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Author
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Topic: A Gödelian Argument Against Darwinism
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William A. Dembski
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Member # 7
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posted 03. April 2003 11:15
A mechanism is a well-defined process where each step of the process leads predictably to the next. A mechanism can be deterministic, in which case one step leads with certainty to the next. Or it can be stochastic, in which case one step leads with a given probability to the next. Mechanisms are often embodied in objects but need not be. Hilbert's program for "mechanizing" mathematics attempted to show that all mathematical truths could be proven by mechanically applying logical rules of inference to manageable sets of axioms (manageable sets being those that are "recursive" as defined by mathematical logic). Hilbert's program failed (at the hands of Kurt Gödel), but a point worth noting is that the program's underlying mechanism was a consequence relation on an abstract class of symbol strings, and thus not located in any material object but rather in an abstract computational space.
The mechanism in Hilbert's program was deterministic. Other mechanisms are stochastic. Preeminent among stochastic mechanisms is, of course, the Darwinian mechanism of natural selection and random variation. The Darwinian mechanism is supposed to make it possible to get from anywhere in biological configuration space to anywhere else provided one can take small steps. How small? Small enough that they are reasonably probable. But what guarantee is there that a sequence of baby-steps connects any two points in configuration space? There is none. In fact, mounting evidence from biochemistry suggests that biological configuration space is extremely disconnected in this regard.
According to intelligent design, Darwin's theory fails for essentially the same reason that Hilbert's program failed. Hilbert's program for mechanizing mathematics failed because Gödel was able to demonstrate that logical rules of inference could not connect all mathematical truths back to a reasonable set of starting points (that is, a recursive set of axioms). Likewise Darwin's program for mechanizing biological evolution fails because it can be demonstrated that the Darwinian mechanism lacks the capacity to connect biological organisms exhibiting certain types of complex biological structures (for example, irreducibly complex or complex specified structures) to evolutionary precursors lacking those structures.
Note that to attribute such an incapacity to the Darwinian mechanism isn't to say that it's logically impossible for the Darwinian mechanism to attain such structures. It's logically possible for just about anything to attain anything else via a vastly improbable or fortuitous event. For instance, it's logically possible that with my very limited chess ability I might defeat the reigning world champion, Vladimir Kramnik, in ten straight games. But if I do so, it will be despite my limited chess ability and not because of it. Likewise, if the Darwinian mechanism is the conduit by which a Darwinian pathway leads to an irreducibly complex biochemical system, then it is despite the intrinsic properties or capacities of that mechanism. Thus, in saying that irreducibly complex biochemical structures are inaccessible to Darwinian pathways, design proponents are saying that the Darwinian mechanism has no intrinsic capacity for generating such structures except as vastly improbable or fortuitous events. Accordingly, to attribute irreducible complexity to a direct Darwinian pathway is like attributing Mount Rushmore to wind and erosion. There's a sheer possibility that wind and erosion could sculpt Mount Rushmore but not a realistic one.
Gödel's demonstration of the failure of Hilbert's program was strictly deductive. Intelligent design's demonstration of the failure of Darwin's program is a combination of empirical and theoretical arguments. In both cases, however, the issue is one of connectivity—can the mechanism in question supply a step-by-step path connecting two otherwise disparate elements (distinct mathematical propositions in the Hilbert-Gödel case, distinct organisms in the Darwinian case). Of course, while Gödel's anti-mechanistic argument for mathematics is entirely uncontroversial, intelligent design's anti-mechanistic argument for evolutionary biology has yet to win the day. I've argued in a number of my writings that the logic underlying this argument is sound (e.g., here).
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Pim van Meurs
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posted 03. April 2003 12:30
I see two problems with Dembski's argument.
First one:
Dembski asserts that:
"Likewise Darwin's program for mechanizing biological evolution fails because it can be demonstrated that the Darwinian mechanism lacks the capacity to connect biological organisms exhibiting certain types of complex biological structures (for example, irreducibly complex or complex specified structures) to evolutionary precursors lacking those structures. "
It has _NOT_ been shown that irreducible complexity or complex specified structures (*) cannot arise through Darwinian (or other natural) pathways. Thus the argument seems to fail at a crucial junction
Second:
Dembski has to allow for the possibility of Darwinian pathways although he argues, without much supporting evidence, that such pathways are unlikely. But the mere possibility of such pathways seems to undermine the argument from a design inference which relies on the absence of false positives and elimination of chance and regularity to infer design.
