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About intelligence and ID – a response to scordova

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My post intends to be a response to a previous UD article by scordova. Scordova, who asks “should ID include AI as a form of intelligence?” and answers “I think so”, is aware to have put on the table a critical topic because himself writes:

I know many of my ID colleagues will disagree or will remain skeptical of adopting such a convention.

I am one of his ID colleagues who disagrees and I will explain why.

Scordova wrote:

So what is the evidence of intelligence? I would suggest the ability to construct artifacts or events with Specified Improbability (the usual term is Specified Complexity, CSI, etc. but those terms are too confusing).

This is an extremely reductive way to consider intelligence. Why consider only the construction of artifacts? Are people not constructing artifacts all stupid? There are countless evidences of higher activities by human intelligence. For example: the elaboration of logic, languages, mathematics, philosophy, sciences… To reduce intelligence only to its practical uses is pragmatism/materialism of the worse kind. A movement that names itself “intelligent design movement” cannot have a conception of intelligence so low.

Thus factories with robots, smart cruise missiles, genetic algorithms, bacteria, a collective network of ants, etc. can be considered intelligent systems. The problem is that we have no means of distinguishing real from artificial intelligence in any formal way.

“Factories with robots, smart cruise missiles, genetic algorithms” are not “intelligent systems” because what they produce is entirely due to the intelligence of their human designers. It is not the artificial system to be “intelligent”, rather its designer.

With no disrespect intended toward those with severe mental handicaps, yes such people are conscious, but there is a point a robotic automaton might be capable of generating more Specified Improbability than such an individual.

Conscious persons with mental handicaps, also if unable to produce “Specified Improbability”, are far more than robots because consciousness is always ontologically superior to any machine.

Some of us have imagined building robots that will land on a planet and tame it and build cities. They will act pretty much like human engineers and construction workers… Hence, the line between real and artificial intelligence gets blurred.

Again, robots build cities because they are programmed to do so by human engineers. In this case, the “line between real and artificial intelligence” is the clear hierarchical demarcation between “who programs and what is programmed”. “Who” are the human robotics engineers, “what” are the robots.

From an empirical standpoint, I don’t think it does ID much good to try to distinguish the outcomes of real vs. artificial intelligence, since we can’t formally demonstrate one from the other anyway, at least with regard to Specified Improbability.

On the contrary, I think that ID should carefully distinguish between real vs. artificial intelligence. (A general exhortation of Scholasticism was “distingue frequenter” in all fields.) One of the goals of ID theory is indeed to show that chance and necessity cannot produce information. Machines belong to “chance and necessity” because they are “necessitated” by their designer, so to speak. Therefore an IDer who denies the above ID proof self-contradicts.

We can even assume the process of natural selection is AI (where Natural Selection is an AI genetic algorithm in the wild), given it’s level of intelligence, we do not expect it to build extravagant artifacts.

To consider natural selection an “AI genetic algorithm” is to attribute it a merit that it doesn’t deserve. Not only natural selection is unable to build “extravagant artifacts”, it is unable to build the least artifact.

We can say an adding machine is intelligent, but we do not think, in and of itself it will build a space shuttle.

Actually I have on my desk an old mechanical adding machine. If you call it “intelligent” then why don’t call “intelligent” the reading lamp or the paperknife?

We rate the capability of various intelligence systems, and it is reasonable to affix limitations on them.

True, but here you contradict what you said before “we have no means of distinguishing real from artificial intelligence”. In fact, if we can rate various intelligences, we can see they form a hierarchy where at the top there is the real intelligence and at the bottom the artificial “intelligence”.

Whether the Intelligence that made the wonders of life is God, A Computer in Sky, Aliens, the Borg Collective, some mechanistic intelligence…it is irrelevant to the design inference. We might however be able to make statements about the level of capability of that intelligence.

Here again I see an inconsistence. I agree that we are able to grasp the level of capability of intelligence. But then, before a design inference on the universe as a whole, we cannot suppose that it was designed by “a Computer in Sky, Aliens, the Borg Collective, some mechanistic intelligence”. See here.

To sum up, to scordova’s question “should ID include AI as a form of intelligence?” my answer is: “no, we cannot consider an artificial system really intelligent”. Here I explained that real intelligence is direct connection to what I called “Infinite Information Source” (God). Here I explained that without such direct connection no comprehensibility of the world, also at the least degree, is possible. Here I explained that artificial systems (also those more sophisticated considered by AI) can show only false intelligence.

