Gödel, Human Intuition, and Intelligent Design

_{Jonathan Bartlett

September 1, 2012

Intelligent Design}

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This is a great video on the interplay between the ideas of Gödel and Turing on what Gödel’s incompleteness means for the mind. This is of great importance to ID, because it indicates what it means for “design” as opposed to “mechanism”, and the limitations of any mechanistic/physicalist model of reality and humanity.

Kurt Gödel: Incompleteness Theorem and Human Intuition

Someone pointed me to this video a while ago, but I don’t remember who – thanks to whoever it was – it was certainly worthwhile! Also, does anyone know what video this is taken from?

For those interested in more modern advances on the subject, you might check out these talks on the subject from the recent Engineering and Metaphysics conference:

Comments

ba77#8:
Neil you indignantly claim that I misrepresented the (your) atheistic/Darwinian position,,, a ‘strawman’ you called it. Yet the fact of the matter is that nobody has EVER seen purely material processes generate any non-trivial functional information, and Intelligent agents (humans) routinely, almost as a force of habit, generate non-trivial amounts of functional information (as your very own words testify to every time you write a post).
My own view is that information is not a natural kind; it is a human artifact. It follows that DNA is not information, though when we write down particular gene sequences as sequences of letters, that is information. The arguments about CSI all seem empty to me, because they critically depend on the dubious assumption that information is a natural kind.Neil Rickert_{September 1, 2012
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johnnyb#9:
First of all, I think that either Penrose has changed his mind on this, or you misunderstood his point. I have not read his books, but I did listen to a recent talk of his on the subject. Your criticisms apply much better to my own views on the subject rather than Penrose’s.
That's a long talk, and I have not yet finished listening. I doubt that Penrose has changed his underlying intuition. I am inclined to agree with that intuition (if I understand it correctly). The problem comes when he tries to turn that intuition into a logical argument. And that always fails (as it did for Searle). His approach in his books, was to use Gödel to argue that formalistic mathematics is limited, compared to platonist mathematics. I agree with that on the intuitive level. And Gödel might have agreed with that, too. But you cannot turn that into a formal argument, because platonism is not formalized. If we assume that, as an intuitive conclusion, Penrose then argues that an AI system could only be a formalist mathematician but could not be a platonist mathematician. That argument fails, in my opinion. It depends too much on unpersuasive hand-waving. Let's suppose that Penrose is correct, even though his argument does not work. That still would not help ID, as best I can tell. It might suggest a problem with a strict mechanistic materialist account of mind. But ID itself would seem to depend on a mechanistic materialist view. How else could a putative intelligent designer carry out an intelligent design process, except by reliance on mechanistic materialistic methods to carry forward the design? Footnote: I am about 20% through that Penrose video. Thus far he has given some of the reasons that support his intuition against AI. I mostly agree with that. He is now moving on to talk of mathematical truth. It looks as if he is about to argue: An AI system can only do formalist truth, and formalists truth is different from mathematical truth as understood by platonists. Therefore AI is wrong. But why not consider an alternative conclusion, namely our ordinary common sense notion of truth is incoherent and inconsistent. And that's about my view. Mathematics and science work quite well, because they depend only on a restricted use of truth.Neil Rickert_{September 1, 2012
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Neil - First of all, I think that either Penrose has changed his mind on this, or you misunderstood his point. I have not read his books, but I did listen to a recent talk of his on the subject. Your criticisms apply much better to my own views on the subject rather than Penrose's. Penrose uses Godel/Turing to argue for a different Physics - one which depends on more complex dynamics than is available in a computable system. However, this is not the same as his argument for the mind. Penrose's argument for the mind is that physics, as such, has nothing in it that contributes to understanding. That is, physics can calculate, but not understand or comprehend. It is very much similar to Searle's Chinese Room argument. Now, regarding your arguments - you say that "any plausible account of the mind would be a finitistic one". Rather than getting around the Godel/Turing result, it rather intensifies it. For the question is not about understanding our own mind, but about how we understand reality. Therefore, to make the mind smaller than a Godel/Turing machine, you actually place greater limitations on the ability of human knowledge than either of them did. The core of rationality is being able to reason to higher-level verities. If we do not have access to something greater than a Godel/Turing machine, then the ability to reason is itself suspect. As an example, most of number theory is reducible to Turing machines, and the ability to make progress in number theory is based on human's ability to surpass the Turing limit.johnnyb_{September 1, 2012