Thus while Godel's argument was deterministic, Dembski's argument is probabilistic and thus the similarity, if any, ends quickly.
Furthermore when Dembski states that "But what guarantee is there that a sequence of baby-steps connects any two points in configuration space? There is none. In fact, mounting evidence from biochemistry suggests that biological configuration space is extremely disconnected in this regard." he seems to be arguing against recent and not so recent findings about the structures of genotype phenotype mappings in proteins and RNA.
(*) CSI is argued to be limited through the fourth law of thermodynamics but as I have argued elsewhere on ISCID the fourth law seems to be nothing more than the second law for closed systems. In fact I have argued that for open systems CSI/entropy can locally increase/decrease through exchange with the environment. In experiments by Adami it is indeed the environment which increases CSI/decrease entropy.
[ 03. April 2003, 12:40: Message edited by: Pim van Meurs ]
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warren_bergerson
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posted 03. April 2003 13:40
While Dr. Dembski’s argument is an interesting one, it is, IMO, based on two fundamentally flawed assumptions.
First, IMO, both his assumed ‘probability bound’ and his interpretation of this bound are inappropriate. The appropriate probability bound in science is 99.99%plus not 10^-150. A scientific hypothesis is valid if it has a very high probability which can be demonstrated. "It could have happened if probability is greater than 10^-100" is not scientific validation. If, in science, a claim can not be demonstrated with a high degree of confidence, then the conclusion is ‘we don’t know’ or ‘we aren’t sure’.
Second, and more substantive, is the question of ‘mechanistic searches of large discontinuous spaces’. If I am interpreting his argument correctly, Dr. Dembski suggests that ‘intelligence is defined by the ability to find a highly improbable adaptive solution in a very large and discontinuous fitness landscape’. A mechanistic system, by this definition, would exhibit intelligence if it could solve a problem where there was 1 adaptive solution for every 10^200 or 10^1000 possibilities, (and all non-adaptive solutions are lethal).
Starting with this definition of intelligence- there are four questions to be addressed:
1. Are ‘non-human’ biological systems capable of solving ‘1 in 10^1000’ adaptive problems?
2. Can Darwinian or neo-Darwinian systems solve such problems?
3. Can artificial systems solve such problems without human assistance or front loading?
4. If biological systems exhibit intelligence(as defined), are there mechanistic explanations for the intelligence?
Dr. Dembski and I would agree that 1)biological systems exhibit intelligent design as defined, and 2)such design is not explainable by Darwinian mechanisms. We disagree, however, on the ability of mechanical systems to exhibit intelligence (as defined). I suggest that a mechanical systems has the ability to solve very complex or highly improbable problems if 1)the problem can be addressed with parallel processing (i.e. the problem can be factored in a number of smaller simpler problems) and 2)multiple selection operations or processes can be performed within each lifetime.
As I have stated previously, Dr. Dembski’s specified complexity argument is a strong argument for the inadequacy of Darwinian mechanisms. It is not, IMO, a strong argument against materialistic ID.
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RBH
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posted 04. April 2003 00:20
I'm a little perplexed. The title of the thread implies a formal/mathematical argument against 'Darwinism.' But Dembski wrote quote:
Preeminent among stochastic mechanisms is, of course, the Darwinian mechanism of natural selection and random variation. The Darwinian mechanism is supposed to make it possible to get from anywhere in biological configuration space to anywhere else provided one can take small steps. How small? Small enough that they are reasonably probable. But what guarantee is there that a sequence of baby-steps connects any two points in configuration space? There is none. In fact, mounting evidence from biochemistry suggests that biological configuration space is extremely disconnected in this regard.
My perplexity derives from Dembski's question "But what guarantee is there that a sequence of baby steps connects any two points in configuration space?" As I noted, this thread is titled "A Godelian Argument Against Darwinism," implying a formal mathematical issue, but the question is an empirical one.
My best guess (based on working with evolutionary algorithms in high-dimensioned spaces with multiple operators for 12 years or so) is that there is no guarantee; that it's entirely possible that you can't get there from here in some instances. But the question of whether one can get from here to there can't be answered by considering the form of the argument, which is implied by Dembski's use of "Godelian." Rather, it is a question of fact, a question of the substantive content of an assertion. So anonymous "here" and "there" have to be replaced by substantive terms that refer to specific entities or processes in the world. Then the answer to the question lies in doing the research necessary to ascertain whether one can or cannot plausibly get from (substantive) here to (substantive) there. (See below: "plausible".)
