A while back, Lukeprog of Commonsense Atheism began writing a series of posts on the Gambit found in The God Delusion (henceforth: TGD). There, as I’ve done elsewhere, I attempted to defend Dawkins against what I saw as misinterpretations of his argument against the existence of God. This was not so much because I thought Dawkins was entirely clear, but more because I felt assumptions were being made that Dawkins need not be committed to. This post is an attempt to take what I’ve denied on behalf of Dawkins, and turn it into a positive account of the Ultimate 747 Gambit.
What is the Argument?
I’ll begin by pointing out what the argument is not. It is not the series of six numbered points that end chapter 4, which Dawkins introduces thus:
“This chapter has contained the central argument of my book, and so, at the risk of sounding repetitive, I shall summarize it as a series of six numbered points.” ~ TGD, p.157
Note the ambiguity of the pronoun – on one interpretation, what “it” refers to as being summarized is the “central argument” of TGD, but on a better interpretation, “it” refers to “[t]his chapter” which contains said argument. Why is this a better interpretation? Firstly, because the six points do not look like an argument: each point contains multiple assertions making it unlikely that these are intended as premises; further, the points have no conclusion, which would be marked by ‘therefore’ or similar1. Secondly, because the argument is variously signalled as already have been made prior to some of the points having been broached2. Thirdly, because the responses considered in the section “An Interlude at Cambridge”, which recounts the argument’s reception, only pertain to the material in the chapter’s first section, “The Ultimate Boeing 747”. Fourthy, because Dawkins himself sums up the argument, leaving out points 5 and 6…
“How do they cope with the argument that any God capable of designing a universe, carefully and foresightfully tuned to lead to our evolution, must be a supremely complex and improbable entity who needs an even bigger explanation than the one he is supposed to provide?” ~ TGD, p.147
..and fifthly, because interpretive charity demands of us that we take Dawkins as offering a solid argument if we can, whereas the series of numbered points needs reconstructive surgery to give it logical integrity3.
So, on a more positive note, what is the argument? Whilst I don’t think there is enough textual support to claim any particular argument with certainty, Dawkins’ third summarized point…
“3. The temptation is a false one, because the designer hypothesis immediately raises the larger problem of who designed the designer. The whole problem we started out with was the problem of explaining statistical improbability. It is obviously no solution to postulate something even more improbable. We need a ‘crane’, not a ‘skyhook’, for only a crane can do the business of working up gradually and plausibly from simplicity to otherwise improbable complexity.” ~ TGD, p.158
..seems to contain the kernel of his argument. Putting it into formal dress, we might get something like…
1. An acceptable explanation is an account of something improbable in terms of what is more probable.
2. The hypothesis that God designed the universe should therefore, if it is to be explanatory, account for the universe in terms of what is more probable than the universe.
3. God himself would have to be more complex than the highly complex universe.
4. What is complex is improbable, and is improbable to the degree it is complex.
5. So, the hypothesis that God designed the universe is not an acceptable explanation.
Where God is defined as..
“a superhuman, supernatural intelligence who deliberately designed and created the universe and everything in it, including us.” ~ TGD, p.31
As yet, we do not have an argument with the desired conclusion, that God almost certainly does not exist. But we’re not far away. We can reuse 3 and 4 like so..
3. God himself would have to be more complex than the highly complex universe.
4. What is complex is improbable, and is improbable to the degree it is complex.
6. God is highly improbable. That is, he almost certainly does not exist.
..to arrive at our destination. (Compare with the previous quote from p.147). Certainly there are hints of other arguments here – e.g. Dawkins suggests “The whole argument turns on the familiar question ‘Who made God?’… God presents an infinite regress” – but I think this simple formulation captures what is essential to what Dawkins calls an “argument from improbability” (TGD, p.109). This will be the argument of concern from here on out.
Before we get on to assessing the argument as I have presented it, it would be instructive to look at Eric Wielenberg’s interpretation, given in “Dawkins’ Gambit, Hume’s Aroma, and God’s Simplicity“. Here it is4:
(A) If God exists, then God has these two properties: (i) He provides an intelligent-design explanation for all natural, complex phenomena in the universe and (ii) He has no explanation external to Himself.
(B) Anything that provides an intelligent-design explanation for the natural, complex phenomena in the universe is at least as complex as such phenomena.