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Neil you indignantly claim that I misrepresented the (your) atheistic/Darwinian position,,, a 'strawman' you called it. Yet the fact of the matter is that nobody has EVER seen purely material processes generate any non-trivial functional information, and Intelligent agents (humans) routinely, almost as a force of habit, generate non-trivial amounts of functional information (as your very own words testify to every time you write a post). In spite of this glaring deficiency of empirical validation for a (the) basic premise of the atheistic/materialistic/Darwinian position, and despite your seemingly insane denial to the contrary, Darwinists dogmatically cling to this unsubstantiated premise that material processes can create stunning levels of informational complexity (parallel processing) in life that our best computer programmers can only dream of imitating! In fact there is a name for this dogmatic belief atheists have imposed on science, it is called methodological naturalism! You don't believe me??? Well here is a infamous quote:
Darwinian Fundamentalist Manifesto: Richard Lewontin's Commitment to Materialism Excerpt: Our willingness to accept scientific claims that are against common sense is the key to an understanding of the real struggle between science and the supernatural. We take the side of science in spite of the patent absurdity of some of its constructs, in spite of its failure to fulfill many of its extravagant promises of health and life, in spite of the tolerance of the scientific community for unsubstantiated just-so stories, because we have a prior commitment, a commitment to materialism. It is not that the methods and institutions of science somehow compel us to accept a material explanation of the phenomenal world, but, on the contrary, that we are forced by our a priori adherence to material causes to create an apparatus of investigation and a set of concepts that produce material explanations, no matter how counter-intuitive, no matter how mystifying to the uninitiated. Moreover, that materialism is absolute, for we cannot allow a Divine Foot in the door. The eminent Kant scholar Lewis Beck used to say that anyone who could believe in God could believe in anything. To appeal to an omnipotent deity is to allow that at any moment the regularities of nature may be ruptured, that miracles may happen. - quote from Richard Lewontin's January 9, 1997 article, Billions and Billions of Demons, http://darwinianfundamentalism.blogspot.com/2005/07/darwinian-fundamentalist-manifesto.html
Ironically this fear of atheistic materialists that 'at any moment the regularities of nature may be ruptured, that miracles may happen' is exactly what you get when you insist on methodological naturalism (purely material answers) and you deny God His rightful place as being the author of all reality, especially including, His rightful place being the author of all science!:
BRUCE GORDON: Hawking's irrational arguments - October 2010 Excerpt: The physical universe is causally incomplete and therefore neither self-originating nor self-sustaining. The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world. Neither is it the case that "nothing" is unstable, as Mr. Hawking and others maintain. Absolute nothing cannot have mathematical relationships predicated on it, not even quantum gravitational ones. Rather, the transcendent reality on which our universe depends must be something that can exhibit agency - a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what "breathes fire into the equations and makes a universe for them to describe.,,, the evidence for string theory and its extension, M-theory, is nonexistent; and the idea that conjoining them demonstrates that we live in a multiverse of bubble universes with different laws and constants is a mathematical fantasy. What is worse, multiplying without limit the opportunities for any event to happen in the context of a multiverse - where it is alleged that anything can spontaneously jump into existence without cause - produces a situation in which no absurdity is beyond the pale. For instance, we find multiverse cosmologists debating the "Boltzmann Brain" problem: In the most "reasonable" models for a multiverse, it is immeasurably more likely that our consciousness is associated with a brain that has spontaneously fluctuated into existence in the quantum vacuum than it is that we have parents and exist in an orderly universe with a 13.7 billion-year history. This is absurd. The multiverse hypothesis is therefore falsified because it renders false what we know to be true about ourselves. Clearly, embracing the multiverse idea entails a nihilistic irrationality that destroys the very possibility of science. http://www.washingtontimes.com/news/2010/oct/1/hawking-irrational-arguments/ The Absurdity of Inflation, String Theory & The Multiverse - Dr. Bruce Gordon - video http://vimeo.com/34468027 Here is the last power-point slide of the preceding video: The End Of Materialism? * In the multiverse, anything can happen for no reason at all. * In other words, the materialist is forced to believe in random miracles as a explanatory principle. * In a Theistic universe, nothing happens without a reason. Miracles are therefore intelligently directed deviations from divinely maintained regularities, and are thus expressions of rational purpose. * Scientific materialism is (therefore) epistemically self defeating: it makes scientific rationality impossible.
bornagain77_{September 1, 2012
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ba77:
..., then why did you just provide further empirical evidence for ID by writing your post?
Quite simply, I didn't. If you want ID to be taken seriously, then you need to get away from ridiculous mischaracterization of what others say, and actually start working on real evidence.
Premise One: No materialistic cause of specified complex information is known. Conclusion: Therefore, it must arise from some unknown materialistic cause