So the issue is not Godelian - that is, an argument from form/syntax - but rather empirical, a question of facts in the world. And questions about facts in the world get answered by doing research, not speculating about the formal properties of abstractions. On occasion the formal properties of an argument may help illuminate a weakness of that argument, but that's not the case here since Dembski over-states ("guarantee") the requirements of the substantive argument.
I will also remark that once again, the "baby steps" Dembski refers to are (at least implicitly) taken to have to occur on one single topography. But, of course, a biological population is evolving on multiple high-dimensioned landscapes simultaneously; each evolutionary operator (point mutation, deletion mutation, gene duplication, recombination, etc., etc.) induces a different landscape from a given fitness function. (I illustrated that and gave references a while back somewhere here or on ARN, but I'll be darned if I can find the posting now.) A "baby step" must refer to a single application of an evolutionary operator, not to the resulting appearance or effect. A "baby step" on the landscape induced by the point mutation operator will likely be smaller in its phenotypic effect than that of a "baby step" on the landscape induced by a recombination operator. Further, the phenotyopic effect of a "baby step" involved in processes at an early stage of development will likely be very different from the effects of one involved later in development.
I'm plain baffed by the meaning of Dembski's remark about baby steps having to be "Small enough that they are reasonably probable." The size of the "baby steps" (if "size" has anything to do with phenotypic effect exposed to selection) is governed by the evolutionary operators and fitness function. I have no idea what probability has to do with how small "baby steps" are. The conflation of "small" and "probable" obscures more than it illuminates.
Thus the notion of "baby step" in the OP is formally and substantively ill-defined and is of no particular help when considering the ways a population might traverse the multiple fitness landscapes on which it evolves. However, it is the case that evolutionary theory supposes that if there is a "baby step" (defined below) pathway from here to there via some combination of the evolutionary operators governing movement on the several fitness landscapes, then it is possible to get from here to there by evolution. But the test of that argument is not formal, it's empirical. Can one reconstruct a plausible sequence (i.e. likely in view of the evidence/data, a Bayesian interpretation of 'plausible') of "baby steps" defined as repeated single applications of the several evolutionary operators (keeping in mind this is occurring in a massively parallel system)?
Finally, "random variation" deserves a little attention. It has one primary meaning in evolutionary biology as I understand it, the "random with respect to current and future selective environments" meaning. That translates to "the distribution of the mutations that occur is not biased by the selective environment." That's an empirical issue, too, not answerable on purely formal grounds. I'm not sure if that's the meaning Dembski intends in his phrase "random variation." If so, then the burden of this meaning is that given a population sitting on the slopes of its several fitness landscapes, the mutations that occur (though not necessarily the occurrence of all evolutionary operators) are indifferent to the directions of the slopes. Some will be such as to move the population upslope on one or another landscape, some downslope on one or another, and some neither on any.
It follows that any estimate of the probability that one application of an evolutionary operator will move the population upslope on that operator's landscape (a selectively "beneficial" change) cannot be performed in ignorance of the location of the population on the slopes of the several landscapes on which the population is situated. Again, that can't be done purely formally. Most such estimates ignore three things. First is that except in the very beginning of life, evolution has never begun from scratch; it always starts with a functioning system that is more-or-less well adapted to its current environment. Second, selective environments tend to be correlated. Neighboring points (points that are one operator application from each other) on fitness landscapes tend not to be too dissimilar from one another in fitness values. Third, fitness landscapes are dynamically deforming, not static. The combination of those three facts means that one cannot naively estimate the probability of movement on the landscape as though one were sitting at the bottom of a (multi-dimensional) fitness cliff. Biological structures and processes are not generally discrete combinatorial objects. Rather, one must know a fair amount about the fitness surroundings of the population. Once again, that is an empirical question, not a formal question.
On another Brainstorms thread several people are beginning to work on the notion of "random," especially as it is used in evolutionary biology. Gedanken's remarks there on 'random as ignorance' (= no foresight/predictability) are germane, as are his remarks about constrained randomness. I'll watch that thread with interest.
I conclude that this thread is mis-titled. The questions raised in the OP are at base empirical questions, not formal questions. Godel is of no use here. The analogy is flawed.
