Re: meanings of model

[Tim Gwinn <***>]

Howard,

I am unclear what you mean by "physical laws" in your post. To me, "physical
laws" are just those formal theories and their mathematical formulations
that we humans create. In your rephrasing of my question, it sounds like you
equate the phrase "physical laws" with something like "effective processes
of nature". Is that the case?

Regards,
Tim

> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Howard
> Pattee
> Sent: Monday, December 13, 2004 2:17 AM
> To: ***
> Subject: Re: meanings of model
>
>
> At 08:09 AM 12/12/04 -0500, Tim wrote:
>
> >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)?
>
> HP: There are at least two schools of thought (or two ontologies)
> that bear
> directly on  the form of your question. At the extremes there are the
> Platonists who see physical laws as derivatives of abstract
> forms. "In the
> beginning was the word" (John 1;1). And  there are the
> Constructivists who
> see the semantics of formal symbols  limited by physical laws.
> "Words grew
> out of the womb of matter" (Laotzu, Tao Teh Ching 1).
>
> I am a Constructivist, so I would phrase your question
> conversely: when do
> the limits of physical laws impinge on the capacity of formal symbols to
> have meaning? That is, when do the purely syntactic expressions of formal
> mathematics go beyond what can be measured or encoded by nature?
>
> Also Constructivists, like most computer modelers, see no reason why the
> formal concept of Turing computability should limit how we actually write
> programs. Many programs for physical and biological models are not even
> algorithms because they do not halt by themselves. In fact, strictly
> speaking, our computers are not Turing-equivalent. They are finite memory
> and finite state machines, and all theorems on computability
> depend on the
> syntax of infinite sets.
>
> This is a classical metaphysical controversy. Henri Poincare (the
> constructivist) and Bertrand Russell (the formalist) argued this
> for years
> and finally agreed to disagree. Rosen and I were closer to agreement than
> Poincare and Russell, but there was no doubt Rosen was not as
> constructivist as I am. We will not resolve this issue here, but I think
> understanding why there is an issue might help the discussion.
>
> Poincare's basic argument is that there is no empirical, ontological, or
> semantic evidence for infinite sets and certainly none for transfinite
> sets. He saw infinite sets as useful but purely syntactical games with
> symbols. He saw Richard's and Russells's paradoxes (and would have seen
> Goedel's and Turing's theorems) as just limits on how you can play
> syntactic games, but semantically irrelevant for models of
> physical reality.
>
> Of course, the constructivist agrees that there are formal
> symbolic models
> (in my first, right-hand sense) that he cannot compute by Goedelian
> conditions; but to convince a constructivist that this is scientifically
> relevant requires an example of physically observable behavior that he
> cannot adequately model (in my holistic second sense) by satisfying only
> the Hertzian conditions.
>
> Howard