The direct connection to the Infinite Information Source (IIS) is the reason why the potentiality of knowledge of the real intelligence is infinite, as its source. No machine has this direct connection. As such the potentiality of real direct knowledge of a machine is zero. From the point of view of potentiality, the difference between real intelligence and its caricature – artificial “intelligence” – is like the difference between infinite and zero.

To deny the IIS and its connection to man is to consider man as an isolated finite system, whose potentialities are necessarily limited, due only to the configuration of its parts. This way real intelligence with its infinite potentiality of knowledge remains entirely unexplained. Said in theological terms: if man is not image of God, then man couldn’t have the potentiality of understanding he effectively has. If this simplistic materialist conception is supported by evolutionists/materialists no wonder. If it is supported by an IDer/creationist I am a bit bemused.

Comments
I would like to learn about these temporal principles. Could you refer me to some literature or resources on the topic?tragic mishap
November 21, 2013
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tragic mishap:
What you are essentially arguing is that this “watcher” has nothing to do with human intelligence, but you’re wrong. The “watcher” is the programmer. It has everything to do with human intelligence. It writes human intelligence into the brain. Just because the brain is an automaton doesn’t mean it’s intelligent beyond its programming, which is what you’re claiming for artificial intelligence.
I disagree that the watcher is the programmer. The brain programs or wires itself automatically based on known temporal principles. It automatically learns from its sensory stream and creates its own intelligent behavioral sequences automatically. The watcher simply decides which one it likes and selects them for activation. The watcher also has the ability to influence the attention mechanism of the brain so that it will pay attention to the things that gives it pleasure, such as music and beauty. Some people who suffer from certain forms of autisms have defective attentional mechanisms and the watcher is largely helpless in guiding attention.Mapou
November 21, 2013
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boranagain77 @101, quoting Dr. Dembski:
Dennett on Competence without Comprehension – William A. Dembski – June 2012 Excerpt: In 1936 Turing proposed a universal mechanism for performing any and all computations, since dubbed a Turing machine. In the last seventy-plus years, many other formal systems have been proposed for performing any and all computations (cellular automata, neural nets, unlimited register machines, etc.), and they’ve all been shown to perform the same — no less and no more — computations as Turing’s originally proposed machine.,,, ,,,, it’s obvious that a Turing machine can do nothing unless it is properly programmed to do so.
Ha! I was waiting for this. An intelligent robot's brain consists of one or more neural networks. A neural network is not a Turing machine for the following reasons: 1. It does not have a single long or infinite tape. 2. Unlike a Turing machine, it is not a single algorithm (sequences of instructions) with a single input and output. It has a huge number of inputs and outputs that can be active at any time during its operation. 3. It consists of multiple independent (parallel) devices each of which performs a single operation on an operand in response to an external signal. 4. Unlike a Turing machine, a neural network is not subject to the halting problem precisely because it is not a single algorithmic computer. 5. Unlike a Turing machine, a neural network is not designed to halt. 6. Unlike a Turing machine, a neural network will not fail catastrophically if one of its operations fails. A network fails gracefully and it takes many component failures in order to completely halt its functioning. 7. Last but not least, a Turing machine is atemporal, i.e., there is no way to determine whether two of its operations are concurrent or sequential. A neural network could not work without this capability. It is imperative for an intelligent program to be able to determine when events occur and in what order: sequential or concurrent. If two events or operations are sequential, the program must have a way of knowing the temporal interval between the two. A Turing machine has no such capability. There are other reasons but the above will suffice. In addition, I disagree with the idea that a neural network, or any modern computer for that matter, can do only what they are program to do. Computers can be programmed to use multiple sensors to respond to and learn from their environment. The programmer has no way of knowing what will be learned or when and therefore no way of knowing how the computer will behave. In addition, modern computers can be be programmed to use true random number generators for decision making. All of these things render such computers non-deterministic, whereas a Turing machine is fully deterministic.Mapou
November 21, 2013
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scordova #94
I include AI as intelligence, because to me, it looks like AI makes designed artifacts that would pass the EF.
