Posted by
Günther Greindl on
URL: http://friam.383.s1.nabble.com/Welcome-Jim-tp526087p526102.html
Dear Glen,
>> The principal claim of Rosen - that life is not mechanically emulable -
>> is shown to be false by the second recursion theorem
>>
> I disagree. I don't believe that theorem refutes RR's claim, which I
> prefer to think of as "non-well-founded sets cannot be realized". But,
> I admit that I'm not as well-versed in computability as I should (or
> would like to) be.
>
> How does the recursion theorem refute RR's claim? Can you be a bit more
> precise?
I actually wanted to call into question that life is a non-well founded
set. Why should it be? Could you present arguments for that? (I looked
at Rosen's (M,R) Model of the cell and did not see any principal problem
in modelling this computationally -> that is where the 2nd rec. theorem
comes in; indeed, this is necessary and a quite deep insight, Descartes
could not solve this, but of course he did not have modern logic at his
disposal).
If non-well founded sets are then computationally realizable is another
question, but why not (a non halting computation?)?
Two other things:
Category Theory, which RR employs, is not at odds with computer science:
"From the 1980s to the present, category theory has found new
applications. In theoretical computer science, category theory is now
firmly rooted, and contributes, among other things, to the development
of new logical systems and to the semantics of programming. (Pitts 2000,
Plotkin 2000, Scott 2000, and the references therein)."
Quote from SEP
http://www.science.uva.nl/~seop/entries/category-theory/See also the paper from Baez Et al. (Rosetta stone) which has already
been recommended by someone on this list.
RR's approach seems to attract followers because of this:
(two quotes from abstract of online paper by Donald C. Mikulecky)
http://www.people.vcu.edu/~mikuleck/PPRISS3.html"It is so because the world of the machine is a "simple" world. Its laws
and inhabitants are simple machines or mechanisms."
This is a basic misunderstanding of what is a machine: when talking
about machines, people think about clockworks and DVD players and cars.
But machines can be much more profound than this, and how profound is
revealed by logic/set theory/recursion theory.
Indeed, there is nothing in empirical physics known at the moment which
would contradict viewing nature as a machine (esp. as a CA) (see for
instance Wolfram/Schmidhuber and even one or two papers by Nobel
laureate 't Hooft)
Another quote by Mikulecky:
"It isn't the atoms and molecules that are at the hard core of reality,
it is the relations between them and the relations between them and
things called processes which are at the core of the real world!"
Hmm - in theoretical physics one only models mathematically -
"particles" are not "things" anymore, they are mathematical relations;
all nicely in a mechanist framework; in the end, the more we go into
physics, the more the things we study are only true insofar as they have
mathematical content (Roger Bacon said similar stuff around 1200, and he
had it from the Moors ;-). A mechanist would be very fine with "all is
relation".
I have not yet seen any substantial claim (except handwaving) coming
from RR's work which goes against traditional mechanist/computationalist
traditions.
Cheers,
G?nther