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Re: Mathematical logic, computability, and "rigor"



Hmmm, it appears that both Torkel and Calvin continue to equate scientific rigor with computability and precise mathematical (formal) logic. This continues to be the case, in spite of plenty of evidence that: A.) The property of being computable represents an incomplete (and therefore erroneous) definition of the terms "logic" and "scientific rigor"; and B.) Plenty of evidence has been presented both here on the list including detailed suggestions of where to look in two of Robert Rosen's easily available books for far more well-documented evidence. The conclusion that begins to suggest itself to me, in the face of these facts, is that neither of you are really interested in understanding the work. So, perhaps you can help me with something that I have already asked the list subscribership to see if they could attempt: Let's see if you can come up with any real way to "debunk" the scientific conclusions my father arrived at.
 
What I'm after is a (relatively) quick way to solve, once and for all, the arguments over whether or not these theories are indeed representing aspects of the universe that are not included in current scientific capability. I trust you both will agree that if Robert Rosen is right about that, it behooves humanity to know it-- and begin work developing new scientific capability that will rectify the situation? And, if it is possible to prove that he was not correct in his conclusions, then let's do so and save ourselves a whole lot of breath.
 
What do you say? Are you game?
 
Judith
 
----- Original Message -----
To: ***
Sent: Thursday, August 11, 2005 1:02 AM
Subject: Re: [ROSEN] Impredicativity in Rosennean parlance

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.