Reality Conditions

Monday, June 11, 2007

An examination of Dawkins’ “Ultimate 747” argument

Richard Dawkins’ master argument against the existence of God is spelled out in the fourth chapter of The God Delusion, which is confidently titled “Why there almost certainly is no God”. It may be summarised as follows:

1- God is supposed to be an ultimate explanation for everything there is in the universe, and especially (according to design arguments) for its organized complexity and its friendliness to life.

2- But any God that was responsible for consciously designing the Universe must have a huge degree of complexity itself –at least equal to that of the whole universe.

3- Things with large degrees of complexity are statistically unlikely and stand in need of explanation.

4- So God is an inadequate “ultimate explanation” for the universe –the only possible explanations of complexity are those which, like natural selection or anthropic selection, build up complexity from simple underlying natural laws. (Cranes, not skyhooks, in Dennett’s motto.)

It is obvious that the whole argument rests upon the notion of “complexity”. Just exactly what sense of this concept does Dawkins have in mind, for which very complex things need explaining?

Can it be mathematical complexity as defined in information theory (Shannon information)? But in this sense, a set of particles organized as a living organism would have less complexity than the same particles in a random, uncorrelated state, because you would need more information to specify the latter state than the former. This does not seem right. Can it be the inverse of Shannon information, then –a measure by which random, uncorrelated states have low complexity and highly correlated, low-entropy states have high complexity? But then Dawkins argument fails completely, because physics tells us that the initial state of the universe had very low entropy, and entropy has been growing since. While Dawkins would like to say that in the history of the universe complexity is built from simplicity via the mechanisms of natural selection.

I think there is no rigorously definable sense of “complexity” that has the properties Dawkins requires of it. Ironically, it seems close to the “specified complexity” of Dembski and other creationists! A concept which, as Mark Chu-Carroll’s and others’ criticisms have made clear, has no more technical definition than “something that looks designed”; or, in Behe’s more pedantic but no more precise phrase, “purposeful arrangement of parts”. We can accept the notion, however, as something we understand intuitively and recognize in living beings but cannot at the moment define rigorously, and go on examining the argument. (Accepting this concept as meaningful does not entail accepting Dembski’s creationist arguments, which pretend to prove pseudo-mathematically that complex things in this sense cannot arise by natural selection; because they can.)

Next, let us examine whether this concept of complexity applies to God. Many theists dig their heels here, asserting that the God they believe in is simple. I don’t think this is the best strategy for them. Whether or not there is some metaphysical sense in which their concept of God is simple, I think it is clear it is not the one that Dawkins has in mind. If God is all-knowing, then he must contain at least as much information as the universe, and not only information in the mathematical sense that applies also to random sequences, but information that contains organization, purposeful patterns, and all the marks of “complexity” in the sense we are interested in. A human mind is hugely “complex” in this sense, and God’s mind must be incommensurably more complex.

No, the key premise that must be examined critically is the third one. First, let us clear off that confusing talk of “statistical unlikeliness”. Something “complex” is also “statistically unlikely” only if it appears as result of a stochastic process whose underlying laws do not single out that particular result among many others. For example, the proverbial tornado blowing through a junkyard and assembling a Boeing 747 would be miraculous, because the “complex” outcome results from a process that could also produce billions of other outcomes which are not complex, and we know that the laws governing the behaviour of tornados do not discriminate among those outcomes singling out the complex result as more likely. Just as throwing a coin a thousand times and obtaining always heads is surprising only if we thought that neither the coin nor the way of throwing it were biased. But in the case of God we do not have this knowledge of an underlying process with laws blind to the results; in fact, it would be absurd to postulate such a process, because God is supposed to be an ultimate explanation.