(C) So, if God exists, then God has these two properties: (i) He is at least as complex as the natural, complex phenomena in the universe and (ii) He has no explanation external to Himself. (from A and B)
(D) It is very improbable that there exists something that (i) is at least
as complex as the natural, complex phenomena in the universe and (ii) has no explanation external to itself.
(E) Therefore, it is very improbable that God exists. (from C and D)
As you can see, the argument somewhat builds together the two arguments I have given. But there are some differences. One minor difference is that Wielenberg includes A’s condition (ii) in the argument, writing that4..
“Although he does not explicitly say so in this passage, I think Dawkins also understands this supernatural intelligence as lacking an external explanation. Dawkins understands the God Hypothesis as positing an Uncreated Creator; his aim is to prove that such a being almost certainly does not exist.”
I see no need to introduce this assumption. Although it is true that Dawkins probably believes this, and though no doubt the lack of external explanation for God would ramify the conclusion, it is superfluous to establishment of the improbability of God. Perhaps Wielenberg thinks that, were God to have a cause he might turn out to be probable, but this is mistaken – the relevant probabilities are prior or antecedent probabilities, and so a caused God would remain improbable in just the same sense as a royal flush is improbable, even if one’s senses testify to the fact that a royal flush is what one has been dealt5.
More substantial is my disagreement with Wielenberg’s interpretation of this argument, rather than the argument itself. Oddly, Wielenberg decides that if (ii) is true, this lack of external cause “seems to imply that God came into existence all at once entirely by chance”6. He then attributes this view to Dawkins, despite the fact that Dawkins explicitly recognizes elsewhere as possible the non-origination of God:
“It may even be a superhuman designer – but, if so, it will almost certainly not be a designer who just popped into existence, or who always existed.” ~ TGD, p.156 (Emphasis mine.)
This attribution then becomes the failure of Dawkins’ Gambit. Wielenberg tells us that the argument overlooks the possibility that God is a necessary being, who “did not come into existence all at once entirely by chance because He did not come into existence at all”7. Supposedly, the necessity of God is a tenet of traditional monotheism8, and so, for the most part, Dawkins misses the mark.
As may be obvious, I disagree with this attribution, which seems textually unwarranted. Perhaps the reason Wielenberg introduces it is because he believes that a beginningless God would have no charge of improbability to answer. Yet this isn’t self-evident, and indeed, I believe it to be false. To see why we need to look at why complexity of any sort would be improbable.
Complexity and Improbability
It is somewhat of a mystery exactly what Dawkins has in mind when he writes of complexity in TGD. The closest Dawkins comes to giving us a definition is to remark…
“Indeed, the biologist Julian Huxley, in 1912, defined complexity in terms of ‘heterogeneity of parts’, by which he meant a particular kind of functional indivisibility.” ~ TGD, p.150
Elsewhere, in The Blind Watchmaker, Dawkins summarizes a more lengthy discussion of complexity..
“We were looking for a precise way to express what we mean when we refer to something as complicated… The answer we have arrived at is that complicated things have some quality, specifiable in advance, that is highly unlikely to have been acquired by random chance alone.” ~ The Blind Watchmaker, p. 9
Yet neither of these definitions seems fit to the purpose at hand – the former, because the link with improbability is obscure, the latter because there may be some doubt about whether it is applicable to an eternal being9. Thus, we’re essentially left to find our interpretation of complexity, one which might reasonably be attributed to Dawkins, which supports 3 and 4, and, I suggest, one whose technical explanation might be reasonable to leave out of a popular level book. Because it is left out of the book, readers could be forgiven for thinking that what follows isn’t correct as an interpretation of Dawkins, but I’d ask that they see how well my explanation fits with what Dawkins is trying to do, before they decide against it.
I suspect what Dawkins has in mind here draws upon information theory. According to the concept of ‘Kolmogorov complexity‘, the complexity of a string of symbols can be measured in terms of the shortest program able to reproduce the string10. This definition can be extended to objects, since an adequate description of an object is constituted by a string of symbols, and so we can measure the object’s complexity by the complexity of its description.
