In chapter 4 of his book The God Delusion, Richard Dawkins advances an argument for atheism he calls the “Ultimate Boeing 747 Gambit,” in reference to Fred Hoyle’s famous comment about a Boeing 747 arising by chance in a junkyard. Just as Hoyle’s argument appeals to the (alleged) improbability of evolution, Dawkins’s argument appeals to the (alleged) extreme improbability of God. Indeed, the title of chapter 4 is, “Why There Almost Certainly Is No God.”
Dawkins is not a philosopher writing for other philosophers; he is a biologist writing for a popular audience. For this reason, it is entirely understandable that he does not provide his argument for atheism in its logical form. My goal now is simply to figure out what Dawkins’s argument is; I will defer an assessment of Dawkins’s argument until later.
Before I summarize Dawkins’s chapter, let us first review how Dawkins defines “God” so that we can properly interpret his argument. In chapter 2, “The God Hypothesis,” Dawkins defines the “God Hypothesis” (hereafter, “GH”) as follows:
There exists a super-human, supernatural intelligence who deliberately designed and created the universe and everything in it, including us. (31)
In contrast to the God Hypothesis, Dawkins explains that he will argue in The God Delusion for a rival hypothesis:
Any creative intelligence, of sufficient complexity to design anything, comes into existence only as the end product of an extended process of gradual evolution. (31)
Dawkins does not name this competing hypothesis, so I shall call it the “evolved intelligence hypothesis” (hereafter, “EIH”). EIH is an “alternative view” to GH in the sense that EIH and GH are logically incompatible: if EIH is true, then any creative intelligence came into existence as the end product of an extended process of gradual evolution. This contradicts GH, which entails that at least one intelligence, God’s, is not a late arrival in the universe. In Dawkins’s words:
Creative intelligences, being evolved, necessarily arrive late in the universe, and therefore cannot be responsible for designing it. God, in the sense defined, is a delusion… (31).
With GH (and EIH) clarified, let us now turn to a summary of Dawkins’s chapter. It divides into seven sections (numbering is mine):
1. The Ultimate Boeing 747
2. Natural Selection as a Consciousness-Raiser
3. Irreducible Complexity
4. The Worship of Gaps
5. The Anthropic Principle: Planetary Version
6. The Anthropic Principle: Cosmological Version
7. An Interlude at Cambridge
Here is a brief summary of each section.
(1) The Ultimate Boeing 747: Dawkins argues that the “argument from improbability” can be turned on its head and made into an argument for atheism, which he labels “the Ultimate Boeing 747 Gambit” (113). This name derives from Fred Hoyle’s famous argument against abiogenesis, which claimed that the probability of life originating from nonlife by chance is as probable as a tornado blowing through a junkyard and creating a fully assembled Boeing 747, ready to fly. Other creationists revised or expanded the argument as an argument against the chance origin of a molecule, a complex organ, a living creature, or even the universe itself.
Let B the event of a fully assembled Boeing 747 originating from a tornado blowing parts in a junkyard; y be the number of combinations of all the parts of a Boeing 747; x be the number of combination of parts which give a functional Boeing 747; L be the event of life originating from nonlife; let Ch(p) represent a probability value as interpreted by the classical interpretation of probability, viz., the chance of p; and ‘<!!’ mean “very much less than.” Then Hoyle’s argument may be summarized as:
Ch(L) ≈ Ch(B) = x/y <!! 1/2.
As Dawkins points out, however, natural selection is the opposite of chance (113). Whereas “chance” means “the spontaneous arising of order, complexity, and apparent design” in a single step (so-called “single-step selection”); evolution by natural selection is the hypothesis of the gradual accumulation of order, complexity, and apparent design over time (“cumulative selection”). Thus, the probability of evolution of complex living bodies by chance is literally irrelevant to the hypothesis of evolution by natural selection.