This is really a key point. Dawkins says, in effect: “Look at the typical ID examples of “complexity”; be it the eye of an organism, or the fine-tunedness of laws of nature. They are very statistically unlikely, and so they need an explanation. Design is useless as an explanation because the designer would itself be in need of explanation for the same reason. So “cranes” that build them up from simple things, such as natural selection, are the only possible answer.” But the sentence I have bolded is by no means obvious in absence of context and underlying laws that make the complex thing really “statistically unlikely”. It is certainly not an a priori truth. Think of an Aristotelian view of nature, for example: imagine that species are fixed, each has a “form” or essence which all individuals of the species embody better or worse, and the organisms come to exist and develop by teleological laws, striving to fulfil their potentiality as befits their essence. This is a consistent way the world could have turned out to be, and in it “complex” things do not need any special explanation: the basic laws and principles of the universe make reference to them.

Of course, the real world turned out not to be like this. In the real world the basic laws as far as we know them do not make reference to complex beings, but are completely “blind” to them. Or at least, the whole tendency of the past four centuries leads towards such a conclusion. It is only in the context of this worldview where the apparent design of living organisms raises a problem. Aristotle (to my knowledge) did not use design arguments for the existence of God. Even in the eighteenth century, Hume in his Dialogues still feels free to counter the Design argument by pointing to causes acting in nature such as “generation” and “vegetation”, that are different from design but can produce complexity. But once the post-Newtonian view of the basic laws of the universe as purely “mechanical” (devoid of all teleology) became dominant, how living organisms can come to exist became a pressing problem: for they are really “statistically unlikely” given blind, mechanical underlying laws. Both Paley and Darwin tried to address this problem –only the latter doing it successfully, in a way fully consistent with mechanism and borne out by the evidence.

What Dawkins is doing is to take this story and elevate it to the cosmological or even the metaphysical level. The problem I have with him is not so much taking this step; it is more not acknowledging that it is a step, that it needs to be justified, and that it may reduce the certainty of the conclusion. Taking as a given that complexity is statistically unlikely and needs explanation, Dawkins thinks that God as ultimate explanation is extremely unlikely; I think the “almost certainly” qualifier in the title of the chapter refers really to the infinitesimal probability that something as complex as God may exist “by chance”; hence the “Ultimate 747” moniker. But as I argued, to discuss statistical unlikeliness in absence of underlying laws is vacuous. So Dawkins should have instead argued: “In our experience, and according to the scientific knowledge we have gained in the last centuries, complex things are explained by cranes that build them up from simple tings and laws of nature that are ultimately blind to the complex things. In our experience, complex things stand in need of explanation. So to postulate a very complex thing (such as God) as ultimate, unexplained explanation to the universe is unlikely to be true.”

I think this is a reasonably strong argument, one that may justify someone in calling himself an atheist instead of an agnostic. I am willing to endorse it myself. But it is much less powerful that Dawkins thinks his argument is. The “unlikely” in the conclusion is purely epistemic, not statistical as Dawkins’. The argument makes an inductive leap extrapolating from the current picture we have of how the universe works to say that it is unlikely that its trend will reverse at the cosmological or metaphysical level. If the appearance of teleology is reducible to mechanism or explainable from it in the biological world, then it is most unlikely than teleology (in the form of the intentions of a God) can be an ultimate explanation at a metaphysical level.

This argument assumes, of course, that all instances of teleology are reducible, including its more sophisticated offshoots at a human level, such as consciousness, intentionality and morality. In other words, the argument assumes the naturalistic program in philosophy and stands or falls with it. It must be admitted that this program has not been fully completed yet, but I see the whole course that science has taken since Darwin (if not since Galileo) as pointing towards the plausible truth of naturalism. As long as we don’t have a complete naturalistic account of these higher and more complex forms of teleology, however, I will see theism as a “reasonable” stance someone can take: mind, meaning and morality are pervading in such a way in all our human life, and they come so naturally and irresistibly to our prescientific imaginations as “basic” things, things that can explain things but require no explanation, that it is perfectly understandable that most people think they must be part of the ultimate cause of the universe, instead of late newcomers ultimately built upon blind mechanism, as I am confident they are.

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  • This comment has been removed by the author.