The interesting thing about Kolmogorov complexity is that it provides a conceptual bridge between computation, which has become the foundation of modern cognitive science, and objects themselves. That is, if we take a measure of the complexity of the universe, then this measure is in terms of the shortest possible program able to reproduce the string describing it, and given that the mind works on computational principles, this implies a minimum complexity of the mind which is able to store this information. But this amounts to saying that a mind must be at least as complex as that which it conceives, as we have defined the complexity of the conceived in terms of the complexity of that which conceives it. More formally:
7. The complexity of an object is measured by the shortest program able to reproduce a string of symbols which accurately describe that object. (Complexity is inversely proportional to the length of the program).
8. A program exists insofar as it is instantiated in a substrate.
9. A program which is instantiated in a substrate can itself be considered as an object, whose complexity is measured by the shortest program able to reproduce a string of symbols which accurately describe that object.
10. If P1 is the shortest program describing an object O1, and P1 is instantiated as an object O2, then P1 is likewise the shortest program which describes O2.
11. So, the complexity of a given object O1 is either equivalent to, or less than, the complexity of an object O2 which instantiates a program describing O1.
12. The mind works on computational principles – that is, the information held by a mind consists in such programs, instantiated in a substrate.
13. Therefore, the complexity of an object as conceived by a mind cannot be more than the complexity of the mind itself, as instantiated in a substrate.
Explanation: Premise 7 explicates the notion of complexity we’re working with. 8 treats a program as an abstraction, a form of sorts, which requires a substance for existence. 9 is obvious, but 10 may not be. Suppose that 10 is false: then P1 is the shortest program describing O1, is instantiated in O2, and some other program P2 describes O2, where P2 is shorter than P1. But if that’s so, then P2 also describes O1, for by describing the object in which P1 is instantiated, it thereby describes the object P1 describes. Given that both P1 and P2 describe O1, and that P2 is shorter than P1, it follows that P1 is not the shortest program which describes O1, and so we’ve derived a contradiction. The negation of a contradiction is always true, so premise 10 is true.
11 draws on 7 and 10: if P1 is the shortest program describing both O1 and O2, then the complexity of O1 and O2 is equivalent. 12 is a deliverance of cognitive science. 13 is inferred from 11 and 12. Suppose O1 is an object conceived by a mind, and P1 is the shortest program describing it, then the instantiation of P1 in O2 is of equal complexity to O1. But, ex hypothesi, O2 is itself part of the mind. So the mind, being at least as complex as O2, is also at least as complex as O1.
If you’ve followed me so far, it should be dawning on you how this would justify 3. But this reasoning only gets us so far as saying that a designer is at least as complex as the designed, not that God would be even more complex than his universe. I think there would be several ways to to reach this strong conclusion, focussing on God’s presumed mental powers, but the simplest way from here to there I can think of would go..
14. A designer is a person, having a conception of some particular object of design prior to the creation of that object.
15. Self-conception is a necessary feature of personhood.
16. Therefore, a designer conceives of himself/herself as a person, as well as the designed object, prior to the creation of that object.
17. A conceived person and conceived object are together more complex than the conceived object alone.
18. So, a designer is necessarily more complex than the object conceived (via 17 and considerations of the previous argument).
19. God, if he exists, is the designer of the universe.
3. So, God himself would have to be more complex than the highly complex universe.
.. and thus we arrive at 3†.
What about premise 4, that what is complex is improbable, and is improbable to the degree it is complex? What justification is there for this premise? As we’ve already linked the complexity of an object to its shortest possible description, we might look for the correlation in features which lengthen an object’s description. Glancing at Dawkins’ citation of Julian Huxley, two of these jump out: first, that an object is more complex the more parts it has, and second, that an object is more complex the more kinds of parts it has. But why should these make for improbability? Here we can return to TGD for clues. Dawkins tells us..
“My name for the statistical demonstration that God almost certainly does not exist is the Ultimate Boeing 747 gambit. The name comes from Fred Hoyle’s amusing image of the Boeing 747 and the scrapyard… Hoyle said that the probability of life originating on Earth is no greater than the chance that a hurricane, sweeping through a scrapyard, would have the luck to assemble a Boeing 747… The odds against assembling a fully functioning horse, beetle or ostrich by randomly shuffling its parts are up there in 747 territory.” ~ TGD, p.113
The thought is that complex objects are improbable because they have many and various kinds of parts, because this multiplicity allows many possible arrangements of these parts, and that therefore, any singular functional arrangement of the parts is unlikely. That is, the improbability of complex objects is a matter of statistics, where the more detail we have to pack into our description of an object, the more ways in which our description may fail to be satisfied, and so the less likely that description is to be actual.