RBH
[ 04. April 2003, 00:38: Message edited by: RBH ]
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Rex Kerr
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posted 04. April 2003 20:20
I've mentioned this before, but I'm unsure that distinguishing between "multiple high-dimensional landscapes simultaneously" and a single composite landscape is at all instructive. Given any set of operators W, and real life frequencies f_i for each application of an operator w_i in W, we can form the composite operator v = sum(f_i*w_i), and then consider baby steps in the topology induced by v on genome space.
Further, I am baffled by RBH's bafflement about a definition of a baby step as one that is "small enough that it is reasonably probable". From any given starting genome G there is a probability that G will become G' after a certain number of applications of our composite mutational operator and fitness function. Some of these probabilities can be rejected as not worth considering--for example, that a mouse would spontaneously give birth to a tarantella or a ruby-throated hummingbird. (Okay, that would be fatal during development--but you get the point.) In any case, there will be some number of applications of the mutational operator necessary to transform G to G', and if this number is too large ("not small") and the probabilities for each step are too low, then the G to G' transition will be improbable. This seems straightforward enough to me.
There are a few things that I am puzzled by, however. When Dembski says
quote:
But what guarantee is there that a sequence of baby-steps connects any two points in configuration space?
I am not sure that this is even the right question. Almost no points in biological configuration space are actually realized. Isn't the more relevant question whether or not there are such steps between extant organisms? (Note: you obviously have to allow forwards and backwards steps, as the process is not symmetric in time.)
Also, Hilbert's goal was, in essence, to create the Ultimate Mathematica, where you would plug in any question, apply rules, and get an answer (at least in theory). His goal was provably false. However, Mathematica, mechanically applying logical rules of inference to manageable sets of axioms, is amazingly good at large branches of mathematics (including proving theorems in first-order logic).
So in a way, Hilbert was vindicated on a pragmatic level, despite Godel's Incompleteness Theorem. Evolution is very much a pragmatic theory, not an abstract mathematical proof. If it is not possible to evolve between any pair of organisms (going forward only), that's fine. If there could exist well-functioning organisms that could not be evolved, that's fine too. The key is--do such organisms exist? And unlike Godel's counterexample to mechanized provability, this is very much a case-by-case, pragmatic issue. A very different kettle of fish.
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RBH
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posted 04. April 2003 21:16
Rex wrote quote:
Further, I am baffled by RBH's bafflement about a definition of a baby step as one that is "small enough that it is reasonably probable". From any given starting genome G there is a probability that G will become G' after a certain number of applications of our composite mutational operator and fitness function. Some of these probabilities can be rejected as not worth considering--for example, that a mouse would spontaneously give birth to a tarantella or a ruby-throated hummingbird. (Okay, that would be fatal during development--but you get the point.) In any case, there will be some number of applications of the mutational operator necessary to transform G to G', and if this number is too large ("not small") and the probabilities for each step are too low, then the G to G' transition will be improbable. This seems straightforward enough to me.
My bafflement is due to the use of "probability" as the metric. That seems to me to be not only unhelpful, but incalculable except on the most artificial and indefensible assumptions about PDFs. In addition, the probability metric is wholly uninformative about the processes that generate movement in the space of phenotypes exposed to selection. So I find it baffling that it is taken to be a measure of anything useful here.
It's obvious that one can construct a composite operator and work with the single topology it induces given a fitness function, but the fact that it is composite often escapes notice. There's a good deal of criticism out there that implicitly or explicitly takes the point mutation topology as somehow canonical, with no consideration given to the expansion of "neighborhoods" and complexification of the topology induced by additional operators. Hence I emphasize that. I don't take on faith that the evolution critics take it into account.
RBH
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gedanken
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posted 04. April 2003 22:35
Let me preface my comments by stating that I am not a biologist, and what I have to say is strictly based on second hand information -- let actual biologists please correct any errors.
Dr. Dembski said:
quote:
… The Darwinian mechanism is supposed to make it possible to get from anywhere in biological configuration space to anywhere else provided one can take small steps. How small? Small enough that they are reasonably probable. But what guarantee is there that a sequence of baby-steps connects any two points in configuration space? There is none. In fact, mounting evidence from biochemistry suggests that biological configuration space is extremely disconnected in this regard.