My criticism basically was that real intelligence is not a mere producer of CSI. Therefore, also if AI makes CSI, one cannot state that AI is real intelligence. I know that ID theory per se doesn't need to investigate what real intelligence is, beyond to be a CSI producer. But, it seems to me that if the ID movement accepts such reductive conception of intelligence, it de facto passively embraces the same materialist atheist scientistic worldview of evolutionists. At the very end our disagreement is this: you seem favourable to this embracement and I am not. My OP wanted "only" to underline this possible "little" strategic difference among folks of the ID big tent.niwrad
November 21, 2013
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Mapou
What makes humans different than robots is not the nature of their intelligence but the fact that, unlike the robot with its fixed pre-programmed motivations, the human brain is controlled by another entity. This entity essentially sits there and watches the brain go about its business automatically. Most of the time, that is all it does. But, every so often, it takes over and changes the brain’s focus or attention. It may even initiate a behavioral sequence.
The definition usually used in debates like this is Turing's implicit definition, that is that human intelligence is the definition of intelligence. Robots do not have the "watcher", as you call it, that humans do. Therefore they will never be "like" humans in that way. What you are essentially arguing is that this "watcher" has nothing to do with human intelligence, but you're wrong. The "watcher" is the programmer. It has everything to do with human intelligence. It writes human intelligence into the brain. Just because the brain is an automaton doesn't mean it's intelligent beyond its programming, which is what you're claiming for artificial intelligence.tragic mishap
November 21, 2013
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niwrad @100, Here's your original objection:
Obviously the “another entity” (“the captain of the ship”) is not an automaton, otherwise why should you state #2 + #3? You could simply maintain #1 and stop so. Therefore human intelligence (the ship + the captain) is not an automaton (because the captain is not an automaton). In other words, (#2 + #3) contradicts #1.
I am simply saying that your claim of a contradiction depends on how you define intelligence. Notice how you are defining human intelligence. You say it's "the ship + the captain" and I say it's just the ship. Having said that, how do you know that the captain of the ship is not an automaton? You don't know that. Spirits are unchanging, in my opinion. Spirits are either good or evil. Christianity teaches us, for example, that all humans are evil/bad but that only 1/3 of the angels are bad. We are what we are and that is that.Mapou
November 21, 2013
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"I’m still waiting for that quote where Dr. Dembski excludes AI from his definition of intelligence." Dennett on Competence without Comprehension – William A. Dembski – June 2012 Excerpt: In 1936 Turing proposed a universal mechanism for performing any and all computations, since dubbed a Turing machine. In the last seventy-plus years, many other formal systems have been proposed for performing any and all computations (cellular automata, neural nets, unlimited register machines, etc.), and they've all been shown to perform the same -- no less and no more -- computations as Turing's originally proposed machine.,,, ,,,, it's obvious that a Turing machine can do nothing unless it is properly programmed to do so. http://www.evolutionnews.org/2012/06/dennett_on_comp061451.html#sthash.pIAPWiRP.dpuf As to solving engineering problems: Applied Darwinism: A New Paper from Bob Marks (W. Dembski) and His Team, in BIO-Complexity - Doug Axe - 2012 Excerpt: Furthermore, if you dig a bit beyond these papers and look at what kinds of problems this technique (Steiner Tree) is being used for in the engineering world, you quickly find that it is of extremely limited applicability. It works for tasks that are easily accomplished in a huge number of specific ways, but where someone would have to do a lot of mindless fiddling to decide which of these ways is best.,, That's helpful in the sense that we commonly find computers helpful -- they do what we tell them to do very efficiently, without complaining. But in biology we see something altogether different. We see elegant solutions to millions of engineering problems that human ingenuity cannot even begin to solve. http://www.evolutionnews.org/2012/04/applied_darwini058591.htmlbornagain77
November 21, 2013
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Welcome back scordova, thank you! -- Now I have to say this to Mapou:
Well, since I believe intelligence is in the brain, I see no contradiction. The other entity simply changes the course of the brain’s behavior every once in a while for whatever reason. It lets the brain do its intelligent work. It does not provide the intelligence, just the motivational push.
The other entity simply changes the course of the brain’s behavior? and just provide the motivational push? Your defence somehow reinforces my objection... :)niwrad
November 21, 2013
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After thinking about it for a while, I now find myself fully agreeing with scordova's claim that AI can create CSI. However, CSI requires intelligence or an act of creation and since AI is itself full of CSI, we cannot have an infinite regress of AIs creating AIs. At one point there was a beginning and that beginning was triggered or created by entities in the unchanging spiritual realm.Mapou
