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.
Wielenberg’s Take
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.”.
Objections
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.
Notes
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.
Omnis affirmatio est negatio 
I have only rushed through a read on this but I think it’s great. I’d like to read it when I have more time and post some other comments after I’ve had time to consider it better. But, man, do I appreciate the work on this one. A pleasure to read.
This is superb.
Here is another relevant article, on complexity:
http://www.paul-almond.com/WhatIsALowLevelLanguage.htm
Thanks guys!
[…] TaiChi has offered a masterful interpretation of Dawkins’ argument that strips out the (perhaps unnecessary) assumptions that make other […]
You make an obvious mistake: if a program P produces many different outputs, it is simply not true that the Kolmogorov complexity of each of its outputs must be less than the Kolmogorov complexity of P. Simple counterexample: write a program P that on input i outputs all binary strings of length i. Then the Kolmogorov complexity of P is a constant C, and the Kolmogorov compexity of i is at most log_2 i + C’. On the other hand, at least one of P’s outputs has Kolmogorov complexity i. So we have complexity log_2 i + constant giving rise to an output of Kolmogorov complexity i.
So your argument could fail if we think of something that created many different universes, only one of which we inhabit. Our particular one can be complex even if the process that created our universe is simple – provided that process created many different universes.
Hey there. Sorry I haven’t jumped back into your POE discussion yet. I intend to.
Regarding this post, I’ve never bought Dawkins’ argument or other arguments that appear to be variants of “who designed the designer.” For one, they all seem to be superflous tu quoque-type arguments. In truth, they remind me of the flippant child who asks “why” to every question while fancying his or herself smart. As in,
On the one had, I feel compelled to note that one can inquire “why” of anything. It’s not a rebuttal to an intelligent position, or even an argument for another intelligent position. On the other hand, it also makes complete sense to trace caused events backwards as far as we can. So what am I really saying? Dawkins wrote,
We have empirical knowledge of the universe’s complexity and/or statistical improbability. IOW, we have something that needs to be explained. We’ve run equations, tens if not hundreds of thousands of times. We know the universe corresponds to what we call “complexity,” and we know there is a high degree of statistical impossibility therein.
When it comes to God, we’ve not measured a damn thing. We don’t know if there actually is any complexity or statistical impossibility to explain. Dawkins commits the genetic fallacy and puts the cart before the horse. Does he provide any supporting arguments for the above assertion in TGD, philosophical, empirical or otherwise? If he did, I sure missed them. Dawkins simply assumes that any designer responsible for the complexity we see must be at least as complex as the complexity that we see. On what grounds? Why couldn’t the Designer be simply powerful, like water? Is water more complex than the Grand Canyon it ‘designed?’
I suppose that’s where we shift from discussing Dawkins’ argument as stated, to yours. AFAICS, your 3 and Wielenberg’s B suffer from the same flaw. Your 17 would also be true even if the mind was “less complex” than the object.
To the “simplicity” objection, you say,
In this post? Are you referring to the premises 7-14?
I would agree, but again, I need to hear in greater detail this “evidential argument” you allude to.
Regarding Objection D,
If God is non-contingent, eternal, uncaused, etc., then there is no logical probability to discuss. The term “statistical probability” can only have meaning in reference to contingent entities. The minute the theist proffers a non-contingent God, the discussion’s over, at least AFAICS.
Truly masterful. I think you do capture well the heart of the argument, although I doubt Dawkins thought of it so rigorously or formally, or explicitly in terms of Kolmogorov information.
A few points,
a) I’m not a big fan of premise (1) in general, but I think it needs to be refined to something like “reducing explanations” or somesuch, and in that case it is valid. That is, I think it’s important to realize that we aren’t looking for an explanation in general, which may indeed refer to a prior layer of even-more improbable/complex assumptions (e.g., the tool which implies a tool-maker). We are interested in particular types of explanations that seek to explain away some inexplicable fact, such as the fact that the universe, in all its complexity, exists. Providing a non-reductive explanation (such as causal explanation why the universe exists that is based on a prior even more complex multiverse) will do nothing to alleviate our preplexity over this worrisome fact
b) I believe your premise (10) is in error – P1 is at least as long as any program describing object O2, but it may be that O2 requires a longer program for its description, so that P1 is not the shortest program describing O2. This is implicitly acknowledged in premise (11), and does not affect your argument.
c) I think the weakest link of this argument is that complexity/logical improbability implies implausibility. To give a counter-example, a universe where there is a single human being, and nothing else, would arguably have a lesser Kolmogorov complexity than one where there is the human and all the earth and stars and so on – but I would say that the latter is far more plausible. Humans don’t just exist, they exist as the natural ramifications of a broader background, against which their existence makes sense. You can see that as rescaling the meter-stick, to redefine the program in terms of the laws of nature rather than the state, but that brings up complicated questions as you now have two measures of complexity (the state/universe plus the laws of nature). As another counter-example, I think having very uniform laws of nature is more plausible than having non-uniform but simpler ones [it’s a long-standing aesthetic of science]; who can say I’m wrong? I find the entire justification of premise (1) problematic.
d) As a physicist, I find the idea of non-physical information (objection B) nonsensical, and its application to an entity that supposedly interacted (or even interacts) with us absurd. It doesn’t matter if God’s ideas have no mass, or weight, or whatever – if they exist, they are physical, to say otherwise is to misunderstand what physics is all about. It seems to me such objections are stuck to Cartesian physics, that sticks the corporeal in the box of “physics” and anything that doesn’t “extend” into a separate box. That is totally untenable in light of modern physics, that talks of abstract spin chains, a zero energy/mass universe, timeless existence, arbitrary (even no) number of dimensions, systems with dynamics and ones with no, and so on. Physics has advanced beyond the point where the concept of “nonphysical information” makes sense, if it ever did.
At the end of (c), that’s supposed to be “premise 4”. I hate that there is no edit on these things.
Well, you assumed that thinking can be explained as “programs” on a “substrate”. With the denial I’ve quoted, haven’t you simply smuggled that assumption into dualism? The assumption that thoughts, dreams, etc. are “programs running on a substrate” seems like a massive one.
CL: “Dawkins simply assumes that any designer responsible for the complexity we see must be at least as complex as the complexity that we see.”
Actually, I think that Dawkins has spent a career carefully explicating how complex things come about from more simple replicators. I would say that Dawkins assumes that the theist does not believe that God evolved in the same way that things in our universe evolved, because if she did she would find her argument excised by Occam’s razor.
CL: “Dawkins simply assumes that any designer responsible for the complexity we see must be at least as complex as the complexity that we see. On what grounds?”
On the ground of Paley and the others have laid down as their argument. Let’s not forget that Dawkins “argument” is a response to theist claims about complexity in the universe being impossible without God.
