meanings of model

[Howard Pattee <***>]

Tim and Boris,

Your discussions raise a problem I have had with definitions of "model" 
that appears to me to have two profoundly different usages. One meaning of 
"model" refers to the structures of the formalism itself. Essentially this 
usage refers to "the formal model" as the right half of the modeling 
diagram. In this formal sense we can speak of all possible models and other 
formal concepts such as infinite sets, formal mappings, equivalence 
relations, duality, direct sums, Cartesian products, and the largest 
model.  In this formal context, analytic and synthetic are used as in 
formal logic, analytic referring to purely syntactical propositions where 
proof by contradiction is allowed. Synthetic expressions are not true or 
false by virtue of syntax alone, but among logicians I can't find any 
consensus on its precise meaning.

The other meaning of "model" is an empirically testable representation, 
implying the WHOLE modeling relation. In this usage the right-half 
formalism is a model if and only if it satisfies some empirical test such 
as the Hertzian condition that (as a result of measurement or encoding) the 
interpreted consequents of the model's formal syntax matches closely enough 
the consequents of nature. This is definitely not a formal condition since 
neither measurement nor "matching closely enough" is a formalizable process 
or condition.

Since empirical models are always finite, non-formal approximations, I do 
not see how exact logical conclusion about model formalisms necessarily 
apply to reality in other than the Hertzian testable sense. Except for 
practical speed/complexity issues, like NP-completeness and all that, I am 
not aware of any biological modelers that feel limited by or are even 
concerned about the formal aspects of computability. Other problems seem 
more important.

Yet Rosen apparently argues that they are limited and they should be 
concerned when trying to model complex systems. I accept his formal 
conclusions about "the formal model" as correct, but I don't follow the 
informal argument that would preclude   empirically testable models of some 
aspects of life. What am I missing?

Howard