Dear Glen, thanks for taking the time to write such a long response, here some comments:
>> complexity (=uncomputability in the Rosen sense) >> For my problems with his "uncomputability" see below. > > Living systems are just the particular example set of the (possibly very > large) category of complex_rr* systems. It doesn't _start_ with life. > Life just happens to be what RR (Robert Rosen) was interested in. Ok - but are all Rosenites sure about this? complex_rr is a thesis which I find scientifically ok because it does not introduce an arbitrary distinction between matter in different organizational forms (animate vs inanimate), although I disagree (with complex_rr) ;-) > He does, however, seem to avoid being explicit about the influence of > Goedel's theorems on his own ideas. As far as I can tell, he never even > approaches a technical explanation that extrapolates from Goedel to his > work. His exposition is purely philosophical and others claim to be > able to map what he said directly to Goedel's results. Yes I did also not find any explicit mapping; but if one is not given, I am always very skeptical, because Gödel is abused for all kinds of things. (see the excellent book by Torkel Franzen: Gödel's Theorem: An Incomplete Guide to Its Use and Abuse http://www.amazon.com/Godels-Theorem-Incomplete-Guide-Abuse/dp/1568812388/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1199723625&sr=8-1) > A better exposition comes in Penrose's work, in which tries to argue > that math (as done by humans) regularly involves hopping outside of any > given formal system in order to catch a glimpse of a solution, then > hopping back inside the formal system in order to develop a formal > proof. And in this regard, RR's rhetoric is not inconsistent. The Penrose/Lucas argument has been debunked many times. In the Torkel Franzen book above, in Rudy Rucker's "Ininity and the mind" (another excellent book, recommended reading, good fun and educational) and in a number of philosophy papers. But it still sticks around :-)) > RR's basic claim would be that math is _more_ than computation > (automated inference... formal systems... whatever you want to call it). > Namely, it involves jumping levels of discourse to provide entailment > when none such can be provided inside the formal system. If you take > that to its logical conclusion, you can imagine a _holarchy_ of formal > systems that each patch up the entailments for other formal systems in > the holarchy. In order to avoid an infinite regress or an infinite > progression, however, the level hopping _must_ loop back in on itself. I like the holarchy idea, I think this is important, but I don't see why this should not be capturable via computation. We can model formal systems in other formals systems (indeed is being done in foundations of math, as ZFC is currently seen as basis for math together with classical logic, but that is another discussion entirely). > The part that RR seems to think is not covered is the force or influence > that "guides" a living system in its behaviors. In many contexts, > people tend to make vague claims that "natural selection" or the > "environment" provide such pressure in the form of limited resources or > optimization or even co-evolution. But, those sorts of answers to _why_ > a living system assembles and maintains itself are really just question > begging... they put off the question without answering it. Either one is strictly materialist like Dawkins, then natural selection is indeed enough of an explanation. (that what can stay will stay, because if it couldn't it wouldn't) :-)) Or you assume a purpose to the universe, maybe something like Teilhard de Chardin's Omega point (which "draws" evolution toward it). Maybe Rosen is somewhere in between? > It's this "why" that leads him to consider "final cause". He takes the > most prevalent answer to the why question seriously: living systems do > what they do in order to benefit _themselves_. But how can an organism > at time t_0 know what actions will benefit that organism at time t_100? It does not know. It it chooses wrongly, it will not be here to complain. > The question he asks specifically is: "How can we have organization > without finality?" I.e. How can we say that an activity of an organism > is purposeful without some external _agent_ declaring the purpose of the > organism? In the end, he comes to the idea that effects cause their > causes, which is obviously cyclic. So he not also challenges the "mechanist/computationalist" thesis but also standard neo-darwinism? > makes perfect". These positive feedback loops where the effect of a > process is to reinforce the process are the heart of RR's idea. Sounds a bit like converging toward an attractor - that is a nice idea (and would also fit nicely with the Omega point) - but one does not need any final causation for that - rather it is normal causality which inevitably produces a result. Like a stone which is dropped on