Re: Impredicativity, Rosen, life, formalism, open causality

[David Macy <***>]

Calvin,

    Come on man.  You must be joking, right?

You wrote...
A "non-living system" -- that is
not so clear.   Do rocks fall?  Is that something they do?  Maybe.

Do you imply, or do I infer from this that you believe that rocks have
intention?  Now that's magical, mystery stuff right there.

David


----- Original Message ----- 
From: "Calvin Ostrum" <***>
To: <***>
Sent: Thursday, August 11, 2005 3:35 PM
Subject: Re: Impredicativity, Rosen, life, formalism, open causality


On 8/11/05, Dan Fiscus <***> wrote:

> 1) Life systems, while self-constructing, are also formal or
> have aspects that are analogous to, similar to, perhaps
> well-modeled as  formal structures. So it seems life presents
> examples of "formal" systems that self-construct, something
> Calvin seemed to say was impossible.

No, I was talking about formal systems, not life.  A formal
system in the usual parlance is a set of abstract objects and
a set of ways of deriving new objects from old.   A formal system
in this sense is an abstract object and doesn't "do" anything;
a fortiori, it does not "self-construct".   Something in the
world, the causal order, may be modelled by a formal system
in some way or other, and this thing may self-construct.
Further, I suspect (and apparently so do you) that a fully
decent account of its doing  so may be captured in some
formal system that models it, which I take Rosen  to be
denying.

(I am using "model" here in only a vague sense at the current
time, and not referring to that (1) = (2) + (3) + (4) thing that
Rosen  frequently talks about -- which itself seems hardly any
less vague.   One thing to note is that the (3) in this vague
statement, insofar as it is characterized as "inference", will
not in general in a formal system correspond directly to
the causal powers (1) in the modelled system, and this
is again precisely because inference does not "do" anything.
With a general formal system one can take inference in
any direction one wants, picking at each step any outputs
of any previous steps and applying an inference rule.  The
rules do not have to be applied in any particular way at all.
You may of course define a much more limited sort of
formal system, but characterizing the derivations in it
as "inferences" is probably then misleading)

> 2) If Rosen's important result above is a valid way to bridge
> between formal systems and life systems, I wonder if his
> statements can in fact be formalized and proven as Calvin
> suggets? I think it would be a great service if he can, either
> prove or disprove for that matter. But I am not sure it is
> possible in a *closed*, formal proof. Just a hunch, largely
> based on...

I am pretty sure that Rosen himself definitely intended that
such claims could be rigorously proven.

> formal systems is causal openness. Just as Calvin said that
> a traditional (non-living, mathematical, logical) formal
> system cannot create/construct itself, neither can such a
> system - by itself or without interacting with another
> living agency (i.e. in closed to efficient cause manner, no
> living mathematician to aid) - create anything new.

Because mathematical and logic systems cannot *do* anything
at all, strictly speaking, yes.  A "non-living system" -- that is
not so clear.   Do rocks fall?  Is that something they do?  Maybe.

> creation. (This assumes a view of life that is ecosystemic
> rather than organismic...my pet topic...but still fits in basic
> concept with Rosen I think.)

Individual things within an ecosystem are alive, but they
probably cannot be characterized as such without considering
that environment in which they are embedded.   This is something
that prima facie seems problematic with Rosen's discussion of
"systems" that are modelled.  It is unclear to me how the
system of organism(s)/environment and the living system itself,
just the organism, are to be related here.

In a more traditional approach to construct a formal model,
one would have a bottom physical level, such as a cellular automaton.
This would be the entire universe (here the derivations would directly
model cause in a trivial manner, as opposed to being characterized as
"inference'), and one would attempt to pick out parts of that universe
that were "alive" in some intuitive  sense, and see if one could give
a rigorous characterization of that property.