November 21, 2013
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blockquote>Now you have insulted my intelligence! :) Well in that case, we're just one big happy family of offenders and offendees. :) PS. I'm still waiting for that quote where Dr. Dembski excludes AI from his definition of intelligence.Mapou
November 21, 2013
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A little note on my invitation to work with Robert Marks and Bill Dembski. Bill in May 2007 encouraged me to study under Dr. Marks and the main project was initially to deconstruct the Avida program. I actually found bugs in earlier versions of Avida like the fact I could crank up the cosmic radiation parameter to insane numbers, and the creatures kept reproducing. So I knew something was up. Avida has been held up as an illustration that new information can be made. There are a number ways to criticize it, because clearly its claims are over-inflated. I'm cautious about saying "information never increases" because the metrics for information are subjective. It was good to compare blind search versus Darwinian search that had no specialized information. That is the proper line of argument against Avida .... although I kind of liked my simpler proof against its earlier versions. Crank up the radiation parameter and show that Avida bogusly lets the creatures keep living. It was so bad, Evan Dorn (Adami's grad assistant on the Avida project) showed up at ARN in my debate with Richard Hoppe (of Pandas Thumb) to say the bug will be fixed. There was some debate whether it was that bug-filled version of Avida was used to give results in the paper the Avida group published in Nature. If so, it only highlights the misleading clams of Avida. I think the better way to frame criticism of evolutionary algorithms (which are an instance of AI), is to state that they have limits as to what they can evolve into. Those limits are rarely obvious, but sometimes we can make credible arguments on a case by case basis. For example: 1. simple chess playing machines will not solve Fermat's last theorem 2. single cell creatures will not evolve into multi-celled creatures The NFL arguments are good at criticizing protein evolution because that is a blind search problem. Avida does not in any prove that protein evolution will happen. However, I use NFL arguments cautiously otherwise. I also am cautious about CSI, partly because of the definition problems, and difficulty in agreeing on exactly how much CSI is in a given system (like 2000 coins).scordova
November 21, 2013
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'It does not matter whether or not it’s in my imagination' Now you have insulted my intelligence! :)bornagain77
November 21, 2013
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bornagain77,
Mapou, only in your imagination did I insult you.
It does not matter whether or not it's in my imagination. I felt insulted and I demand an apology. You do that and I will likewise apologise to you for insulting you.Mapou
November 21, 2013
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Again I apologize. Please reconsider your decision to abandon the discussion. Thank you.
Thank you, and I will continue then since you have invited me to stay. I don't expect we'll resolve the issues, but maybe to clarify. Lines of argument defending ID I feel comfortable with: 1. Irreducible Complexity 2. Population Genetics 3. OOL 4. analysis of rhetorical tricks in Darwinism 5. probably a few others Lines of argument defending ID I don't feel comfortable with (even if I accept some of the axioms as true) 1. consciousness 2. free will 3. some parts of CSI 4. the 2nd law 5. maybe a few others 6. the Bible 7. the Christian faith I accept the Christian faith, but I don't use it to defend ID. I accept the Christian faith because I accept ID, not the other way around. My concerns about CSI I've stated at UD in various threads like: Siding with Mathgrrl on a Point The question of consciousness and intelligence is an interesting one, but Bill in some of his earlier works (ID the bridge between science and theology) argued to leave "intelligence" as an undefined primitive. He later changed his mind, when I think leaving "intelligence" as an undefined primitive was the way to go. Thus I think it doesn't help to argue the ID case by insisting intelligence is necessarily conscious. The effective line of argument basic probability arguments. The basic explanatory filter (EF) by Dembski was good enough to explain what objects have the appearance of Design. No where in the EF was there an assumption that intelligence was conscious, in fact the EF didn't even assume intelligence existed in the first place -- it merely describes what looks designed according to human convention. I include AI as intelligence, because to me, it looks like AI makes designed artifacts that would pass the EF. I can't run away from the fact AI systems (or even simple automatons) make artifacts that pass the EF.scordova
November 21, 2013
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StephenB Thanks for your words. Yes, you are right about scordova, and I offended him. I apologized and hope he comes back (he could be my son...). scordova Have you seen as soon I apologized? I am married, so I am trained about :) Please come back to discuss!niwrad