This explanation justifies premise 4, and so, together with our earlier account of 3, we arrive at the conclusion: “God is highly improbable. That is, he almost certainly does not exist.”.
A. But God is simple!
One obvious reply, which Dawkins mentions in TGD, is for the theist to take a stand and retort that God is simple:
“The strongest response I heard was that I was brutally foisting a scientific epistemology upon an unwilling theology, Theologians had always defined God as simple. Who was I, a scientist, to dictate to theologians that their God had to be complex? Scientific arguments, such as those I was accustomed to deploying in my own field, were inappropriate since theologians had always maintained that God lay outside science.” ~ TGD, p.154
I’ve already given argument against the view that God would be simple, on the basis of current science. But perhaps the inference from the complexity of human minds, to the divine mind can be questioned. Dawkins has no truck with this suggestion..
“The theologians of my Cambridge encounter were defining themselves into an epistemological Safe Zone where rational argument could not reach them because they had declared by fiat that it could not.” ~ TGD p.154
..and I think he is right. There is absolutely no reason to ignore good science merely because it runs against tradition – that would amount to an arbitrary preference for the vicissitudes of history over methods with the best epistemic credentials humans have discovered. In any case, this sophomoric move won’t help the theist. If our best methods of inquiry point to the complexity of a designer, and the theist responds by making God’s simplicity a matter of definition, then all the theist succeeds in doing is to define his God as improbable against the evidential argument that a designer must be complex.
B. You’re assuming materialism!
A second response to the argument is that Dawkins, being a scientistic non-philosopher, is somehow smuggling in the anti-theistic assumption of materialism into his argument. In particular, the use of cognitive science to derive the complexity of a mind might strike some as suspect. Don’t theists typically assume some kind of dualism? So aren’t I, and perhaps Dawkins, begging the question?
In reply, I have three points to make. First, nothing in the foregoing arguments has assumed that the complexity must be material. If theists want to divide what exists into the mental and the physical, and say that mind is mental stuff, then this is perfectly consistent with our argument that the mind would be structurally complex. Second, even if the argument had assumed the complexity to be material, then it would still be justified by today’s science. While the ontological status of consciousness is a question on which science has not yet decided, the reliance of memory and imagination on the processing power of the brain has been known for decades. Third, if dualism conflicts with the deliverances of cognitive science, then so much the worse for dualism. It may be that some versions of dualism contradict the conception of the mind being used in the argument, but because they are already in conflict with science, objecting on the basis of these merely serves to highlight that one is committed to an implausible position.
C. God is necessary!
I’ve already disputed Wielenberg’s reply from God’s necessity, showing that the improbability of complexity need not be read as the improbability of something’s coming into existence. But another way to employ the necessity of God against Dawkins is to deny that God is improbable at all: theists have always held that God is a necessary being, and the probability of a necessary being’s existing cannot be less than 1. Thus, arguing for the improbability of God is a kind of nonsense, not even worth refutation.
But isn’t this begging the question? Surely it is not a requirement of atheists raising an argument against Theism that they agree that God must exist! What the atheist can agree to is that God is a non-contingent being, i.e. that God is either necessary or impossible. However, absent a proof (like the ontological argument), or a disproof (various), we cannot say which disjunct is true. We are therefore required to fall back on probabilistic arguments, just like Dawkins’ Gambit or the fine-tuning argument, taking the necessity or impossibility of God to be the spoils for which the arguments contest.
D. You can’t assign probabilities in the absence of physical laws!
A final objection, raised by Plantinga, Sharlow, and Law, is that if God is the author of physical laws, then he cannot be bound by them, and so assigning God a probability based on these laws is inappropriate. But as we’ve seen, the probability assessments here need not assume such laws. Instead, we would derive the improbability of God’s complexity by taking into consideration all possible arrangements of parts, assigning each an equal probability in accordance with the principle of indifference, and thereby determine the singular probability of the functional arrangement which is God. More generally, there is logical probability and physical probability, and the probability of God is being assessed in terms of the former. Indeed, physical probability is a restriction upon logical probability, so far from being grounds for an objection, the existence of God outside the laws of nature may exacerbate the problem.
