Re: Impredicativity in Rosennean parlance

[Calvin Ostrum <***>]

On 8/10/05, Judith Rosen <***> wrote:

> CO wrote:  it seems that some of Rosen's claims could in
> fact be stated more clearly and precisely in terms of computability 
> and related notions as they are understood at large.   However,
> as far as I can see, this has not yet been done. 
>   
> Ah, indeed it has! Just not in the snippet I posted. For example, look at
> the contents pages of "Life, Itself: A Comprehensive Inquiry Into the
> Nature, Origin, and Fabrication of Life".

I have looked at that book fairly carefully and it doesn't see to
do what I am asking for at all, as far as I can tell.   For starters, the 
crucial relation of modelling is not defined very rigorously.  
Perhaps if I look
at "Anticipatory Systems" it would help, and I intend to do that.

> there is. But, as I described in my earlier post to Torkel on causal loops,
> there are some aspects of systems which cannot be analyzed in a reductionist
> mode without destroying too much information.

I am not a reductionist myself (in the sense that I understand that term 
in  this context) but apparently for different reasons (reasons 
related to the work done in philosophy of mind on mental causation), but I 
don't understand what this actually means, and thus, a fortiori, why it is true.

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.