the Earth will fall toward the Earth and not, say, to the moon. (Aristoteles would have attributed this stone falling to final causation: the stone's resting position would naturally be the earth in his view, so that's where it goes when dropped; final causation is a little en vogue these days, but I think it is a flawed concept; or rather: it is a descriptional heuristic, but not an active force. > The trouble is that they are not _simply_ self-reinforcing. Each > iteration through the cycle _changes_ the system. So, you cannot > _finitely_ list all cycles up until some point UNLESS you actually do > it. Absolutely, I agree. > I.e. the end result of the 4 billion years of iteration is not > analytically predictable from the very first set of axioms we started > with 4 billion years ago. It's incompressible because each iteration > changes the building blocks. (And as our discussion about "informal" > formal systems covers, consistency is not necessarily preserved when new > axioms are added or when the axioms are changed, which means that formal > systems can't accurately model these self-modifying systems.) > True, if hindsight were 20/20, we could finitely list everything that > has already happened; but, we (probably) wouldn't be able to finitely > list everything that will happen from now until, say, 100 years from now > _because_ the underlying ontology changes at each iteration. But the new iterations are not new axioms; also, I am of course not claiming that one could simulate in advance the outcome of evolution - we do not know how the dice fall (in random mutation, crossover etc etc) I just mean it would be computable in principle. >> 4) An ultrafinitistic view would generally rule out noncomputable models >> anyway (see for instance the nice essay by Doron Zeilberger: >> http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf) >> Or: >> http://en.wikipedia.org/wiki/Ultrafinitism >> >> So Rosen's model's also make some mathematical assumptions (which, >> admittedly, are widely shared - but may change, of course) > > I don't understand how ultrafinitism rules out noncomputable models. It > seems to me that even in ultrafinitism, the halting problem is still > noncomputable (as Marcus mentioned). This is not what I meant - at the beginning of my post I wrote: >> complexity (=uncomputability in the Rosen sense) I was talking about Rosen's theory that _reality_ was uncomputable, not if there are uncomputable functions in a mathematical system. If, for instance, space-time is a "continuum" in the math sense, we get a problem, because we can only approximate real numbers on a finite computer. Then complexity_rr would hold (except if you could exploit the power of the continuum in analog computers). The current (Church Turing) model of computation assumes denumerably many states are available for computation. When I spoke of adopting ultrafinitism, I meant that this should hold in regard to reality. In philosophy of mathematics we can speak about two things: the mathematical objects themselves, or their relation to reality. The working mathematician is usually a platonist - he imagines, for instance, the real numbers existing in the mindscape/platonia or whatever. If you adopt an ultrafinitist stance, it only makes sense within a strong coupling to reality: the claim that reality is in the end discrete (QM, loop quantum gravity, holographic principle etc are all theories which give hints in this direction) Ultrafinitism is an extrapolation of the physical world (at least in my interpretation, I am sure one can also hold it as a pure philosophy of math, although it loses much of it's appeal then I would say). >> But the case against computatability is unconcinving. > > I agree... though I would not say "the case against computability"... > I'd say "the case against the expressive power of computation" is > unconvincing. Yes, your formulation "the case against the expressive power of computation" is what I meant - computability of course raises different associations, I was sloppy in the formulation. > I do believe that there are certain processes in reality > that are noncomputable in terms of what we now call "computation". Ok for the computability issues - I can't build a computer which solves the halting problem; but what I was speaking about above was the assumption that the universe could _be_ a computation (Seth LLoyd, Max Tegmark, Jürgen Schmidhuber come to mind). Or do you think there are physical processes which rule this conclusion out? (if yes, I would be very interested to hear about this, because I am currently researching this issue) Best wishes, Günther -- Günther Greindl Department of Philosophy of Science University of Vienna [EMAIL PROTECTED] http://www.univie.ac.at/Wissenschaftstheorie/ Blog: http://dao.complexitystudies.org/ Site: http://www.complexitystudies.org ============================================================ 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
