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Eliezer_Yudkowsky comments on Welcome to Less Wrong! (5th thread, March 2013) - Less Wrong
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Doesn't this argument Prove Too Much by also showing that without a Metagod, God should be expected to have arbitrary and random governing principles? The universe is ordered, but trying to explain that by appealing to an ordered God begs the question of what sort of ordered Metagod constructed the first one.
I don't think that necessarily follows. A sufficiently intelligent mind (and I think I can assume that if God exists, then He is sufficiently intelligent) can impose self-consistency and order on itself.
This also leads to the possible alternate hypothesis that the universe is, in fact, an intelligent mind in and of itself; that would be pantheism, I think.
Of course, this does not prevent the possibility of a Pebblesorter God, or a Paperclipper God. To find out whether these are the case, we can look at the universe; there certainly don't seem to be enough paperclips around for a Paperclipper God. There might well be a Beetler God, of course; there's plenty of beetles. Or a Planetsorter God, a large-scale variant on the Pebblesorter; as far as we know, all the planets are neatly sorted into groups around stars. Order, by itself, does not necessarily mean an order that we would have to agree with.
This begs Eliezer's question, I think. Intelligence itself is highly non-arbitrary and rule-governed, so by positing that God is sufficiently intelligent (and the bar for sufficiency here is pretty high), you're already sneaking in a bunch of unexplained orderliness. So in this particular case, no, I don't think you can assume that if God exists, then He is sufficiently intelligent, just like I can't respond to your original point by assuming that if the universe exists, then it is orderly.
I disagree. Intelligence makes its own rules once it is there; but the human brain is one of the most arbitrary and hard-to-understand pieces of equipment that we know about. There have been a lot of very smart people trying to build AI for a very long time; if the creation of intelligence were highly non-arbitrary and followed well-known rules, we would have working AI by now.
So, yes; I think that intelligence can arise from arbitrary randomness. I'd go further, and claim that if it can't arise from arbitrary randomness then it can't exist at all; either intelligence arose in the form of God who then created an orderly universe (the theist hypothesis), or an arbitrary universe came into existence with random (and suspiciously orderly) laws that then led to intelligence in the form of humanity (the atheist hypothesis).
Fair enough. Then let me put it this way; if God is not sufficiently intelligent, then God would be unable to create the ordered universe that we see; in this case, an ordered universe would be no more likely than it would be without God. An ordered universe is therefore evidence in favour of the claim that if God exists, then He is sufficiently intelligent to create an ordered universe.
I agree that intelligence itself is an optimizing process (which I presume is what you mean by "making its own rules"), but it is also the product of an optimizing process, natural selection. Your claim that it is arbitrary confuses the map and the territory. Just because we don't fully understand the rules governing the functioning of the brain does not mean it is arbitrary. Maybe it is weak evidence for this claim, but I think that is swamped by the considerable evidence that intelligence is exquisitely optimized for various quite complex purposes (and also that it operates in accord with the orderly laws of nature).
Also, smart people have been able to build AIs (albeit not AGIs), and the procedure for building machines that can perform intelligently at various tasks involves quite a bit of design. We may not know what rules govern our brain, but when we build systems that mimic (and often outperform) aspects of our mental function, we do it by programming rules.
I suspect, though, that we are talking past each other a bit here. I think you're using the words "random" and "arbitrary" in ways with which I am unfamiliar, and, I must confess, seem confused. In what sense is the second horn of your dilemma an "arbitrary universe [coming] into existence with random (and suspiciously orderly) laws"? What does it mean to describe the universe as arbitrary and random while simultaneously acknowledging its orderliness? Do you simply mean "uncaused", because (a) that is not the only alternative to theism, and (b) I don't see why one would expect an uncaused universe (as opposed to a universe picked using a random selection process) not to have orderly laws.
OK, but this doesn't respond to Eliezer's point. If you conditionalize on the existence of (a Christianish) God, then plausibly an intelligent God is more likely than an unintelligent one, given the orderliness of the universe. But Eliezer was contesting your claim that the orderliness of the universe is evidence for the existence of God, while also not being evidence for the existence of a Metagod.
So Eliezer's question is, if P(orderliness | God) > P(orderliness | ~God), then why not also P(intelligent God | Metagod) > P(intelligent God | ~Metagod)? Your response is basically that P(intelligent God | God & orderliness) > P(~intelligent God | God & orderliness). How does this help?