    By Blogger William, at 2:43 AM, June 11, 2007  

  • I think that it is possible to come up with a precise definition of complexity in this sense, but I don't think it's Shannon entropy and it certainly isn't "specified complexity".

    Jeff Shallit has a paper criticizing Dembski's specified complexity in which he argues that Kolmogorov complexity is a more appropriate definition in this sort of context (incidentally, he also has an anti-ID blog and was the prof from whom I learned about Kolmogorov complexity).

    I think Dawkins' argument could perhaps be understood in terms of Kolmogorov complexity, it would probably go something like this:

    1. The universe is very complex. K(universe) is very large.
    2. If god created the universe, K(universe|god) is small, so K(god) ~ K(universe).
    3. A good explanation of something should have lower Kolmogorov complexity than what is being described.
    4. Therefore any argument invoking god is not a good explanation for the universe.

    By Blogger William, at 2:45 AM, June 11, 2007  

  • I think there is no rigorously definable sense of “complexity” that has the properties Dawkins requires of it. Ironically, it seems close to the “specified complexity” of Dembski and other creationists!

    I think this is probably right; if you look at Dembski's works, he often takes Dawkins's earlier discussions of complexity (Blind Watchmaker, etc.) and where Dawkins points to natural selection as being able to build complexity from simplicity, Dembski just denies it and says that only intelligence can do it. Indeed, I take it that one of Dembski's arguments largely parallels Dawkins here: i.e., while talking about natural selection in the abstract makes it sound simple, as it in fact occurs it has to be immensely complex (because what does the explaining are all the actual little contributions), so to appeal to something like natural selection simply pushes back the complexity one step, leaving it unexplained; therefore these mechanisms or cranes are an inadequate ultimate explanation. They're twins. As is sometimes the case with twins, one may be healthier than the other, but the healthier twin is still close kin to the sickly one.

    Of course, what this suggests is that this is simply the sort of thing you get when we talk about complexity in this way; I suspect you're right that there's no rigorously definable sense of complexity with the right properties for this type of argument. What we find as labeled as 'complexity', whether in Dawkins or in Dembski, is really a mish-mash of different concepts. (Another sign of this is that when Dawkins talks of simplicity, he really does obviously conflate different things.) So if some version of complexity is even relevant the argument would have to run rather differently.

    By Blogger Brandon, at 3:24 AM, June 11, 2007  

  • William,

    I think there may be something to your argument, but it certainly isn't Dawkins' argument. Just as the Shannon information, the Kolmogorov complexity of a set of random, uncorrelated particles is higher than that of the same particles arranged in an organism. To describe the first set of particles you can't do better than specifying exactly the state of each of them, while in the organism there is a larger degree of redundancy and pattern.

    Taking your argument on its own terms, I suppose theists would question premise 3. I am inclined to question it myself, as I think that what makes an explanation good or bad depends on the context and on lots of factors that cannnot be encoded in a simple, universal mathematical principle like that one. Can you find a way of justifying this premise, and specifically of justifying it for the case of an explanation for the universe?

    By Blogger Alejandro, at 6:48 PM, June 11, 2007  

  • Brandon,

    Yes, I agree that this concept of "complexity" is pretty slippery and both sides of the discussion should refrain from using it. I think the more tentative atheistic arguement I present at the end can be restated easily without talking about complexity, though. It really depends on teleological facts being reducible to (or at least supervenient on, or being explainable in terms of) mechanical facts.

    By Blogger Alejandro, at 6:52 PM, June 11, 2007  

  • Hey Alejandro,
    completely off-topic: tried to send you an email yesterday but it was bounced with an error message. Do you have an alternative address or should I try to resend it? Best,

    By Blogger Bee, at 9:13 AM, June 12, 2007  

  • Hi Bee, I got your email today (the server was down yesterday) and I have just answered it.

    By Blogger Alejandro, at 3:20 PM, June 12, 2007  

  • I didn't think 3 was too controversial. It's really just a statement of Occam's razor and isn't that different from Dawkins' point 3. I'm not sure I could come up with a coherent argument for it, except to say that it seems to have served science rather well.

