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, Günther ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
