Re: meanings of model

[Tim Gwinn <***>]

Howard,
See interposed comments.
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?


TG: (Using you definition of physical laws in your post yesterday ("I
usually mean by physical laws the natural laws that I imagine exist whether
or not I have created a model of these laws.")). I don't really understand
the intent of your rephrasing. Of course there are many - probably
infinitely many - formal symbol arrangements that are not commuting models
of any natural systems. How is this important?


> Also Constructivists, like most computer modelers, see no reason why the
> formal concept of Turing computability should limit how we actually write
> programs.


TG: The limits of Turing computability are inherent in any program that run
on a computer. (Obviously excepting an analog computer, which is an entirely
different meaning of "computer".)


> Many programs for physical and biological models are not even
> algorithms because they do not halt by themselves.


TG: This is rather vague. I have no idea what kind of programs you are
talking about, so I don't know if you are talking about successive numerical
approximation routines or something else. I disagree that they are not
algorithms -- of course they are algorithms: they are running on a computer,
aren't they?


> 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.


TG: The limitations of a universal Turing machine will apply equally (or a
fortiori) in a finite Turing machine.


>
> 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.


TG: Any natural system which possesses closed loops of entailment cannot be
modeled solely by a computable model.

> Howard