As much as I admire everything about this post, I think it’s possible that Dawkins only addresses the second part of a question that has two parts – why does something exist? And, why does something complex enough to contemplate its existence exist?
The question that Dawkins raises, at least under my interpretation is, “What does the theist offer as an explanation of God (if not evolution) that is more probable than the material explanations we have for God-like complexity (personhood, intelligence, consciousness, will, etc.)?
CL: “Why couldn’t the Designer be simply powerful, like water? Is water more complex than the Grand Canyon it ‘designed?’”
I think this seems like sophistry. Do you really think that water has a mind, and that it designed something? Do you really think that the water that shaped the Grand Canyon is a single, simple thing, and not a highly complex, incalculable, meteorlogical, millions of years, billions of variables, vastly complex system, that can be described as the structure of a molecule?
TaiChi,
Thanks for this thought-provoking post. Consider the following objection:
Suppose we re-formulate the argument, substituting literally any productive process X for the God hypothesis:
1. An acceptable explanation is an account of something improbable in terms of what is more probable.
2. The hypothesis that X produced 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. X itself 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 X produced the universe is not an acceptable explanation.
6. X is highly improbable. That is, almost certainly X does not exist.
Haven’t you now called into doubt any possible productive process for the universe? Isn’t this absurd? Yes, it’s absurd, so we conclude at least one of the premises must be wrong.
Why would premise (3) be correct for X? It is correct for God, since God supposedly conceives of the universe in all its complexity and thus must have that information within himself, so must be at least as complex. But why must X be more complex than the universe? Why can’t X be, say, a very simple random-universe generator, generating an infinity of universes of which we are in one?
And why is it absurd to call into doubt any possible productive process for the universe? I don’t find it at all absurd to maintain that whatever exists cannot be understood in terms of what doesn’t exist, so that existence [which may include many universes] cannot be [reductively] explained.
If commitment to (1) a “random-universe generator” and (2) an infinite number of universes comprises the response to this objection, I’m satisfied to let it rest. I really have no conception of what (1) is and am persuaded that (2) is not possible, as I don’t think an infinite number of things could exist.
6 states that X almost certainly does not exist, given 3 and 4. But how can we say that the productive process that generated the universe almost certainly does not exist? Of course it exists, since we are here.
“You make an obvious mistake: if a program P produces many different outputs, it is simply not true that the Kolmogorov complexity of each of its outputs must be less than the Kolmogorov complexity of P.” ~ Jeffrey Shallit
Yes.. you could have, for example, a random number generator that would, given enough time, eventually produce the entire works of Shakespeare. I don’t really have an answer to this at the moment, except to say that this seems to ruin the idea of using program length as a measure of complexity, and so I don’t expect your counterexample to be allowable given a suitably nuanced definition of Kolmogorov complexity. I’ll look into it, thanks.
Hey, cl.
“On the one had, I feel compelled to note that one can inquire “why” of anything. It’s not a rebuttal to an intelligent position, or even an argument for another intelligent position. ” ~ cl
Yes, it’s a rhetorical move. That said, turning a rhetorical move back on one’s opponent is sometimes the only way to get them to see that, and in that context I think there’s nothing wrong with it.
“We know the universe corresponds to what we call “complexity,” and we know there is a high degree of statistical impossibility therein.” ~ cl
I can’t agree. We think that the universe is complex because, thus far, we can’t derive it from simple principles. But if it turns out that simple principles can produce our universe, then the universe will be simple – for example, if physicists hit on a Theory of Everything which shows the physical constants to be necessary. Theists bet against this, they say that the universe is complex, and so God is required. Dawkins, I think, indulges them in this assumption and then turns it back against them. But the jury’s still out on whether the universe is simple or complex.
“Dawkins simply assumes that any designer responsible for the complexity we see must be at least as complex as the complexity that we see. On what grounds?” ~ cl
He does suggest at a couple of points that the functional capacities of designer made for complexity. I didn’t make this up from whole cloth:
“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 ” (TGD 144)
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 right. 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. He even, according to Swinburne, has to decide continuously not to intervene miraculously to save us when we get cancer.” (TGD 149)
“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 neurones, 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.” (TGD 154)
“Why couldn’t the Designer be simply powerful, like water? Is water more complex than the Grand Canyon it ‘designed?’” ~ cl
I think you’ve answered your own question, with those scare quotes. Mere power is not sufficient to design complexity, as opposed to haphazardly causing it.
“In this post? Are you referring to the premises 7-14?” ~ cl
7-13, together with 14-19, and 3. That’s my evidential argument, cl.
“If God is non-contingent, eternal, uncaused, etc., then there is no logical probability to discuss. The term “statistical probability” can only have meaning in reference to contingent entities. The minute the theist proffers a non-contingent God, the discussion’s over, at least AFAICS.” ~ cl
Why can “statistical probability” only have meaning in reference to contingent entities? I need a reason if I’m going to agree with you.
“a) I’m not a big fan of premise (1) in general, but I think it needs to be refined to something like “reducing explanations” or somesuch, and in that case it is valid.”
Yes, I have some serious doubts about the argument 1-5 (which is why didn’t argue for it). Plantinga makes pretty much your point in his review, and although I think Dawkins may be right about the illegitimacy of postulating a designer in the context of cosmology, I think the Plantingian point is enough to show that 1-5 is too unsophisticated to work.
“b) I believe your premise (10) is in error – P1 is at least as long as any program describing object O2, but it may be that O2 requires a longer program for its description, so that P1 is not the shortest program describing O2. ”
Well, that would be true if the object instantiating a program were considered as, say, a computer: a computer can be more complex than the programs it runs, and so could not be described so economically as one of those programs. But I’m using ‘object’ in a very narrow way here, just to capture the structure necessary to instantiate the program, and no more. This is why I phrase it in 9: “A program which is instantiated in a substrate can itself be considered as an object..”, rather than “A program can be instantiated in an object..”.
“c) I think the weakest link of this argument is that complexity/logical improbability implies implausibility. To give a counter-example, a universe where there is a single human being, and nothing else, would arguably have a lesser Kolmogorov complexity than one where there is the human and all the earth and stars and so on – but I would say that the latter is far more plausible. Humans don’t just exist, they exist as the natural ramifications of a broader background, against which their existence makes sense. ”
I’m not at all sure that your lonely human being would have less complexity the universe entire. If the natural laws are simple, and the boundary conditions are given by a few numbers, then you have in essence a simple program which generates apparent complexity, including us. To describe a human without describing the rest of the universe seems to me more complex, as we can’t use the economy of natural laws to do so.
Obviously, much rests on my assumption here that a program measuring complexity would have to produce a description of the object and nothing else. I’ll simply have to do more research on this, but I’m confident for the same reason as I gave to Jeffrey Shallit – without the assumption, Kolmogorov complexity appears to be useless as a measure.