The Import of the Argument
In sum, it seems that Dawkins’ Ultimate 747 Gambit can be elaborated into a forceful argument. Whether or not the details given here would match Dawkins’ understanding is uncertain, but at least showing that there is a good argument to be elaborated here is itself evidence for the interpretation via the principle of charity.
On the other hand, this argument is not decisive. It does not prove the non-existence of God, for the conclusion is probabilistic. More importantly for the theist, the probabilistic conclusion only gives us a low prior probability, so there may be other arguments in the theist’s favor which may succeed in raising the probability above 0.5. For example, a sound fine-tuning argument would balance out most of the prior improbability, and a battery of other theistic arguments could outweigh the rest of it11 – even a steep hill can be climbed. This hill is, nevertheless, very steep.
1 One might take the main body of text to give the conclusion – “If the argument of this chapter is accepted, the factual premise of religion – the God Hypothesis – is untenable.” (TGD p.158) – but it seems unlikely that one would not include this as a seventh point if it were.
2 For example, Dawkins says “My name for the statistical demonstration that God almost certainly does not exist is the Ultimate Boeing 747 gambit.” (TGD p.113), and then says, in what appears to be a summing up “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.” (TGD p.114). The argument is only later mentioned as having been completed: “Yet even so big a gap as this 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.” (TGD p.139).
3 .. Sixthly, because Dawkins assimilates “the argument from improbability – the ultimate 747” (TGD p.157), and the argument from improbability is indexed only as occurring on p.114; and seventhly, because in no lecture on TGD has Dawkins presented the six points as an argument.
4 Wielenberg, Dawkins’ Gambit, Hume’s Aroma, and God’s Simplicity p.115. Numbered premises to the lettered versions you see here.
5 Dawkins’ use of ‘improbable’ reflects this, for he speaks of evolved creatures as improbable: “Some observed phenomenon – often a living creature or one of its more complex organs, but it could be anything from a molecule up to the universe itself – is correctly extolled as statistically improbable.” (TGD p.113/4, emphasis mine).
6 Wielenberg, Dawkins’ Gambit, Hume’s Aroma, and God’s Simplicity, p.114.
7 Wielenberg, Dawkins’ Gambit, Hume’s Aroma, and God’s Simplicity, p.118.
8 Which is not to say that is popularly believed: “Now if God is not a necessary being (and many, perhaps most, theists think that He is not)..” – Plantinga, God, Freedom, and Evil (1974), p.39.
9 It seems obvious to many that this definition cannot apply to an eternal being like God, since an eternal being does not come into existence by chance. This objection is confused – if God could not have into being by chance, then, trivially, it is unlikely that he came into being by chance, and so he satisfies Dawkins’ definition for complexity. Whatever is impossible is unlikely, indeed, it is as unlikely as it can be.
10 Note that by this definition, the apparently complex may be simple. Sharlow argues that fractals are an objection to Dawkins taking complexity to be improbable, concluding that “the simple can logically entail the complex”. But on Kolmogorov complexity, fractals are simple, because they can be generated by surprisingly short programs. Sharlow denies that they are simple, on the grounds that it doesn’t match our informal idea of complexity (and then bizarrely attempts to show that the apparently simple is logically complex, in virtue of the paraphenalia of set theory), but the reader can take the definition of complexity here as stipulative. Whether or not it matches our informal ideas is not then a threat to the soundness of the argument.
11 Which is plausibly why Dawkins turns to the fine-tuning argument after stating the Gambit. It is perhaps the only argument capable of overcoming most of the prior improbability of God.
† Belated Edit: It now seems to me that I haven’t been sufficiently clear on just what it is to conceive an object. In the comments Jeffrey Shallit contends that, however complex the universe is, the multiverse may be less complex, and so the Kolmogorov complexity of the designer of the multiverse may be less than the complexity of the universe. This is correct. However, if a being conceives an object, then it does not follow that she also conceives of the parts of the object (and vice versa). (Analogy: an architect conceives of and designs a house, but does not thereby conceive, nor a fortiori design, the micro-structure of the wood framing). But since it does not follow from the being’s conceiving of the multiverse that the designer conceives of each part of it, and since the conceiving of an object is necessary for its being designed, it does not follow from the being’s designing of the multiverse that the being also designs the universe. The upshot is that, although it is right to say that some being with less Kolmogorov complexity can produce something with greater complexity than itself, this does not mean that the being could design something of greater Kolmogorov complexity than itself.