Furthermore, not only is a designer unnecessary to explain the apparent design in the evolution of complex living bodies, Dawkins argues, but any designer must be at least as improbable as the apparent design to be explained. Thus, God’s existence is statistically improbable. In his words,
“Darwinian natural selection is the only known solution to the otherwise unanswerable riddle of where the information [in living matter] comes from. It turns out to be the God hypothesis that tries to get something for nothing. God tries to have his free lunch and be it too. However statistically improbable the entity you seek to explain by invoking a designer, the designer himself has got to be at least as improbable. God is the Ultimate Boeing 747.” (114)
As we saw earlier, the chance origin of a Boeing 747 is “statistically improbable” in the sense that Ch(B) = x/y <!! 1/2. What then, precisely, does Dawkins mean when he says that “God is the Ultimate Boeing 747″? Presumably, he means that God is the ultimate example of “order, complexity, and apparent design.” But what does that mean? In the Boeing 747 example, “order and complexity” seems to refer to x/y, i.e., the very small ratio of ‘combinations of parts that produce a working Boeing 747′ to ‘the total number of possible combinations of parts.’ So it would seem that, in order to apply the Boeing 747 metaphor to God, we need to think of God as somehow made up of parts.
If we do think of God as somehow made up of parts, we can then make sense of Dawkins’s statement that “God is the Ultimate Boeing 747″ as follows. Let n be the number of logically possible combinations of God’s parts; and k be the number of combinations of God’s parts which would allow a being to be God. Thus, when Dawkins writes, “God is the Ultimate Boeing 747,” this statement may be summarized as:
Ch(GH) = k/n.
Now consider Dawkins’s statement, “However statistically improbable the entity you seek to explain by invoking a designer, the designer himself has got to be at least as improbable.” And suppose a creationist claims that God is needed to explain L, the origin of life from nonlife. Dawkins’ statement may be understood as:
Ch(GH) <= Ch(L) <!! 1/2.
But let’s revisit the idea that God is somehow made up of parts. What could that mean? Let’s consider two possibilities: (i) physical parts; and (ii) God’s properties as parts.
Concerning (i), God is ordinarily understood as a disembodied mind, i.e., not composed of physical matter. So if Dawkins understands God in this way, then he cannot mean God is somehow made up of material parts. What else, then, could Dawkins mean?
Perhaps he has in mind (ii): the idea that God’s properties are His parts. If so, then we can distinguish essential and non-essential properties. A property is an essential property of God if a being must possess that property in order to be God (e.g., omnipotence, omniscience, etc.); a property is non-essential if a being can lack that property and still be God (e.g., God’s knowledge of a specific contingent fact). On the classical interpretation of probability, each logically possible outcome is assigned an equal probability. And if God exists, He has His essential properties necessarily. That entails that the chance of God’s essential properties is one, i.e.:
Ch(God’s essential properties) = 1.
As for God’s non-essential properties, they are contingent. Hence if n is the number of combinations of God’s non-essential properties, the chance of any combination of God’s non-essential properties is 1/n. And “God” is logically equivalent to the conjunction of God’s essential properties plus every possible combination of God’s non-essential properties. Thus, the chance of any combination of God’s non-essential properties is irrelevant. Therefore, the chance of God possessing the particular combination of properties required to be God is one. I conclude, then, that interpreting God’s parts as His properties does not provide support for the improbability of God.
What else, then, could it mean to say that God is somehow made up of parts? I can’t make out what Dawkins has in mind. For now, let us move onto the other sections of his chapter and see what he writes.
(2) Natural Selection as a Consciousness-Raiser: I think this entire section is summed up nicely by the following statement by Dawkins: “Darwinian evolution, specifically natural selection, … shatters the illusion of design within the domain of biology, and teaches us to be suspicious of any kind of design hypothesis in physics and cosmology as well” (118; italics are mine).
(3) Irreducible Complexity: Dawkins notes the magnitude of Darwin’s and Wallace’s accomplishment of explaining order, complexity, and apparent design by evolution. As Dawkins correctly points out, chance and design are not the only possible explanations for statistical improbability (121); natural selection is another option–an extremely successful option.
According to Dawkins, creationists who “deploy the argument from improbability in their favour always assume that biological adaption is a question of the jackpot or nothing” (122). He then defines “irreducible complexity” as another name for the “jackpot or nothing fallacy.” He reviews the reasons why eyes and wings are not irreducibly complex and then draws a general lesson from all this: we should be very reluctant before concluding that something is irreducibly complex. In his words: “The fact that so many people have been dead wrong over these obvious cases should serve to warn us of other examples that are less obvious, such as the cellular and biochemical cases now being touted by … ‘intelligent design theorists’” (124).