@TaiChi
On point c: Well, simple rules can only create complex results through indeterminism, so this is analogous to the random number generator. (Deterministic laws of nature preserve information content, since by definition they allow a 1:1 correspondence between initial and final states, so can’t increase complexity.) Note that even though the generator is simple, it is still impossible to describe the resulting random string by describing the generator that created it – you need to describe the actual string. So we have two options: (A) a description of a deterministic process that led to the creations of the lonely human would be more complex, since it describes the creation of other things as well, while (B) the description of an indeterministic process that created him would be simpler, but would not suffice to describe the actual human being discussed. The bottom line is that the sole human is simpler, even though the process of creating him might be more complex.
At any rate, it still doesn’t appear particularly compelling that higher Kolmogorov complexity is the determinant of how low the prior probability of something is.
I would add that I hold a Descriptive/non-Platonic view on laws of nature, so I don’t think the complexity of the generating algorithm ontologically exists. The laws of nature don’t really exist as-such, they are abstractions out of the stuff that does exist, namely the universe. This implies that the complexity of the laws of nature needed to describe the creation of a sole human isn’t really important here, since it isn’t measuring the complexity of anything that exists in the imagined universe (the one containing the sole human).
“Well, you assumed that thinking can be explained as “programs” on a “substrate”. With the denial I’ve quoted, haven’t you simply smuggled that assumption into dualism? The assumption that thoughts, dreams, etc. are “programs running on a substrate” seems like a massive one.” ~ JS Allen
I wouldn’t call it smuggling – the computational metaphor is foundational to cognitive science, and I’m simply requiring that Dualism observe it also. If you think that dualism really can’t tolerate this view of the mind, such that our best science would preclude dualism altogether, then I’m not inclined to dissuade you – feel free to ignore this spasm of accomodationism.
Hi Thomas,
I have serious doubts about the first argument I extract from TGD (1-5), and I don’t want to defend it – I think it’s too unsophisticated to work, even if there’s something to it. Fortunately, the second argument (3,4,6) does not rely on it, and I concentrate my efforts there.
Still, I’m not sure why you think a productive process would be more complex than the universe. I’d be interested in why you think that.
Of course. I was a little careless with my copy/paste there, sorry about that.
I don’t believe that, no. However, I think the defender of the argument who also affirms that the universe is complex is committed either to the notion that the productive process is more complex than the universe, or to the idea that there are an infinite number of universes.
Hi TaiChi!
This post is perhaps the best defense of Dawkins’ argument I’ve ever read. I think you and I are mostly in agreement about what the argument actually is and about its implications for theism. I’ve made a post on my blog recently referring to your article and listing a couple of blog posts that I’ve written on the subject:
http://aigbusted.blogspot.com/2010/06/dawkins-and-ultimate-747-argument.html
Be sure and leave a comment telling me your thoughts on this.
Ryan
I would be a little nervous at this point. We’ve gone from asserting, without any support whatsoever, that a nuanced view of Dawkins reveals that he was really talking about Kolmogorov complexity. Now we are saying that not even Kolmogorov complexity works, so we need something more “nuanced”. Haven’t we just nuanced ourselves completely out of the universe that Dawkins was operating in? What value is there in pretending like this represents Dawkins?
As someone else pointed out, you seem to be misunderstanding the purpose and application of Kolmogorov complexity. This is a computer science concept used to measure information complexity, and in fact the Kolmogorov-Smirnov test is regularly used to see whether a given set of numbers is random.
Kolmogorov complexity assumes two things 1) a computational language upon which programs can be run, 2) a program that generates information. Note that complexity can vary widely based on the language chosen.
For materialism, #1 is equivalent to “the rules of physics and the material universe”. For materialism, #2 does not exist. There is no program. Materialists believe that the visible universe emerged from only the essential properties of the universe, with no guiding “program”. It would be as if someone wrote a programming language which generated the entire universe simply by starting up.
So when you start talking about Kolmogorov complexity, you’re just begging all of the “fine-tuning” crazies to come out. It’s not a good idea.
Materialism, by definition requires that every observable phenomenon be wholly composed of irreducible physical facts. If you “require that Dualism observe it also”, it’s not dualism — it’s materialism. I don’t see the relevance to physical science. It’s perfectly OK for physical science to operate on physicalist assumptions. Saying that dualism is false because it operates apart from physical science, is kind of like saying that the ocean doesn’t exist because you can’t drive your car on it.
Ironically, I’ve seen materialists do the opposite recently, in an attempt to get around the problems with eliminativism. They essentially smuggle in dualist assumptions and try to call it “materialism”.
In any case, it is false to assert that cognitive science assumes the computational metaphor, in the sense that you’re using it related to Kolmogorov complexity. I don’t know of any serious scientist who believes that the brain is a “programming language”, with our behavior being determined by “programs” in the brain. The brain is a massive neural network (neural nets are not programming languages, and don’t run programs).
I think science was held back for awhile, because people were locked in this mentality about “programs”. Every time you said, “the brain isn’t a computer”, people would say, “OK, then please describe the algorithm that you think the brain uses”. The brain doesn’t use an algorithm in the sense that you can write down. William James (and Dennett) are correct to point out that the brain is faced at first with a “blooming, buzzing confusion”, and that the reasons we give are almost never the real reasons.
However, I think the defender of the argument who also affirms that the universe is complex is committed either to the notion that the productive process is more complex than the universe, or to the idea that there are an infinite number of universes.
Saying this means you haven’t understood my criticism. It is not necessary to have an infinite number of universes for my counterexample to apply, only that there be a large number.
@Thomas Reid
“6 states that X almost certainly does not exist, given 3 and 4. But how can we say that the productive process that generated the universe almost certainly does not exist? Of course it exists, since we are here.”
The argument is that the prior probability of God would be low, just as the prior probability of being dealt a royal flush is low. In both cases, other evidence can suffice to overturn this antecedent improbability.
@Yair
“At any rate, it still doesn’t appear particularly compelling that higher Kolmogorov complexity is the determinant of how low the prior probability of something is.”
I accept your excellent point about indeterminism, so I’ll take a different line. In your first comment, you seemed to accept that complexity made for logical improbability, but denied that this meant implausibility. But in this comment you appear to deny that complexity does result in low prior probability – did you mean to do so? I think I can accept your point about implausibility without harm – it amounts to saying that there are other (conditional) factors than prior improbability which influence our probability assessments – but not your denial of low prior probability altogether.
@Ryan
Thanks. I’ve skimmed a couple of your posts already, but I’ll take another look.
@JS Allen
“I would be a little nervous at this point. We’ve gone from asserting, without any support whatsoever, that a nuanced view of Dawkins reveals that he was really talking about Kolmogorov complexity.”