I find this interesting, in that I started to write something about that very statement that others have commented upon. I backtracked from my initial thoughts, but still find the statement to be some sort of misdirection or misunderstanding of the essential problem. In essence I agree that it is asking the wrong question.
Although based on a false understanding by leaving out certain realistic pathway elements, the notion of “Irreducible Complexity” is supposedly based on precisely the understanding of Darwinian evolution. (Or more precisely on claims of absence of probable pathways in such theory.) Dr. Dembski knows this full well, having devoted chapters of books on the refinement of IC concepts. In fact the supposed “mounting evidence from biochemistry suggest[ing] that biological configuration space is extremely disconnected in this regard” is precisely a restatement of the irreducible complexity argument. I’ve seen this idea presented time and time again at ID seminars and conferences. (And time and time again I see biologists confront such claims with information that convinces me that it is based on misunderstanding of what biologist’s research is showing.) There is no distinction -- find holes in the IC argument, and you find holes in the “disconnectedness” argument. But evolutionary theory is founded on the notion that there are severe constraints on what can be reached from any given point in biological “configuration” (in general). This is how evolutionary theory can be falsified, by simply observing connections that do not obey the constraints of evolutionary theory in terms of the theory of what attributes that descendents must have. If I am not mistaken, some sub-theories of evolution have been falsified on the basis of such conflicts being observed. The details of such conflicts are at the heart of modern day hot topic controversies that actually appear in the sub-theories of evolution.
Dembski correctly notes that Gödel’s points would relate to the recursive nature of attempting to create mathematics purely in terms of mathematics and mathematical logic. (Something that Gödel showed cannot strictly happen.) Dr. Dembski also correctly notes (elsewhere, including his “Logical Underpinnings.. “ paper he references) that biological systems evolution requires information to come from outside the system. (And thus information of biological development is not self-contained, but requires input from the environment that adds to “information” in most versions of concepts of the information content of the biological system population.) The issues debated in ID debates are about the nature of that external information source, for example if it is a proximate or ultimate information content of certain parts of the universe at origin. While we may debate whether the source of such information is a proximate intelligent agent action, the fact of external information input into biological evolutionary systems development is not in question.
Since that external application of information is not in question, the systems description is not of a recursive system. Mathematics is developed from input that comes from outside of mathematics. Biological evolution occurs with input that occurs from outside of the constraints of the pure biological systems themselves -- e.g. from the environment. (Once again whether an intelligent agent is acting in that environment -- even an “unembodied agent” -- is not relevant to whether standard biological evolutionary descriptions have such information coming from outside of the population that is evolving.
Since the biological evolutionary scenario of “Darwinian” evolution does not have the recursive nature that would invoke a “Gödel” like concept, I too question the relevance of bringing a discussion of Gödel to the topic.
“But what guarantee is there that a sequence of baby-steps connects any two points in configuration space? There is none.” Indeed there is no such guarantee for “any two points”. Rather the theory of evolution is that there would be steps (sized according to various theories) that were reasonably likely between any actually observed descendent and genetic information transfer pathways. This is, as commented, simply an issue relating to the correctness of IC concepts, and is not an issue of non-Gödelian construction of or in biological evolutionary concepts.
I guess I would like to see clarification of just what is intended to be the topic of discussion. Is this simply to be another thread about the accuracy of IC concepts? Or is there a different basis intended? If so, how is that different basis not simply and purely dependent on the “accuracy of IC concepts”? What is the basis of the claims of non-Gödelian relationships in biological evolutionary theory?
[ 04. April 2003, 23:27: Message edited by: gedanken ]
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Frances
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posted 06. April 2003 17:04
Reading Dembski's reference to "Logical underpinnings of intelligent design" I came across the following claim:
quote:
But there is now mounting evidence of biological systems for which any slight modification does not merely destroy the existing function but also destroys the possibility of any function of the system whatsoever (see Axe 2000).
Axe 2000, Extreme functional sensitivity to conservative amino acide changes on enzyme exteriors J. Mol Biology 301 585-95
I would like to hear from Dr Dembski how he reached the conclusion that it "destroys the possibility of any function of the system whatsoever" and furthermore explain the issue of 'slight modification'.
