Re: meanings of model

[Tim Gwinn <***>]

Howard,

Rosen's concern with the formal aspects of modeling pertain to determining
the limits of what a given formalism is capable of modeling. If one is
trying to answer the question "why life?" and the answer involves models
with closed loops of entailment, then answering such a question lies outside
the limits of computable models.

Many other questions regarding organisms do not involve closed loops of
entailment or other features that exceed the limits of expression of a
computable formalism, and so can be modelled within the limits of computable
models (aside from technical computing power issues, such as NP, as you
mentioned).

Another way to say it would be: when do the inherent limits of expression in
formal models (in your first sense) impinge on the capacity for them to be
formal models (in your second sense)?

So it is not a question of *if* computable models are useful, but *when*
they are useful. Even regarding complex systems, he notes that computable
models can be used, with the caveat that the model will be valid only
locally and temporarily.[EL 338]

He also explicitly invokes the notion of spectra of observables, as defined
by equivalence relations on them, which provides a formal yet completely
general notion of numerical approximation of measurements and predictions.

Regards,
Tim

> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Howard
> Pattee
> Sent: Sunday, December 12, 2004 12:02 AM
> To: ***
> Subject: meanings of model
>
>
> 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