If a Darwinist actually presented such an argument, they would be ridiculed, and rightly so. If ID is all about attacking a strawman, then I concede. The strawman that ID proponents attack really is as ridiculous as you say it is. But your victory is hollow, for it only serves to show how little there is in ID.Neil Rickert_{September 1, 2012
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Neil snorted:
The only relevance that I can see to ID, is that this supports the view that ID is philosophy, not science.
Neil, if you really believe Darwinian evolution is 'science' and ID is merely philosophy, then why did you just provide further empirical evidence for ID by writing your post? You see Neil if you could get purely material processes to generate just a few sentences of the functional information, which you just 'effortlessly' did ('effortlessly' because it is evident you were not really thinking very hard when you wrote it :) ) ,,,when you wrote your post then you could actually provide a basis for Darwinism within science and forever silence the critics of Darwinism who maintain Darwinism is, in reality, nothing but a pseudo-science with no real empirical basis to appeal to to silence the accusation of fraud against it! Notes: the materialistic/Darwinian argument essentially appears to be like this:
Premise One: No materialistic cause of specified complex information is known. Conclusion: Therefore, it must arise from some unknown materialistic cause
On the other hand, Stephen Meyer describes the intelligent design argument as follows:
“Premise One: Despite a thorough search, no material causes have been discovered that demonstrate the power to produce large amounts of specified information. “Premise Two: Intelligent causes have demonstrated the power to produce large amounts of specified information. “Conclusion: Intelligent design constitutes the best, most causally adequate, explanation for the information in the cell.” There remains one and only one type of cause that has shown itself able to create functional information like we find in cells, books and software programs -- intelligent design. We know this from our uniform experience and from the design filter -- a mathematically rigorous method of detecting design. Both yield the same answer. (William Dembski and Jonathan Witt, Intelligent Design Uncensored: An Easy-to-Understand Guide to the Controversy, p. 90 (InterVarsity Press, 2010).) Stephen Meyer - The Scientific Basis for the Intelligent Design Inference - video http://vimeo.com/32148403 Book Review - Meyer, Stephen C. Signature in the Cell. New York: HarperCollins, 2009. Excerpt: So, it comes down to this: Where did that information come from? The simplest known free living organism (although you may quibble about this, given that it's a parasite) has a genome of 582,970 base pairs, or about one megabit (assuming two bits of information for each nucleotide, of which there are four possibilities). Now, if you go back to the universe of elementary particle Planck time chemical labs and work the numbers, you find that in the finite time our universe has existed, you could have produced about 500 bits of structured, functional information by random search. Yet here we have a minimal information string which is (if you understand combinatorics) so indescribably improbable to have originated by chance that adjectives fail. http://www.fourmilab.ch/documents/reading_list/indices/book_726.html
To clarify as to how the 500 bit universal limit is found for 'structured, functional information':
Dembski's original value for the universal probability bound is 1 in 10^150, 10^80, the number of elementary particles in the observable universe. 10^45, the maximum rate per second at which transitions in physical states can occur. 10^25, a billion times longer than the typical estimated age of the universe in seconds. Thus, 10^150 = 10^80 × 10^45 × 10^25. Hence, this value corresponds to an upper limit on the number of physical events that could possibly have occurred since the big bang. How many bits would that be: Pu = 10-150, so, -log2 Pu = 498.29 bits Call it 500 bits (The 500 bits is further specified as a specific type of information. It is specified as Complex Specified Information by Dembski or as Functional Information by Abel to separate it from merely Ordered Sequence Complexity or Random Sequence Complexity; See Three subsets of sequence complexity) Three subsets of sequence complexity and their relevance to biopolymeric information - Abel, Trevors http://www.tbiomed.com/content/2/1/29 This short sentence, "The quick brown fox jumped over the lazy dog" is calculated by Winston Ewert, in this following video at the 10 minute mark, to contain 1000 bits of algorithmic specified complexity, and thus to exceed the Universal Probability Bound (UPB) of 500 bits set by Dr. Dembski Proposed Information Metric: Conditional Kolmogorov Complexity - Winston Ewert - video http://www.youtube.com/watch?v=fm3mm3ofAYU Here are the slides of preceding video with a clearer view of the calculation of the information content of the preceding sentence on page 14 http://www.blythinstitute.org/images/data/attachments/0000/0037/present_info.pdf
bornagain77_{September 1, 2012