(4) The Worship of Gaps: Dawkins provides an overview of what he calls the “creationists’ love affair with ‘gaps’” in scientific knowledge (127). Whereas scientists “seek out areas of ignorance in order to target research,” creationists “seek out areas of ignorance in order to claim victory by default” (126).
He also discusses Michael Behe’s argument that complex structures, like the bacterial flagellar motor and the immune system, are examples of irreducible complexity. As Dawkins explains, “The key to demonstrating irreducible complexity is to show that none of the parts could have been useful on its own. They all needed to be in place before any of them could do any good” (131). After critiquing both of Behe’s examples, Dawkins questions whether God could be an explanation of anything (133-34).
(5) The Anthropic Principle: Planetary Version: In this section, Dawkins argues that the probability of the origin of life through purely naturalistic means provides no support for design. To make his point, he applies a “planetary version” of the anthropic principle:
We exist here on Earth. Therefore Earth must be the kind of planet that is capable of generating and supporting us, however unusual, even unique, that kind of planet must be. (135)
What this shows, he argues, is that the origin of life on our planet “cannot have been very improbable” (135). This does not mean, of course, that most planets in the universe are life-permitting. Dawkins grants this. Given the sheer number of planets in the known universe, as long as the probability of life arising from nonlife is greater than nonzero, life will arise from nonlife a large number of times:
… even a chemical model with odds of success as low as one in a billion would still predict that life would arise on a billion planets in the universe. And the beauty of the anthropic principle is that it tells us, against all intuition, that a chemical model need only predict that life will arise on one planet in a billion billion to give us a good and entirely satisfying explanation for the presence of life here. (138)
As before, let L be the event of life originating from nonlife on an unspecified planet; let Ch(L) represent a probability value as interpreted by the classical interpretation of probability, viz., the chance of L. Then Dawkins’ argument above can be summarized as follows. He asks us to suppose, for the sake of argument, that:
Ch(L) = 1/1,000,000,000 = 10-9
Let Pr-F represent a probability value, as interpreted by the frequency interpretation of probability, viz., the limit of the relative frequency. An implicit premise of Dawkins’s argument is:
Pr-F(L) = Ch(L).
Let P be the number of planets in our universe. Dawkins proposes that we take the current scientific estimate of the number of planets in the universe (between 1020 and 3 x 1021) and round down to a billion billion (1018). Let FP be the number of life-friendly planets in the universe. Then:
FP ≈ Pr-F(L) x P = 109.
This is the mathematical basis for the first sentence (“… even a chemical model”) quoted above. This point is axiomatic; no one who understands math can deny it. But this doesn’t address the probability of life originating on our planet. In his second sentence, Dawkins seems to be saying that the origin of life from nonlife on Earth is not statistically improbable so long as
Ch(L) >= 1/P.
Dawkins concludes that the “apparent gap in the evolutionary story” of the origin of life “is easily filled by statistically informed science, while the very same statistical science rules out a divine creator on the ‘Ultimate 747′ grounds we met earlier” (139, italics mine).
Regarding the design hypothesis as an explanation for “our planet’s peculiar friendliness to life,” Dawkins argues, it receives no support from the anthropic principle. As he puts it:
“The anthropic principle, like natural selection, is an alternative to the design hypothesis. It provides a rational, design-free explanation for the fact that we find ourselves in a situation propitious to our existence. I think the confusion arises in the religious mind because the anthropic principle is only ever mentioned in the context of the problem that it solves, namely the fact that we live in a life-friendly place. What the religious mind then fails to grasp is that two candidate solutions are offered to the problem. God is one. The anthropic principle is the other. They are alternatives.” (136)
How are the design hypothesis and the anthropic principles alternatives? The anthropic principle is logically consistent with the hypothesis that God miraculously designed the solar system so that Earth is life-friendly. So when Dawkins describes the anthropic principle as a “design-free explanation,” he must mean that the anthropic principle provides a naturalistic explanation for the fact that Earth is life-friendly, i.e., an explanation in accordance with the known laws of nature. This seems to be what Dawkins has in mind later on when he writes, “The design approach postulates a God who wrought a deliberate miracle, struck the prebiotic soup with divine fire and launched DNA, or something equivalent, on its momentous career” (137).