November 21, 2013
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Well, I notice that niwrad beat me to the punch, so all is well (I hope). By the way, niwrad, I love the phrase "evolution & co."StephenB
November 21, 2013
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Sorry Mapou but your argument is incoherent. You say: (1) human intelligence is an automaton (2) the human brain is controlled by another entity [inside man] (3) analogy: the brain is a “ship”, the entity is “the captain of the ship” Obviously the “another entity” (“the captain of the ship”) is not an automaton, otherwise why should you state #2 + #3? You could simply maintain #1 and stop so. Therefore human intelligence (the ship + the captain) is not an automaton (because the captain is not an automaton). In other words, (#2 + #3) contradicts #1.
Well, since I believe intelligence is in the brain, I see no contradiction. The other entity simply changes the course of the brain's behavior every once in a while for whatever reason. It lets the brain do its intelligent work. It does not provide the intelligence, just the motivational push.Mapou
November 21, 2013
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Mapou, only in your imagination did I insult you. You in fact stated an unsubstantiated personal opinion and I thanked you for stating it and asked you for peer-reviewed mathematical evidence to back it up. You took umbrage that someone should dare doubt the integrity of your unsubstantiated personal opinion and started hurling personal insults thereafter. Moreover, as shocking as it may be to you, I have even less repect for your personal opinion now as I had before you started hurling personal insults. Go figure! Reap what you sow and all that!bornagain77
November 21, 2013
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Mapou #76 Sorry Mapou but your argument is incoherent. You say: (1) human intelligence is an automaton (2) the human brain is controlled by another entity [inside man] (3) analogy: the brain is a "ship", the entity is "the captain of the ship" Obviously the "another entity" ("the captain of the ship") is not an automaton, otherwise why should you state #2 + #3? You could simply maintain #1 and stop so. Therefore human intelligence (the ship + the captain) is not an automaton (because the captain is not an automaton). In other words, (#2 + #3) contradicts #1.niwrad
November 21, 2013
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bornagain77 @87, I'm surprised you don't have a quote for that resounding yes.Mapou
November 21, 2013
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Mapou as to: "Does his definition exclude artificial intelligence?" Yes!bornagain77
November 21, 2013
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niwrad, I don't think Sal is fearful of defending arguments on behalf of human intelligence. The real difficulty is that, sadly, he doesn't believe that human reason can apprehend truth in the absence of faith (fideism). His philosophical orientation is dubious, but his moral courage is in tact. His intramural challenges prove that. By the way, I think you are doing a splendid job of dramatizing the unbridgeable gap between human intelligence and artificial intelligence. Keep up the good work.StephenB
November 21, 2013
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bornagain77, You apologize to me first since you started it. And then I'll apologize to you. How's that? :)Mapou
November 21, 2013
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Mapou, "niwrad is out of line and should apologize." and where is my apology from you for your many insults towards me in this thread? :) Morals work both ways you know (lest thou be accused of hypocricy! :)bornagain77
November 21, 2013
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Before I leave the thread, out of gratitude to Tragic Mishap, I'd like to answer his question. At UD I have offered both defense and criticisms of ID theories. It's not that I'm trying to articulate a middle ground, I describe what I think are correct and incorrect statements. I choose sides in as much as I side with the arguments that I think are most correct. For example, I took a lot of heat, and still take a lot of heat because I sided with the Darwinists on the 2nd law. What I believe: 1. free will 2. moral responsibility 3. ID 4. special creation 5. young universe 6. the Bible as the inspired word of God in the original texts 7. God exists 8. human consciousness I confess the Nicene creed, and most of the Westminster Confession, except their views on the Sabbath. I'm a member of the Potomac Presbytery or the Presbyterian Church of America. The things I list above, I accept on reasonable faith. I will not presume to prove them as true, like I would prove a theorem of math.
scordova, you appear to have rejected free will as an axiom upon which to reason. Why? What are the axioms you use instead?
You don't need the axiom of free will to argue against OOL and Darwinism. It is un-necessary. What axioms do I use? Whatever works. One can even start with wrong axioms for the sake of argument in order to prove those axioms are wrong. That is reductio ad absurdum. We don't need the assumption of free-will to argue mindless OOL and Darwinian evolution will fail. I don't emphasize CSI and NFL very much to argue ID. Probably the central argument I'd use is irreducible complexity. I've stated my faith axioms, and like faith axioms go, they are ultimately unprovable, even though they might be reasonably believable.scordova
