting to pcp-discuss@lanl.gov from "Norman K. McPhail" <norm@socal.wanet.com>
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