    I do agree there are other factors in a good explanation. I don't think simplicity is a sufficient condition for a good theory, but I would consider it necessary, or at the very least desirable.

    My main point was not to argue against the existence of god, just to play devil's advocate and try to challenge the statement that "complexity" is not rigorously definable.

    By Blogger William, at 6:25 PM, June 13, 2007  

  • One aspect of Occam's Razor (the original "not multiplying entities beyond necessity" one) does seem related to Kolmogorov simplicitly. But I think the general idea of preferring "simple" explanations cannot be reduced to a clear-cut mathematical preference for K-simple things, but involves many context-depending factors. For example, if we had an explanation that postulated a very "K-simple" cause C for X, but C was utterly different from everything else that works as an explanation in other areas we have knowledge of, then we might prefer a more K-complex cause D that only uses entities and processes we are familiar with.

    Of course, if the explanation C makes new predictions that are borne out by the evidence, while explanation D has to make the postulated cause more and more complex to keep up with the observations, then it is rational to switch to the simpler C. (This summarises many scientific revolutions and paradigm shifts.) But as long as this does not happen, Occam's Razor may suggest keeping explanation D because it only uses principles already known to work in other areas, even if it is more K-complex in a mathematical sense.

    In summary, I would agree that "all other things equal" we should prefer the more K-simple explanation; but I think the scope for applying this principle is rather small, at least in "live" controversies in which there is genuine disagreement.

    By Blogger Alejandro, at 8:22 PM, June 13, 2007  

  • God does exist.
    That's because God did not create man; man created God!
    God's complexity is therefore limited only by the complexity of the human mind. But that is sufficient to serve all the possible and impossible needs of man. Once man expands their mind and wants more, the power of God automatically adjusts to reflect that expansion.
    Isn't that wonderful?

    By Anonymous Anonymous, at 4:24 AM, June 20, 2007  

  • Dawkins take on the "ultimate 747" argument is seductive, but doesn't stack up.
    Put simply, probability is something applicable in time and space - we don't know how and if it can apply to something outside of time and space, which is supposedly transcendent, supernatural and not some kind of organism.
    You can say "we don't see evidence for supernaturality in the universe" which is fine, but that's just the argument " we can't see God so why believe he exists" in different words.

    By Anonymous Anonymous, at 2:13 PM, August 13, 2007  

  • "In our experience, complex things stand in need of explanation. So to postulate a very complex thing (such as God) as ultimate, unexplained explanation to the universe is unlikely to be true."

    'In our experience' is the key phrase here. For theists, God is beyond the scope of our experience, so to postulate a God that is outside the scope of our experience is untestable by scientific methods. This then is problematic for Prof. Dawkins's proposal to subject God to the same scientific rigor as every other theory, that is, by experiment (and not by scenario-building might-have-beens).

    By Anonymous Jego, at 8:54 AM, September 12, 2007  

  • Excellent essay and excellent comments. Enjoyed it. Don't know if anyone will ever respond anymore but here's a thought:
    Science has strong evidence that the Big Bang is the origin of the universe. Now it that complex, since it contains the universe, or is it simple like a Dawkin's crane? Seems like no worse than God as a creator.

    By Anonymous Anonymous, at 8:42 PM, February 05, 2010  

  • Thank you for the great story.

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    By Anonymous Raphaël CONFIANT, at 6:19 PM, April 07, 2010  

  • The ultimate Jumbo argument presupposes that everything, including God Himself, must have a cause. Infinite regression of causes is a deeply unsatisfying idea and, in any case, would have to presuppose that all predicates of causation (material, space/time, "reality") have eternal existence. The only satisfying idea is that of eternal existence, either of the material universe (atheists) or of God (theists). In this contest, it seems there is no winner.

    By Anonymous Anonymous, at 7:30 AM, September 18, 2011  

  • In my view everybody must go through it.

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