November 21, 2013
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Mr. Cordova, I suggest since you are contradicting what Dr. Dembski and Dr. Marks both hold with this statement: “I don’t emphasize the importance of conscious intelligence in creating CSI since, imho, CSI can be made (created?) by non-conscious automatons.” ,,that you e-mail one, or both, of them so as to iron out either your, or their, confusion on the conservation of information matter. It will not be the first time you disagreed with a prominent ID figure, such as the time you disagreed with Dr. Sewell, in a very public way, on the second law.bornagain77
November 21, 2013
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Now that you’re slinging these sort of accusations about my person, I so no reason to continue in this thread.
I, for one, appreciate your comments in this thread. niwrad is out of line and should apologize.Mapou
November 21, 2013
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scordova It wasn't my intention to offend you. Likely I used improper words. I apologize. What I meant is that - as I already said to kairosfocus - the ID enterprise is a defence of the obvious. And it was unbelievable to me that an intelligent person as you cannot see such obvious and don't defend it. Unfortunately I expressed very badly my thought. Again I apologize. Please reconsider your decision to abandon the discussion. Thank you.niwrad
November 21, 2013
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bornagain77 quoting Dembski:
It can be created by intelligence or it can be shunted around by natural forces. But natural forces, and Darwinian processes in particular, do not create information.
Yeah but what does Dr. Dembski mean by intelligence? Does his definition exclude artificial intelligence?Mapou
November 21, 2013
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as to:
"I don’t emphasize the importance of conscious intelligence in creating CSI since, imho, CSI can be made (created?) by non-conscious automatons."
I strongly disagree with Mr. Cordova for, as far as I know, Dr. Dembski has not backed off one iota from this following statement, he made a few years ago, but has in fact gone over and beyond the it with his subsequent work on conservation of information:
LIFE’S CONSERVATION LAW – William Dembski – Robert Marks – Pg. 13 Excerpt: Simulations such as Dawkins’s WEASEL, Adami’s AVIDA, Ray’s Tierra, and Schneider’s ev appear to support Darwinian evolution, but only for lack of clear accounting practices that track the information smuggled into them.,,, Information does not magically materialize. It can be created by intelligence or it can be shunted around by natural forces. But natural forces, and Darwinian processes in particular, do not create information. Active information enables us to see why this is the case. http://evoinfo.org/publications/lifes-conservation-law/ “The Search for a Search: Measuring the Information Cost of Higher-Level Search,” Journal of Advanced Computational Intelligence and Intelligent Informatics 14(5) (2010): 475-486 “Conservation of Information in Search: Measuring the Cost of Success,” IEEE Transactions on Systems, Man and Cybernetics A, Systems & Humans, 5(5) (September 2009): 1051-1061
Chaitin put the problem like this:
At last, a Darwinist mathematician tells the truth about evolution - VJT - November 2011 Excerpt: In Chaitin’s own words, “You’re allowed to ask God or someone to give you the answer to some question where you can’t compute the answer, and the oracle will immediately give you the answer, and you go on ahead.” https://uncommondescent.com/intelligent-design/at-last-a-darwinist-mathematician-tells-the-truth-about-evolution/
i.e. Information can be 'fished out' of a algorithm in a computer program but information cannot magically materialize (be created) without that preexistent information guiding the program along in its search to find a solution (in the search space) to the problem. i.e. Information is not being 'created'! No Free Lunch! Here is the video where, at the 30:00 minute mark, you can hear the preceding "God" quote from Chaitin's own mouth in full context:
Life as Evolving Software, Greg Chaitin at PPGC UFRGS http://www.youtube.com/watch?v=RlYS_GiAnK8
Moreover, at the 40:00 minute mark of the video Chaitin readily admits that Intelligent Design is the best possible way to get evolution to take place, and at the 43:30 minute mark Chaitin even tells of a friend pointing out that the idea Evolutionary computer model that Chaitin has devised does not have enough time to work. And Chaitin even agreed that his friend had a point, although Chaitin still ends up just 'wanting', and not ever proving, his idea Darwinian mathematical model to be true! (How many times have we seen that?!?) Related quotes from Chaitin and Dembski:
The Limits Of Reason - Gregory Chaitin - 2006 Excerpt: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.,,, http://www.umcs.maine.edu/~chaitin/sciamer3.pdf Dennett on Competence without Comprehension – William A. Dembski – June 2012 Excerpt: As it turns out, there are problems in mathematics that can be proved to be beyond resolution by any algorithm (e.g., the halting problem). http://www.evolutionnews.org/2012/06/dennett_on_comp061451.html#sthash.pIAPWiRP.dpuf
Notes:bornagain77
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