I never asserted that. What I said was that I thought Dawkins was appealing to information theory, and then I offered Kolmogorov complexity as doing the job required. That it does so (if it does) is evidence in favor of my interpretation, but not overwhelming evidence.
If you’re nervous, then you can use this substitution premise instead..
“7a. The complexity of a string is the length of the string’s shortest description in some fixed universal description language. The complexity of an object is given by the least complex string which describes it.”
.. which does not have the demerit of allowing simplicity on the cheap (a random number generator does not describe the strings it generates).
“For materialism, #1 is equivalent to “the rules of physics and the material universe”. For materialism, #2 does not exist. There is no program.”
How does applying a computational measure of complexity imply that that which is measured is itself computer-like? It doesn’t. While you’re right that our measure requires a language and a program, that isn’t because what is measured has a language and a program, but because the language and program are the tools by which we measure whatever it is that we’re measuring.
“Saying that dualism is false because it operates apart from physical science, is kind of like saying that the ocean doesn’t exist because you can’t drive your car on it.”
By the same token, let’s not judge Astrology, ESP, or witchcraft by the standards of science, for these too ‘operate apart from physical science’ (whatever that means). Can you be serious?
“I don’t know of any serious scientist who believes that the brain is a “programming language”, with our behavior being determined by “programs” in the brain. ”
I don’t believe that the brain is a programming language either, which would be a category error. As for whether we have programs on the brain, here’s a random quote from a book on developmental psychology:
“The modern answer to this question is that babies are a kind of very special computer. They are computers made of neurons, instead of silicon chips, and programmed by evolution, instead of by guys with pocket protectors. They take input from the world, the flickering chaos of sensations, and they (and therefore we) somehow turn it into jokes, apologies, tables, and spoons. Our job as developmental psychologists is to discover what program babies run and, someday, how that program is coded in their brains and how it evolved. If we could do that, we would have solved the ancient philosophical problems of knowledge in a scientific way.” ~ The Scientist in the Crib, p.6.
@TaiChi: “In your first comment, you seemed to accept that complexity made for logical improbability, but denied that this meant implausibility. But in this comment you appear to deny that complexity does result in low prior probability – did you mean to do so? I think I can accept your point about implausibility without harm – it amounts to saying that there are other (conditional) factors than prior improbability which influence our probability assessments – but not your denial of low prior probability altogether.”
Yes, I meant to. “Logical complexity” is just some measure of complexity we defined here, what I am disputing is any connection it has to plausibility, and specifically to setting prior probability. Should complexity be a factor in determining prior improbability at all? The Kolmogorov complexity, IIRC, essentially measures how much memory a compressed description of the thing will require. Why should we apply the “principle of indifference” at this level? There doesn’t seem to be a good reason to. I’m worried in particular with the thought that there would be two explanations, (I) and (II), where (I) has less complexity but is highly non-uniform but (II) has more complexity but is highly uniform. I would prefer the latter, based on a prior commitment to naturalism which I basically see as uniformity. You are advocating choosing the former (I). I can’t think of very good arguments either way – I suspect my way is related to applying the principle of indifference to the ontological, rather than compressed description, level, but I’m not sure how to make that argument, or even if it would be compelling if successful.
To give a concrete example: the visible universe is only a small (perhaps infinitely small) fraction of the universe considered in the modern cosmological theories. In terms of Kolmogorov complexity, it is therefore much, much simpler, so on your method the preferred hypothesis should be that only the visible universe exists. and the “rest” of the universe is simply there as a mathematical construct of these theories. I prefer to think that the universe is far larger than our little corner of it, and that the math is there because it reflects that.
I’d advocate (I) if it could be described more economically than (II), yes. I think that uniformity is a prima facie ground to choose (II) over (I), since higher uniformity is an indicator of a simpler theory, but this is overturned by complexity considerations, for uniformity only indicates a simpler theory by indicating low complexity.
Concerning your example: anti-realism and realism are meta-theoretical – they are attitudes we can take toward our scientific theories – and so to take the non-visible universe as a mere mathematical construct is not going to result in a simpler theory.
TaiChi,
You wrote:
I know that’s what you mean to argue, but I’m not understanding what are the prior states on which you are conditionalizing.
I’m not conditionalizing, since I’m trying to argue for a prior probability – that prior probability is derived from the large number of possible arrangements of parts which must comprise a divine mind, where only one or few have the required structure to function as a mind. Once we have that prior probability determined we can conditionalize, Bayesian-style, to determine the liklihood of God given various other arguments or evidence.
Sorry if that doesn’t help – I’m not sure what you’re looking for.
That’s helpful, thanks.
It’s hard to see how a computational measure of complexity would be useful for anything which is not computer-like. There is a reason that Kolmogorov IT is used heavily in computation, but not in law or art, for example. Intentions (the focus of law) and passions (the focus of art) do not behave as computations, and if materialism succeeds in reducing these to physical properties, the Kolmogorov complexity would not be measured at the level upon which law and art operate. So it will always be apples and oranges.
You have proposed to apply Kolmogorov IT to “the mind of God”, presumably to refute theism. Since you don’t even believe in a “mind of God”, one would expect you to use the definition that theists use. Theists don’t generally define God in a way that would seem compatible with measurement via computational complexity.
Right. The language that you choose to assume, for sake of measurement (i.e. the computational substrate) makes all the difference in the world. Unless you are asserting that “the mind of God” is equivalent to the binary lambda calculus, which would be absurd on it’s face, then you are burying some massive assumptions about language.
Your definition of “string” matters as well. As we’ve seen, trying to use Kolmogorov IT to measure the complexity of intentions and passions would be stupid, since these presumably supervene on a physical substrate which is actually theorized to be computational, while no materialist philosopher would assert that intentions or passions are computational.
Your line of argument is all the more curious, since neither Dawkins nor any self-respecting materialist would buy the premise that the universe is even “complex”, in terms of Kolmogorov complexity. With regards to Kolmogorov complexity, materialists assert that the universe is very simple.
I’m not arguing on behalf of astrology or even theism at this point. I am responding to your assumption that everything must be reducible to physical causes. I am simply pointing out that you need to assume materialism in order to make your argument about Kolmogorov complexity — but if you assume materialism, then theism is already false, so your Kolmogorov argument is superfluous.
Materialism and dualism both lead to uncomfortable conclusions. Materialism leads to the conclusion that libertarian free will is a mass delusion shared by all of humanity, while dualism leads to the conclusion that there are some things which physical science will never be able to measure.