(6) The Anthropic Principle: Cosmological Version: Dawkins then turns to cosmology, specifically, the so-called “fine-tuning” of the laws and constants of physics. As before with the planetary version, Dawkins pits the anthropic principle and design as competing explanations:
“Yet again, we have the theist’s answer on the one hand, and the anthropic answer on the other. The theist says that God, when setting up the universe, tuned the fundamental constants of the universe so that each one lay in its Goldilocks zone for the production of life. It as though God has six knobs he could twiddle, and he carefully tuned each knob to its Goldilocks value.” (143)
And, as we have seen through his chapter, Dawkins again argues that a designer is at least as improbable as the evidence to be explained:
“As ever, the theist’s answer is deeply unsatisfying, because it leaves the existence of God unexplained. A God capable of calculating the Goldilocks values for the six numbers would have to be at least as improbable as the finely tuned combination of numbers itself, and that’s very improbable indeed – which is indeed the premise of the whole discussion we are having. It follows that the theist’s answer has utterly failed to make any headways towards solving the problem at hand.” (143)
Even without a formal analysis, I think it’s clear that Dawkins is comparing the chance of the Goldilocks values for the six numbers to the chance of God.
Dawkins then compares the multiverse hypothesis with the God Hypothesis (GH) as rival explanations for cosmic fine-tuning. Again, Dawkins argues that GH is at least as improbable as the naturalistic hypothesis (i.e., multiverse):
“The key difference between the genuinely extravagant God hypothesis and the apparently extravagant multiverse hypothesis is one of statistical improbability. The multiverse, for all that it is extravagant, is simple, God, or any intelligent, decision-taking, calculating agent, would have to be highly improbable in the very same statistical sense as the entities he is supposed to explain. The multiverse may seem extravagant in sheer number of universes. But if each one of those universes is simple in its fundamental laws, we are still not postulating anything highly improbable. The very opposite has to be said of any kind of intelligence.” (146-147)
Here is where things get very interesting. In response to Swinburne’s well-known argument that GH is the simplest explanation that fits the facts, Dawkins responds:
“A God capable of continuously monitoring and controlling the individual status of every particle in the universe cannot be simple. His existence is going to need a mammoth explanation in its own rights. Worse (from the point of view of simplicity), other corners of God’s giant consciousness are simultaneously preoccupied with the doings and emotions and prayers of every single human being — and whatever intelligent aliens there might be on other planets in this and 100 billion other galaxies.” (149, italics mine)
What makes this passage so significant is that Dawkins finally provides some much-needed clarification of what might play the role of “God’s parts:” God’s mental states, including his knowledge or awareness and his willing the status of every particle in the universe. Let p be the number of logically possible combinations of God’s mental states; q be the number of actual combinations of God’s mental states; r be the number of possible combinations of the values of physical constants; and s be the number of life-permitting combinations of the values of the physical constants. Thus, when Dawkins writes, God’s “existence is going to need a mammoth explanation in its own rights,” this statement may be summarized as:
Ch(GH) = p/q <= Ch(fine-tuning) = r /s.
(7) An Interlude at Cambridge: Dawkins describes his experience at a recent conference on science and religion at Cambridge sponsored by the Templeton Foundation, where he presented his Ultimate Boeing 747 argument. His description includes an important clarification of what he seems to have in mind when he writes about God’s complexity or improbability:
“Second, a God who is capable of sending intelligible signals to millions of people simultaneously, and of receiving messages from all of them simultaneously, cannot be, whatever else he might be, simple. Such bandwidth! God may not have a brain made of neurons, or a CPU made of silicon, but if he has the powers attributed to him he must have something far more elaborately and non-randomly constructed than the largest brain or the largest computer we know.” (154)
(to be continued)
 Richard Dawkins, The God Delusion (New York: Houghton Mifflin, 2006), 111-59.
 Richard Dawkins, The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe Without Design (New York: W.W. Norton, 1986), 317.