And I would like to know if Dr Dembski is familiar with the 1996 paper by Douglas Axe
Active barnase variants with completely random
hydrophobic cores
quote:
ABSTRACT The central structural feature of natural proteins is a tightly packed and highly ordered hydrophobic core. If some measure of exquisite, native-like core packing is necessary for enzymatic function, this would constitute a significant obstacle to the development of novel enzymes, either by design or by natural or experimental evolution. To test the minimum requirements for a core to provide sufficient structural integrity for enzymatic activity, we have produced mutants of the ribonuclease barnase in which 12 of the 13 core residues have together been randomly replaced by hydrophobic alternatives. Using a sensitive biological screen, we find that a strikingly high proportion of these mutants (23%) retain enzymatic activity in vivo. Further substitution at the 13th core position shows that a similar proportion of completely random hydrophobic cores supports enzyme function. Of the active mutants produced, several have no wild-type core residues. These results imply that hydrophobicity is nearly a sufficient criterion for the construction of a functional core and, in conjunction with previous studies, that refinement of a crudely functional core entails more stringent sequence constraints than does the initial attainment of crude core function. Since attainment of crude function is the critical initial step in evolutionary innovation, the relatively scant requirements contributed by the hydrophobic core would greatly reduce the initial hurdle on the evolutionary pathway to novel enzymes. Similarly, experimental development of novel functional proteins might be simplified by limiting core design to mere specification of hydrophobicity and using iterative mutation–selection to optimize core structure.
Is there any relevance of Axe's work to intelligent design? I understand that Douglas Axe seems to have denied that such relevance exists thus I am wondering if Dr Dembski could address the relevance of Axe's work to ID?
From the summary of Axe's paper we read
quote:
First, highly conservative replacements of exterior residues, none of which would cause significant functional disruption alone, are combined until roughly one in five have been changed. This is found to cause complete loss of function in vivo for two unrelated monomeric enzymes: barnase (a bacterial RNase) and TEM-1 b-lactamase.
One if five change does not seem to qualify as 'slight modification'.
Additionally it seems that the claim that 'also destroys the possibility of any function of the system whatsoever' does not seem to be supported by the work done by Axe in his 2000 paper.
I also understand that the Dembski paper is scheduled to be part of the 2003 "Debating Design: From Darwin to DNA". Is it too late to correct the paper?
[ 06. April 2003, 17:23: Message edited by: Frances ]
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Nel
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posted 06. April 2003 22:59
I am finding this comparison to be useful with regard to ID and Darwinian evolution.
The solution that arose after Godel disproved Hilbert's program didn't require a "Golden Mean" but a completely new paradigm that could not be thought of in terms of Hilbert's realism vs. Godel's idealism. Dembski's specified complexity and Behe's IC may be the cause of a similar paradigm shift. A paradigm shift caused by it's current focus on the origin of life and the irreducible complexity of the very tools of evolution, a new view of evolution through intelligent design.
I am finding more comparisons between Godel's shattering of Hilbert's "hopes" and irreducible complexity with respect to Darwinian evolution. Hilbert was correct when it came to simple arithmetic. It is completely possible, to put 0 + 1 = 1 into Hilbert's program. It requires only very simple rules and axioms. Goedel's theorem did not apply to every system, just those that are so complex so as to imply integer arithmetic.
In like fashion, simple irreducible systems may be explainable by chance/regularity, i.e., two proteins that happened to bind and become indispensible to the other. But Behe and Dembski's arguments against chance/regularity may not apply until the system gets complex enough. The comparison is quite striking. Darwinian evolution can explain finch beaks and antibiotic resistance in bacteria, but it cannot explain complex molecular machines or the cell, or life itself. Godel's incompleteness theorem questions whether we can truly have a "theory of everything" that can be accounted for with simple mathematics. We can not describe the universe with simple mathematics, we cannot describe biology with simple Darwinian mechanisms.
[ 06. April 2003, 23:16: Message edited by: Nelson_Alonso ]
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Frances
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posted 06. April 2003 23:17
Nelson:
quote:
The comparison is quite striking. Darwinian evolution can explain finch beaks and antibiotic resistance in bacteria, but it cannot explain complex molecular machines or the cell, or life itself.
This seems to be a truly unsupported assertion and I doubt that it can be supported in any meaningful manner. I hope that in interest of discussion and brain storming such comments can be avoided. Surely Godels arguments were supported on a more mathematical foundation than these not very helpful assertions of what evolution supposedly cannot explain.
Is that not the whole argument behind ID and is that not why ID seems to be having so many troubles since it relies on such sweeping claims?
