Posted by
glen ep ropella on
Apr 28, 2008; 4:44pm
URL: http://friam.383.s1.nabble.com/Welcome-Jim-tp526087p526138.html
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G?nther Greindl wrote:
> It is neither a mathematically rigorous nor an empirically grounded
> refutation, I agree, but rather in the sense of Occam's razor/Laplacean
> "I do not need this hypothesis".
Excellent! We pretty much agree. The only area where I might disagree
is in attempts to develop measures of complexity. Forget the whole
"life <=> non-life" red herring. The simple <=> complex spectrum,
however, can be useful.
And, in that sense, Rosen's attempts to formalize simple systems as
"defined from the outside" versus complex systems as "defined from the
inside" is interesting. Albeit, we may not NEED such a theorem because
we have plenty of measures of complexity which work to greater or lesser
extent in different contexts. (I'm fond of "logical depth" myself,
though I admit that I haven't used it successfully.)
But I can imagine that certain concepts that are currently used all the
time in complexity circles, and which are always horribly vague despite
the credentials of the users, ... I can imagine that these concepts will
never become clear and concrete until we have such a theorem.
And that's where non-well-founded set theory seems useful. What is the
ultimate difference between formalisms (models) requiring the foundation
axiom and those that do NOT require it?
It seems to me that formalisms built without the foundation axiom will
lack some of the definiteness we find and expect in our mathematics.
And, surprise, we also see a lack of definiteness in complex systems.
Now, I'm not just trying to combine two unknowns in an attempt to use
one to explain the other. [grin] My point is that this circularity
Rosen points out is fundamentally related to cycles in non-well-founded
set theory. And it also seems related to the rampant abuse of concepts
like iteration (e.g. recursion).
Anyway, my thoughts are a jumble of unjustified nonsense at this stage.
I need a sugar-momma to pay me to sit around and think. Any takers? [grin]
> Have you perchance read
>
> Wells, A. J. In Defense of Mechanism Ecological Psychology, 2006, 18, 39-65
Nope. It sure sounds familiar, though.
> ? He takes on Rosen's claims, I have queued the paper for reading, will
> probably get there in July (have a lot to do at the moment ;-)); and
> would be glad to continue the conversation.
I'll add it to my queue, too, though I'm way beyond being able to commit
to it or estimate when I would ever read it. I've always been a slow
reader ... though when I do read something, I usually remember it.
It'll help if you spontaneously re-start the conversation when you get
to Wells' paper. Then make fun of me if I haven't read it, yet.
That'll coerce me into reading it.
- --
glen e. p. ropella, 971-219-3846,
http://tempusdictum.comThe fear of death follows from the fear of life. A man who lives fully
is prepared to die at any time. -- Mark Twain
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