Re: Mathematical logic, computability, and "rigor"

[John M <***>]

Judith,

great post! I was (superficially) reading the zillion
posts of mathematically inclined minds (the ones which
are incapable to delv into a Rosen-complexity) while
waiting for one - what I feel is - Rosen theory
oriented. You touched on that (not surprizingly). 

When - as I understood the RR-positions - a natural
system, a Rosen-complexity, a maximum model (=the
'thing' itself), the 'organization' are reaching into
the 'totality' (what I call: wholeness) and are
(Touring?) non - computable, also called:
impredicative, how on Earth can we compare statements
of the old mathematicians (Hilbert etc) how they
tackled a term they named impredicative? I repeat what
I lately wrote: when I asked a good friend (prof. of
Math at a NE name-univ.) how he feels about the math
of a (wholistic) 'system' with infinite variables and
unidentified functions included, he mused a bit and
said: "well, that sounds steep". 
I take the 'rap' of being vague in this new field
which has not even the proper words for the just
approached new ideas. We should not 'give in' to the
comfort of the old maxims in ancient science.

IMO (no matter how "mathematically" Rosen's education
impressed his ways of thinking) the RR worldview  idea
is 'impredicative' in the conceptual sense that we
cannot precisely predicate - predict its composition
or its construct. What we can identify in "scientific
rigor' is a model-view, with well defined limitations
in its boundaries. (I feel it is not far from what you
wrote under "A.)")

I feel distant from the "Platonic type" thinking,
based on the epistemic level and information of 2,500
years ago (no matter how great geniuses Plato and
Aristotele  were. Furthermore, (what on another list
the lister mathemaitically inclined pointed to): the
number theory as the basis of 'reality' evaded my
question "and how was 'reality' in 520 AD, before the
invention of the zero? The answer was: the fact that
we did not know about it THEN, did not change its
truth<G>. Of course, now we are already omniscient.
 
I would not base a Rosen-compatible thinking on some
earlier theoretical tools invented by the human mind
in the course of its evolution (development) of any
models. That pertains to formal logic as well. 

Sorry, Tim, you will say that I again got carried away
well, I am not happy when the Rosen-idea gets squeezed
into 'rules' - too narrow for its (endogenous?) 
impredicativity. Not on this list. 

Thanks again, Judith, for standing up and posting in
favor of a worldview which is designed to exceed the
ongoing "scientific" rules of reductionst sciences. 

John M

--- Judith Rosen <***> wrote:

> 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 ----- 
>   From: Calvin Ostrum
>   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.
>