If your whole Kolmogorov refutation of theism depends on an incredulous, “But if you don’t accept that premise, then science may have limitations! You’re kidding!”, then you have lost already. Besides the fact that half of philosophers, including many atheists, reject materialism; it is not a good idea to accept a philosophical argument simply because we want something to be true. Saying, “This is true, since we would hate for science to be limited!” is not a valid argument. By that same measure, one could reject materialism because he wishes that libertarian free will was true.
With regards to Kolmogorov complexity, materialists assert that the universe is very simple.
I don’t see any evidence that this is (i) asserted by materialists or (ii) true. For all we know, the Kolmogorov complexity of the fine structure constant could be infinite.
while no materialist philosopher would assert that intentions or passions are computational.
You seem to believe a lot of things about materialist philosophers that aren’t so.
Materialism leads to the conclusion that libertarian free will is a mass delusion shared by all of humanity,
Or perhaps that “free will” is ill-defined and incoherent.
@JS Allen:
Your primary objection seems to be that it is wrong to apply “computational” notions to a [dualist] mind. But such conceptions are not “materialist”, they stem from contemplation of the nature of information and, if anything, the law of contradiction. If some thing, including a mind, contains information, then it must contain this information, regardless of any “computation” or “materialism”. Materialism conforms to this, but the applicablility of information theory is broader.
Naturalists (well, some – including me) find the dualist’s insistence that mental content not count as information unreasonable. They see it as incoherent or as hiding the informational requirements “beneath the carpet”. You can’t on one hand say God knows A and B and on the other claim he has no parts – insofar as he knows both A and B, he must at least have both these mental-objects in his mind, so his mind has parts. (And insofar that he knows that A has features Aa and Ab he needs that content too, and so on, leading to the entire informational bits.) Waving your hand and saying “non-physical” does not get you a “get out of logic free” card.
In short, the naturalists don’t find the traditional theistic ideas on the mind of god workable, and employ instead the ones reason provides.
As another note – I find the idea of “mental”, as in “non-physical”, to usually be mistaken in that mental content is supposed to be causal, yet by definition that makes it a subject-matter of physics. Some forms of dualism escape this trap, but even then I find the mental is only “non-physical” in a rather trivial sense, as it falls under a physics-like description in any reasonable formulation of the theory (one that doesn’t brushes off mental content under the carpet).
As you ought to know “hard materialists”, or “eliminativists” insist that intentions are illusory, so you will never see these materialists endorsing computation where intentions are discrete units. “Soft materialists”, or “supervenience naturalists” admit that intentions do exist, but insist that intentions are wholly determined by their physical parts. it is at the physical layer that the deterministic “computation” takes place, and the layer of intentionality is a projection.
Can you provide any links to materialists who endorse the use of intentions or passions, rather than physical entities, in computation?
People don’t believe in free will because they’ve been given a “definition”. It’s innate, inborn, and you can ask any man on the street what “freedom of choice” means, and he’ll tell you.
You can create as specialized a definition as you want, for as tiny an audience of experts as you want, but that will not change the fact that materialism denies the very definition that every human believes without being told.
This reminds me of the time that I told a friend, “I’m going to get coffee”, and he responded, “Why? I’m not thirsty”. I just explained that materialism is incompatible with the intuitions of billions of humans, and you said, “Why? I don’t have that intuition”.
Dawkins has spent his entire career arguing that the apparent complexity of the world can be explained in terms of very simple principles — a blind watchmaker, climbing mount improbable, using chance mutation and random selection.
Then we have occam’s razor; a model of physics which needs less than 30 constants to explain everything, and so on. Science is generally allergic to theories which explain apparent complexity with even greater complexity. Science is generally a process of proving that apparent complexity is not really so complex.
I’m very interested in your comment about the fine structure constant, though. Can you provide more context? I always understood that the fine structure constant was fairly simple, although dependent on pi. I’ve always heard that the Kolmogorov complexity of pi is very low.
If everything the brain does can be modeled by a computer, then intentions and passions are just as computational as anything else done by a brain.
It’s innate, inborn, and you can ask any man on the street what “freedom of choice” means, and he’ll tell you.
Really? I have never heard anyone – man on the street or otherwise – give a coherent definition of the term. Perhaps you can tell me where to look.
materialism denies the very definition that every human believes without being told.
In exactly the same sense as we “deny” other kinds of intuitions we have about the world, like our intuition that velocities add, or that the earth is flat. So what?
Dawkins has spent his entire career arguing that the apparent complexity of the world can be explained in terms of very simple principles
You’re confusing the process – evolution – with the initial conditions. The initial conditions could be quite complex. Furthermore, if mutations are really random in the Kolmogorov sense, then the process itself has high Kolmogorov complexity. So I think your Kolmogorov-interpretation of what Dawkins is saying is flawed – which is no surprise, since few commenters on this thread seem to have a good grasp of the theory.
I always understood that the fine structure constant was fairly simple, although dependent on pi.
You’ve understood incorrectly. No one has any idea how many bits it takes to specify it. Furthermore, it has nothing to do with pi and is not dependent on it, to the best of our knowledge. Where did you get that idea? Please don’t say Gilson.
The brain doesn’t use an algorithm in the sense that you can write down.
I don’t know how anyone can assert this with so much confidence. It seems much more likely to me that it does use an algorithm that could, in principle, be written down – even if it amounts to simulating the molecules and electromagnetic fields that make it up.
Sure, you can look at John Searle, on pages 87-88 of “Minds, brain, and science” [0]. He says that “human freedom is just a fact of experience”. Other supervenience naturalists agree. Across the two pages, he gives a pretty good description of the way that people innately perceive free will; I would recommend reading both pages.
That’s exactly my point. I’m not trying to argue one side or the other (materialism versus dualism); I’m just pointing out why this Kolmogorov complexity argument for the 747 is flawed. TaiChi insisted that we presuppose materialism in order for the Kolmogorov argument to work, since “If materialism is false, then phyical science is limited”. I argued that this is wrong for two reasons:
1) Presupposing materialism makes the Kolmogorov argument superfluous.
2) Disbelieving something just because we don’t like the consequences of believing, is not valid argument form. People who refuse to accept materialism “because it negates free will” are similar in this way to people like TaiChi who refuse to accept dualism because “then science would be limited”.
I happen to believe that we will be able to accurately model intentions and passions with a computer. But that is very different from saying that intentions and passions are discrete objects that we would use to compute things (in the physical world or otherwise). Like materialists, I would insist that the actual deterministic computations take place at the “physical” level. I don’t know how you assert otherwise without falling into teleological argument. I asked you to supply an example of a single materialist philosopher who would assert otherwise — that intentions and passions are units which are used in deterministic computations of the physical state rather than vice-versa.
NIST says that it’s dependent on pi [1] (presumably because of the reduced Planck constant), and the formula doesn’t look all that complex to me. I was just speculating about the reason that you would claim it’s complex. Do you have any pointers to a more official definition that doesn’t include pi, or that explains why it “might be infinitely complex”?
