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

[Dan Fiscus <***>]

Calvin, Torkel, Glen, Judith, Tim, all,

Thanks for great debate! Learning a lot, but slowly and
perhaps mainly metaphorically/analogically/intuitively
at this point. Not really trained in math, sets, logic, etc.
(I am an ecologist with some training in biomath and
modeling) but this discussion has me wanting to be more
so... I have Vicious Circles out from the library now and
it is hard for me to read.

One comment/question re: this:

Calvin Ostrum wrote:

> I might guess that it simply follows from some kind of statement such
> as the following:
>
> "Any system which is closed to efficient causation has no maximal
> model, and further,    systems closed to efficient causation are
> possible".
>
> This or something like it appears to be one of Rosen's important results. 
> Since it appears to be a purely conceptual result, a result of pure thought,
> it should be possible to formalize it and prove it as a theorem.   
>
> At the very least, it should be not too difficult to state it
> rigorously by formally
> defining all the terms in it, so at least it is amenable to proof.  
> If no one else
> has done this anywhere carefully in a perspicuous and efficient manner,
> it is something I will try doing myself.

In commenting on this, I also would drag back in Calvin's
comments from prior posts to the effect of (paraphrasing)
1) formal systems cannot construct themselves as life does
and 2) construction - bringing into existence - is importantly
different from definition - picking out something from the
already existing...

So...I woud add:

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. This could be one way
to link Rosen's comments about formalisms and life, even if
still problematic in the details, meaning, accuracy, etc. and
to hint at the fact that this link/leap/bridge is perhaps
inherently problematic due to fundamental concepts like
construction.

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...

3) Another aspect I am curious about is "open causality"
and how this idea might relate to these discussions on
impredicativity, circularity, self-construction, Rosen,
formalism, computation, etc. It seems to me that yet
another way to describe a key difference between life and
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. Life
systems in contrast do create new things, by themselves,
without interaction with other living agencies or efficient
causes. They need only interact with material causes (solar
energy, chemical energy, nutrient inputs, etc.) to achieve
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.)

Some mathematically untrained comments...hopefully not
more confusing than helpful...my trial balloons to try to
learn from...

Dan