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To my knowledge, Penrose actually has three books on the topic. In addition to the one you mentioned, there are "Shadows of the Mind" and "The Large, the Small and the Human Mind." My memory of the last of those is hazy - I didn't spend as much time on it as on the other two. In "Shadows", Penrose recasts his argument from "Emperor's New Mind" so as to base it on Turing rather than on Gödel. Here are two problems that I have with Turing's argument: 1: The Gödel proof and Turing's Halting problem are for infinite systems (the Peano axioms for Gödel, the Turing machine for Turing). However, any plausible account of the mind as a computer would be a finitistic one. That is, the mind would have to be seen as a finite automaton, not as an infinite Turing machine. And the halting problem does not apply to finite automata. 2: The claim that humans can do better than the Turing machine, with respect to the halting problem, is an illusion. The Turing machine is a solipsistic system. It begins with data on its tape, but thereafter has no access to any data that might come from the real world. By contrast, real mathematicians are constantly visiting libraries, reading journals, having discussions with colleagues. And that gives the real mathematician a stream of new information that is not available to the solipsistic Turing machine. In short, the argument that Penrose uses does not work because it does not fit the actual problem.Neil Rickert_{September 1, 2012
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Neil: In my opinion, Penrose’s arguments are a complete failure. Personally, I disagree with computationism, so if anything I should be biased toward favoring Penrose’s argument. However, the problem is that the argument simply does not work. I'm sure you're talking about the The Emperor's New Mind. I'm curious why you think his argument fails. I found it convincing. We'll probably not change the other's view, but I am curious what you found lacking.PaV_{September 1, 2012
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I'll suggest that you are barking up the wrong tree. As a mathematician, my assessment is that most mathematicians think that Gödel is important in mathematical logic, but has little or no relevance to their own primary field within mathematics. Roger Penrose has written several books, attempting to show a problem with AI (roughly, the thesis that cognition is computation). Penrose bases his argument on Gödel's and Turing's work. In my opinion, Penrose's arguments are a complete failure. Personally, I disagree with computationism, so if anything I should be biased toward favoring Penrose's argument. However, the problem is that the argument simply does not work. The Gödel proof does not actually show a limitation of logic. Rather, it shows problems with how we have attempted to extend logic to cover infinite realms. Any reasonable assessment would be that a cognitive agent's interactions with the world are finitistic, and thus problems with extending logic into the infinite have no persuasive force, as applied to a cognitive agent. The only relevance that I can see to ID, is that this supports the view that ID is philosophy, not science.Neil Rickert_{September 1, 2012
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As to the Godel's incompleteness of mathematics, Turing's halting problem of computers, and, as Godel pointed out, the necessity of 'human intuition' to overcome the limitations imposed on material processes to 'figure out' greater levels of computational complexity, I believe this following paper drives the point firmly home about how all this relates to Intelligent Design in molecular biology:
"Complexity Brake" Defies Evolution - August 2012 Excerpt: "This is bad news. Consider a neuronal synapse -- the presynaptic terminal has an estimated 1000 distinct proteins. Fully analyzing their possible interactions would take about 2000 years. Or consider the task of fully characterizing the visual cortex of the mouse -- about 2 million neurons. Under the extreme assumption that the neurons in these systems can all interact with each other, analyzing the various combinations will take about 10 million years..., even though it is assumed that the underlying technology speeds up by an order of magnitude each year.",,, Even with shortcuts like averaging, "any possible technological advance is overwhelmed by the relentless growth of interactions among all components of the system," Koch said. "It is not feasible to understand evolved organisms by exhaustively cataloging all interactions in a comprehensive, bottom-up manner." He described the concept of the Complexity Brake:,,, "Allen and Greaves recently introduced the metaphor of a "complexity brake" for the observation that fields as diverse as neuroscience and cancer biology have proven resistant to facile predictions about imminent practical applications. Improved technologies for observing and probing biological systems has only led to discoveries of further levels of complexity that need to be dealt with. This process has not yet run its course. We are far away from understanding cell biology, genomes, or brains, and turning this understanding into practical knowledge.",,, Why can't we use the same principles that describe technological systems? Koch explained that in an airplane or computer, the parts are "purposefully built in such a manner to limit the interactions among the parts to a small number." The limited interactome of human-designed systems avoids the complexity brake. "None of this is true for nervous systems.",,, to read more go here: http://www.evolutionnews.org/2012/08/complexity_brak062961.html
Of course, much more could be said, but for now, I think the paper pretty much says it all.bornagain77_{September 1, 2012
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johnnyb, The video clip comes from this BBC documentary:
BBC-Dangerous Knowledge http://video.google.com/videoplay?docid=-8492625684649921614 video description: In this one-off documentary, David Malone looks at four brilliant mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing - whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide. The film begins with Georg Cantor, the great mathematician whose work proved to be the foundation for much of the 20th-century mathematics. He believed he was God's messenger and was eventually driven insane trying to prove his theories of infinity.
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