I don’t think so. I’m saying that the initial conditions are postulated to be simple, relative to all of the apparent complexity we see around us. A big bang and 30 constants. I don’t know what it means to be “random in the Kolmogorov sense”. Evolutionary theory functions just fine if “random” is determinstically pre-determined by the big bang and the laws of physics.
Spam filter is stripping links. Try this one:
physics.nist.gov/cgi-bin/cuu/Value?eqalph|search_for=fine+structure
And this:
books.google.com/books?id=yNJN-_jznw4C&lpg=PA88&dq=%22Human%20Freedom%20is%20just%20a%20fact%20of%20experience%22&pg=PA88#v=onepage&q=%22Human%20Freedom%20is%20just%20a%20fact%20of%20experience%22&f=false
NIST says that it’s dependent on pi [1] (presumably because of the reduced Planck constant), and the formula doesn’t look all that complex to me.
This is very confused. The fact that one particular definition has a pi in it does not mean alpha is “dependent on pi”, any more than the number -1 is “dependent on pi” because I can express it as e to the i pi. And whether the formula defining it is simple or complex has nothing to do with the Kolmogorov complexity of its value as a real number.
I was just speculating about the reason that you would claim it’s complex.
Confused again. I never claimed it is complex or simple; I simply observed that no one has any idea if there is a simple algorithm that on input n produces (say) an approximation good to within 10^{-n}. For all we know, there might be no finite program to calculate it. So confident pronouncements about the Kolmogorov complexity of the initial conditions of the universe are, at present, unfounded.
A big bang and 30 constants.
And for each of the constants, nobody knows what their Kolmogorov complexity is. It could be infinite. So minimizing it by saying “30 constants” is quite misleading.
I don’t know what it means to be “random in the Kolmogorov sense”.
When biologists say that “mutations are random”, they mean “random with respect to fitness”. I was trying to make it clear what I meant by random by saying “in the Kolmogorov sense”. This just means that the Kolmogorov complexity is high.
Oh – and I’ve read Searle, and he seems exceptionally confused about many things, such as the importance of his “Chinese room” argument.
I asked you to supply an example of a single materialist philosopher who would assert otherwise — that intentions and passions are units which are used in deterministic computations of the physical state rather than vice-versa.
Actually, in your original argument you never said anything at all about “units which are used in deterministic computations”. But I’m happy that you are willing to withdraw your original claim. Perhaps I’m simply too dense to see what you were driving at.
From my comment just before you responded:
It’s hard to see how a computational measure of complexity would be useful for anything which is not computer-like. There is a reason that Kolmogorov IT is used heavily in computation, but not in law or art, for example. Intentions (the focus of law) and passions (the focus of art) do not behave as computations, and if materialism succeeds in reducing these to physical properties, the Kolmogorov complexity would not be measured at the level upon which law and art operate. So it will always be apples and oranges.
You have proposed to apply Kolmogorov IT to “the mind of God”, presumably to refute theism. Since you don’t even believe in a “mind of God”, one would expect you to use the definition that theists use. Theists don’t generally define God in a way that would seem compatible with measurement via computational complexity.
I was simply explaining why he needed to presuppose materialism to make his argument, which then makes it an extraordinarily bad argument against theism, since materialism refutes theism already.
If, as you say, we have no idea whether Kolmogorov complexity of the fundamental constants is low, high, or infinite; I guess that’s another strike against this formulation of the 747 argument.
Intentions (the focus of law) and passions (the focus of art) do not behave as computations.
How do you know? Many of your responses seem to be confident assertions of things that we simply don’t know. They could well be the result of computations. But maybe I don’t know what you mean by vague terms like “behave as”.
Yes, they could be the result of computations. If they were, that would presuppose materialism, which would make the whole argument unnecessary.
What I meant by “do not behave as computations” is what I said in comment #26: “It is at the physical layer that the deterministic ‘computation’ takes place, and the layer of intentionality is a projection.”
If one assumes that intentions can “compute” things and cause results, then one is either arguing for dualism (in which case the argument falls apart), or implying a sort of materialism which I have never, ever seen articulated. I don’t think you can find any materialist philosopher who would say such a thing.
Therefore, the argument falls apart either way.
@TaiChi – You can delete the first two duplicates if you want; they were trapped in the spam filter and I re-posted.
“It is at the physical layer that the deterministic ‘computation’ takes place, and the layer of intentionality is a projection.”
I must be stupid, but I don’t know what you mean by ‘layer’ or ‘projection’ here.
BTW, I agree with you on this. I normally think of neural nets and bayesian classifiers as being in a different category than “algorithms”, but this is absurd for the reason you point out. And the fact that we can simulate neural nets on a computer proves that the neural net can described in terms of machine code.
You don’t seem stupid to me; my terms may be poor. How familiar are you with supervenience naturalism? Even Dennett, who is kind of between eliminativist and supervenience naturalism, describes intentionality as being a different level, which “supervenes on” (is wholly caused by) the material. He describes this layer/level/stance being constructed by skycranes, which is distinct from the physical, but does not influence the physical.
In supervenience naturalism, the intentions are like the output of a program, they are not actually the program. If you are running some monte carlo simulation on your computer, and looking at the numbers projected onto your screen, you would not say that these numbers were the program or the actions of the code. They are the side-effect. That’s what I meant by saying that intentionality is a “projection”.
@JS Allen
“Right. The language that you choose to assume, for sake of measurement (i.e. the computational substrate) makes all the difference in the world. ” ~ JS Allen
Only if what you measure isn’t very complex. A string can be appended with a prefix specifying the language it is to be interpreted in, and the size of the prefix is negligible for long strings.
“I’m not arguing on behalf of astrology or even theism at this point. I am responding to your assumption that everything must be reducible to physical causes.” ~ JS Allen
You’re responding to a strawman. If I assume anything, it’s that our current science is correct, and that minds roughly function how that science says they do. If it is a consequence of that view that dualism is false, then so be it, but please note that an assumption is not the same as a consequence, and that I choose not to draw this consequence anyway, since I’d rather be charitable and allow for the possibility that a sophisticated dualism can be made to fit with science.
“If your whole Kolmogorov refutation of theism depends on an incredulous, “But if you don’t accept that premise, then science may have limitations! You’re kidding!” then you have lost already.” ~ JS Allen
I don’t see how the limits of science have been reached here. Plainly, science tells us a bunch of things about the mind, which means that minds (or at least the aspects of the mind on which science has something to say) fall within the purview of science. I apply some of these things to another mind to reach my conclusions. No limit has been trangressed here. In fact, I could not transgress the limits of science with a scientific argument by definition, so I don’t see how invoking the limits of science could ever be a proper objection to a scientific argument.
