-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Günther 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.com The fear of death follows from the fear of life. A man who lives fully is prepared to die at any time. -- Mark Twain -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.6 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org iD8DBQFIFf8ApVJZMHoGoM8RAt+gAKCB20DpxiyJ8nwVJeSXVYFG/xHR1wCfX5dG w6gansrDVkGFmZ4GoCQIx5I= =yHDb -----END PGP SIGNATURE----- ============================================================ 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