[ 06. April 2003, 23:21: Message edited by: Frances ]
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Nel
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posted 06. April 2003 23:28
Francis,
As with Godel's theorem, Dembski's work shows that with complex systems, slight modifications halt function, and therefore are a problem for Darwinian evolution. These complex systems are not only IC because of loss of function, but because of fine-tuned intelligent design, if you modify it you won't get any function at all anymore. Which is why your quote states:
quote:
First, highly conservative replacements of exterior residues, none of which would cause significant functional disruption alone, are combined until roughly one in five have been changed. This is found to cause complete loss of function in vivo for two unrelated monomeric enzymes: barnase (a bacterial RNase) and TEM-1 b-lactamase.
One in five is indeed a slight modification. Whether Axe himself agrees with intelligent design is irrelevant. There is no need to "correct" Dembski's paper.
With respect to my assertion, indeed it is supported, in that there are unselectable steps and other co-option type events that usher in too many random events in order to get the IC system such as the bacterial flagellum, for example, there are unselectable steps from C ring to FliE (for starters). With respect to IC systems like combinatorial immunity (a topic that I plan to start a thread shortly) we see that IC matter of life and death of whole populations for the reasons I discussed in Organisms using GAs vs. Organisms being built by GAs .
[ 06. April 2003, 23:35: Message edited by: Nelson_Alonso ]
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gedanken
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posted 06. April 2003 23:47
Alonso, others,
The objection or confusion that some of us have here is the looseness of the analogy to “Gödelian” concepts is that there is such a wide range of possible subject matters. For example this discussion is already into the nature of IC itself. The analogy is so loose (the mathematical proof level of logic of Gödel’s theorems as compared to issues of whether evolution theory is recursive as compared issues of whether ID is empirical -- all topics engendered in or directly stimulated by the basic comments Dr. Dembski made). Even though the original topic was supposedly focused on this analogy of evolutionary theory so-called problems to Gödelian theory. Various posts have been given that show how loose the association is, and specifically the lack of such association.
Since almost any ID topic can be part of that issue of relating (or contradicting the relationship) of potential recursive nature of evolutionary theory to Gödelian theory, there is very little focus in this thread. That is the problem.
What I would like to have is a focus defined for this thread. Presumably as thread starter, Dr. Dembski should be the one to provide that focus -- but he seems to seldom participate in ISCID threads, even ones he starts.
[ 06. April 2003, 23:50: Message edited by: gedanken ]
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Nel
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posted 06. April 2003 23:51
Ged,
My post was to contradict such attempts at asserting that the analogy is loose. In fact, as I showed, the analogy is tighter than your belt after thanksgiving dinner. Hilbert's program attempted to reduce mathematics to mechanism. Godel showed that there is a "show stopper" when the system is complex. This is identical to what intelligent design is doing to Darwinian evolution. As Dembski stated:
quote:
In both cases, however, the issue is one of connectivity—can the mechanism in question supply a step-by-step path connecting two otherwise disparate elements (distinct mathematical propositions in the Hilbert-Gödel case, distinct organisms in the Darwinian case). Of course, while Gödel's anti-mechanistic argument for mathematics is entirely uncontroversial, intelligent design's anti-mechanistic argument for evolutionary biology has yet to win the day. I've argued in a number of my writings that the logic underlying this argument is sound (e.g., here).
[ 07. April 2003, 00:11: Message edited by: Nelson_Alonso ]
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gedanken
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posted 07. April 2003 00:13
I didn't really want to focus too much on arguing that point on page one, as per rules. Dembski's original post was somewhat a criticism of Darwinism, so I took some liberties -- but did so in making an issue that the focus was too loose and requesting a focus.
Can you help set a focus? If a more narrowly defined focus is developed (or laid out as consistent with Dr. Dembski's original post) then I'll be happy to continue in page 2 when I can make my views more plain. At present I disagree with so many aspects I can't really make a positive contribution, and am simply asking for the focus to be defined.
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Nel
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Member # 614
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posted 07. April 2003 00:18
Ged,
I already laid out the focus. As I said, the focus is on Godel's incompleteness theorem = IC
Hilbert's program = Darwinian evolution.
Godel's incompleteness theorem showed that you can't reduce mathematics to simple rules. IC shows that you can't reduce complex systems to simple components, thus the simple Darwinian rule of "step by selectable step" is ruled out.
[ 07. April 2003, 00:19: Message edited by: Nelson_Alonso ]
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