@Jeffrey Shallit
“You make an obvious mistake: if a program P produces many different outputs, it is simply not true that the Kolmogorov complexity of each of its outputs must be less than the Kolmogorov complexity of P. Simple counterexample: write a program P that on input i outputs all binary strings of length i. Then the Kolmogorov complexity of P is a constant C, and the Kolmogorov compexity of i is at most log_2 i + C’. On the other hand, at least one of P’s outputs has Kolmogorov complexity i. So we have complexity log_2 i + constant giving rise to an output of Kolmogorov complexity i.” ~ Jeffrey Shallit
I’d like to revisit this. Reading it again, you seem to take me as saying that complexity cannot arise via simple processes. But whether or not complexity can arise from simplicity is irrelevant to the argument, for all I say is that a designer of the universe would need to be as complex as the universe, not that a cause of the universe would need to be as complex as the universe. So I think my argument remains intact.
BTW, you wouldn’t be the Jeffrey Shallit who has written on Dembski, would you? If so, it seems a waste of time for me to be trying to construct a defensible interpretation of Dawkins, when you have the knowledge to set us straight on the matter. So: What do you think is behind Dawkins argument? And do you think Dawkins is right to argue so?
Physical science currently has no explanation for how intentionality could emerge from the physical. Materialists have faith that there will one day be a plausible explanation (and I am sympathetic to this faith). You need to take it as a matter of faith, and you apparently do.
It seems that you assume more than this, though. You assume that physical science will eventually be able to explain everything, including a “sophisticated dualism”. Correct me if I am wrong.
Sure, if you assume that physical science’s explanatory powers encompass everything, then you’re right. But then you are not refuting theism — you are refuting some strawman version of theism which doesn’t match any normal version. And you’re wasting your time anyway, since materialism automatically refutes theism without needing Kolmogorov IT.
Here’s how it works:
Materialism
1)Materialists assert that our intentionality is strongly reducible to the physical. Theism is completely incompatible with this view, as is libertarian free will. More troubling for this stance is the fact that even talking about science is unintelligible, as Paul Feyerabend pointed out. People who hold this view of “strong materialism” have come to be known as “eliminativists”, because they eliminate the possibility that science or reason can truly exist.
2) Supervenience naturalists, or “soft materialists”, assert that our intentionality is not strongly reducible, but “supervenes on” the physical. That is, the physical wholly determines the intentional, but the intentional is truly distinct from the physical. The intentional does not follow the rules of the physical. This preserves science and reason, and fits more closely with common sense. However, it is completely incompatible with theism and libertarian free will. It is important to note that science has no theory (yet) about how this “supervenience” happens.
3) Emergentists assert the same supervenience relationship as #2, but additionally assert that intentions can somehow reverse the supervenience relationship and impose upon their own physical substrate. This view is kind of weird, and also seems to be incompatible with libertarian free will and theism.
Theism
None of the above theories of materialism are compatible with classic theism, so assumption of materialism is synonymous with refutation of theism. I’m not an expert in theories about theism, but I believe that the two most basic ones are:
4) The physical supervenes on the spiritual/intentional. God is first intentional, and the physical supervenes on (is fully determined by) intentions. The God of theists is generally simple and intentional; not physical. He unifies mercy and justice, love and hate, etc. He is one, while creatures are many. Since this follows the rules of intentions, rather than physical computations, Kolmogorov complexity doesn’t apply (indeed, as it does not apply to intentions in the #2 form of materialism above)
5) Dualism. The spiritual/mental is in some part non-physical. The part that is non-physical, by definition, does not follow physical laws and thus it outside the purview of physical science. Note that there are atheist dualists; this is not just a theist conception, although it is compatible with theism.
“Physical science currently has no explanation for how intentionality could emerge from the physical. ” ~ JS Allen
Please point to the place where I mention intentionality.
“You assume that physical science will eventually be able to explain everything, including a “sophisticated dualism”. Correct me if I am wrong. ” ~ JS Allen
You’re wrong. First, there will always be facts which science can’t explain, because every explanation presupposes some basic facts in terms of which explanations are to be given. Second, if dualism is true, I do not presume that science will explain it, only that science will indicate it. Third, I see no reason to suppose, as you do, that dualism would be extra-scientific, and you have given no argument for this. All you have done is to refer to science as “physical science” in an attempt to secure your conclusion by tautology. But physicalism/materialism is only a recently popular addition to the scientific worldview, and there is no reason to suppose that science would not survive the ejection of its assumptions.
“Sure, if you assume that physical science’s explanatory powers encompass everything, then you’re right. ” ~ JS Allen
You’ve missed the point by a mile. Scientists are already studying the mind, they already draw conclusions about its nature, and my argument above merely applies those conclusions to another mind. Perhaps there are some other facts undiscoverable by science, and for which we need dualism, but I could hardly offer those facts in a scientific argument, now could I?
“5) Dualism. The spiritual/mental is in some part non-physical. The part that is non-physical, by definition, does not follow physical laws and thus it outside the purview of physical science. ” ~ JS Allen
If this is your view of dualism, I can hardly see why you complain – you accept that at least part of the mental could be physical, and from my point of view, this may as well be the complexity I argue for. If you want to say that consciousness itself is different (the observer is different from the information observed), and that we require dualism to account for it, then be my guest – it’s entirely compatible with the argument.
I haven’t missed your point at all. You are attempting to apply a materialistic measure of complexity to something which theists believe to be non-material.
As I already explained, theists believe that the non-material component could follow completely different rules than the physical; for example, with intentionality being a primary unit of composition (rather than a reflection of massive underlying physical complexity).
And as I’ve also explained, using Kolmogorov complexity is senseless on something like intentionality. If the non-material follows intentionality, it would likely be significantly less complex, and may even find unity in God.
You keep evading the issue. Please show me a single form of theism for which your weird theory about “sophisticated dualism” would work. Do you know of any, or are you just making up a strawman so that you can find something that (you think) works wih Kolmogorov IT?
That makes no sense. Even if it were 99.9% material; the 0.1% intentionality could encompass something that would take a billion times as much to supervene on pure physical terms. Unless you know exactly what the nonmaterial is, it makes no sense to talk about the ratios.
Seriously, you need to read a book and find out what dualists and theists believe. You’re refuting something nobody believes.
Well, this argument demonstrates that no rational argument can shake a closed minded theist, who will simply define God as being whatever God needs to be in order to refute whatever argument is at hand, without needing even the slightest bit of evidence to support his claim. On the one hand, God is first omnipotent, wielding the power to create the universe and intervene in it to manipulate matter and energy in any fashion he chooses which is not logically impossible, and second omniscient, having the mental capacity to hold in his mind everything that has ever happened, everything that is happening, and everything that ever will happen. And yet while having the capacity to wield absolute power and the mind to hold absolute knowledge, God is also simple, and so needs no explanation for his existence. Anyone who can believe both those things at the same time can’t be reasoned with.
For those who can be reasoned with, it should be fairly obvious that the pre-Big Bang singularity is vastly simpler, and therefore vastly more probable, than God. Physicists have even developed several theories as to how the universe could have started, and research producing experimental data to give us more insight is even conceivable, unlike an explanation for the existence of God, which will never extend beyond hand waving. This makes God superfluous-even if God isn’t so improbable that he could somehow come into existence, the universe would’ve started long before, rendering God unnecessary
Theists have always defined God as being non-material and irreducible, for at least 3,500 years.
The only one redefining God to try to win an argument is Tai-Chi, who insists that God must be reducible to some complexity of parts, and that the immaterial must follow the same “computability” rules as the material.
As Jefferey has already explained, the Kolmogorov complexity of the initial state of the universe may well be infinite. If you’re going to claim that it’s simple, you need to defend why. I was unable to do so, and I doubt you’ll be able to.
“Theists have always defined God as being non-material and irreducible, for at least 3,500 years.
The only one redefining God to try to win an argument is Tai-Chi, who insists that God must be reducible to some complexity of parts, and that the immaterial must follow the same “computability” rules as the material.”
The ancient wisdom of people making stuff up isn’t impressive. The Theistic God intervenes in this universe to manipulate matter and energy as he pleases-to do that, he has to have some sort of structure in order to generate and wield massive amounts of energy. He also needs some form of structure to store his omniscient knowledge-he can’t just be some celestial fog bank. Theists can no longer win this debate by simply throwing out terms like “spirit” without anyone, including them, having the slightest idea what that term actually means. There is absolutely no evidence that “God” is a blob of non-material theists have stuck the label of “spirit” on.
Regardless of whether or not singularities have “Kolmogorov” complexity, they are simply compressed matter without structure and are common in the universe, thus there is a high probability of a singularity forming. If Kolmogorov complexity says a singularity is more complex than God, then that definition of complexity doesn’t have much relationship to reality.
You accused them of changing their definition of God to win arguments with anonymous Internet trolls. That is pretty impressive, if they did all of that 3,500 years ago.
Let me remind you what you said:
You must admit, that was a shockingly ignorant thing to say.
You’re trying to change the subject. Nobody is talking about “theists winning this debate”. We’re talking about the validity of this specific instance of the 747 gambit, something that atheists should be concerned about.
Such a God would be absurd, and wouldn’t need any form of the 747 gambit to refute. Since no theist believes in such a God, you’re refuting a belief that nobody has. It’s kind of like mental masturbation; you’ve constructed something wholly from your imagination and now you’re pretending that it submits to you.
You are welcome to posit that materialism is true (or that the immaterial is strongly reducible like the material); but if you succeed in doing so, then the Kolmogorov argument is irrelevant. If you don’t succeed, then the Kolmogorov argument is inapplicable. So it’s a worthless argument either way.
We have absolutely no way to estimate the probabilities of the big bang and all 30 of the fundamental constants. We have never observed any big bangs that have completely different fundamental constants, so we can’t estimate probabilities. It could happen all the time, or only once in eternity. We don’t know.
BTW, are you trying to defend this Kolmogorov gambit, or are you just a troll?
@ JS Allen
“I haven’t missed your point at all.” ~ JS Allen
You have, again. Since I’ve already explained it twice, and you persist in grinding your particular axe instead of trying to understand what I’m saying, I won’t bother repeating it.
“As I already explained, theists believe that the non-material component could follow completely different rules than the physical; for example, with intentionality being a primary unit of composition (rather than a reflection of massive underlying physical complexity).” ~ JS Allen
Fine, have it your way. Theists believe that the mind could work in a way that flatly contradicts everything science tells us about how a mind works. Satisfied?
“You keep evading the issue. Please show me a single form of theism for which your weird theory about “sophisticated dualism” would work. Do you know of any, or are you just making up a strawman so that you can find something that (you think) works wih Kolmogorov IT?” ~ JS Allen
How bizarre. I charitably allow that what science tells us of the mind is compatible with some form of dualism, and you complain I’m being uncharitable. Again, have it your way: there is no version of dualism which is consistent with cognitive science. Happy?
“Even if it were 99.9% material; the 0.1% intentionality could encompass something that would take a billion times as much to supervene on pure physical terms. Unless you know exactly what the nonmaterial is, it makes no sense to talk about the ratios.” ~ JS Allen
I see. It would be presumptuous of me to say anything about what the immaterial must be like if it instantiates a mind, but you can speculate freely that it can accomodate all your ontological wishes. The net’s only up for my serve, is that how it is? Well, you can find someone else with whom to play.
Relevant:
http://lesswrong.com/lw/jp/occams_razor/
http://realityconditions.blogspot.com/2007/06/examination-of-dawkins-ultimate-747.html
http://richarddawkins.net/discussions/476608-information-theory-complexity-dawkins-747-gambit-little-help
http://www.ekklesia.co.uk/node/5721
This seems to be way over my head, but it looks fascinating and I still quite appreciate this effort. Dawkins amazingly has recruited more people to think… and there’s a phenomenal blooming of discussions all over the place, regardless of individual stance and major field of interest. Though, I’m much more hooked into looking at the cognitive psychology of religious belief myself. My feeling is that real-world consequences of beliefs in some god(s) carry much more weight at the level of basic day-to-day human interaction and cognition, since, anyway, most people operate at this level. But I’ll try to re-read this post again when I can devote more time.
[…] objections to theism. (One can give a “Who made God?” objection to theism that has some meat, but that’s not the one Hitchens gave. Hitchens’ objection concerned an infinite […]
[…] onsubstantive objections to theism. (One can give a “Who made God?” objection to theism that has some meat, but that’s not the one Hitchens gave. Hitchens’ objection concerned an infinite regress of […]
Tai Chi,
You may be interested in defending your defence of Dawkin’s argument against Randal Rauser, who seems to think little of it. Randal is a very nice guy, and he’s clever, so I think you might enjoy the challenge.
Check it out:
http://randalrauser.com/2011/04/why-no-professional-philosopher-would-use-dawkins-argument/
http://randalrauser.com/2011/04/can-dawkins-or-at-least-his-argument-be-saved/
SB
Thanks for passing this on, Silver Bullet. I don’t have much time to look at it right now, but I’ll certainly do so later.
[…] é uma entidade consistente e provável?” que sejam mais ricas e sólidas, como esta aqui, em “Dawkins e a aposta do 747 máximo” (inglês) ou essas, em português, no artigo “Opiniões, mentes e peixes”, por Eli […]