What I mean is, not planned. If I toss a fair coin ten thousand times, I have an outcome (a string of heads and tails) that would be arbitrary and random. It is possible that this sequence will be an exactly alternating sequence of heads and tails (HTHTHTHTHTHT...) extending for all ten thousand tosses (a very orderly result); but if I were to actually observe such an orderly result, I would suspect that there is an intelligent agent controlling that result in some manner. (That is what I mean by 'suspiciously orderly' - it's orderly enough to suggest planning).
Well, it makes sense that P(intelligent God | Metagod) > P(intelligent God | ~Metagod). And therefore P(Metagod | Metametagod) > P(Metagod | ~Metametagod), and so on to infinity; but an infinity of metagods and metametagods and so on is clearly an absurd result. The chain has to stop somewhere, and that 'somewhere' has to be with an intelligent being. Therefore, there has to be an intelligent being that can either exist without being created by an intelligent creator, or that can create itself in some sort of temporal loop. (As I understand it, the atheist viewpoint is that a human is an intelligent being that can exist without requiring an intelligent creator).
And my point was that P(intelligent God | ~Metagod) is non-zero. The chain can stop. P(Metagod | intelligent God) may be fairly high; but P(Metametagod | intelligent God) must be lower (since P(Metametagod | Metagod) < 1). If I go far enough along the chain, I expect to find that P(Metametametametametametametagod | intelligent God) is fairly low.
Does that help?
That's not clear.. There is presumably something like that in Tegmark's level IV.
You haven't established the 'has to' (p==1.0). You can always explain Order coming from Randomness by assuming enough randomness. Any finite string can be found with p>0.5 in a sufficiently long infinite string. Assuming huge amounts of unobserved randomness is not elegant, but neither is assuming stacks of metagods. Your prreferred option is to reject god-needs-a-metagod without giving a reason, but just because the alternatives seem worse. But that is very much a subjective judgement.
Assume that P(%5E{x+1})
god | ^{x})
god) = Q, where Q < 1.0 for all x. Consider an infinite chain; what is P(^{\infty})
god|god)?
This would be P(^{x})
god|god) = 
. Since Q<1.0, this limit is equal to zero.
...hmmm. Now that I think about it, that applies for any constant Q. It may be possible to craft a function Q(x) such that the limit as x approaches infinity is non-zero; for example, if I set Q(1)=0.75 and then Q(x) for x>1 such that, when multiplied by the product of all the Q(x)s so far, the distance between the previous product and 0.5 is halved (thus Q(2)=5/6, Q(3)=9/10, Q(4)=17/18, and so on); then Q(x) asymptotically approaches 1, while P(^{\infty})
god|god) = 0.5.
You're right, and thank you for pointing that out. I've now shown that p<1.0 (it's still pretty high, I'd think, but it's not quite 1).
You seem to be neglecting the possibility of a cyclical god structure. Something which might very well be possible in Tegmark level IV if all the gods are computable.
Huh. You are right; I had neglected such a cyclical god structure. That would appear to require time travel, at least once, to get the cycle started.
I don't really follow this. Things in Platonia or Tegmark level IV don't have separate probabilities Any coherent mathematical structure is guaranteed to exist. (And infinite ones are no problem). So the probabilty of a infinite stack of metagods depends on the coherence of a stack of metagods being considered a coherent mathematical structure, and the likelihood of our living in a Tegmark IV.
Ah. I was trying to - very vaguely - estimate the probability that we live in such a universe.
I hope that closes the inferential gap.
I don't really follow this. Things in Platonia or Tegmark level IV don't have separate probabilities Any coherent mathematical stucture is guranteed to exist. (And infinite ones are no problem). So the probabilty of a infinite stack of metagods depends on the coherence of a stack of metagods being considered a coherent mathematical structure, and the likelihood of our living in a Tegmark IV.
It's not arbitrary in the sense of random. It's arbitrary in the sense of not following obvious apriori principles. It may impose its own higher-order rules, but that is something that happens in a system that already combines order and chaos in a very subtle and hard to duplicate way. Simple, comprehensible order of the kind you detect and admire in the physical unverse at large is easier to do than designing a brain. No one can build an AGI, but physicists build models of physical systems all the time.
Agreed. The human brain is the output of a long, optimising process known as evolution.
Yes. Simple, comprehensible order is one of the easiest things to design; as you say, physicists do it all the time. But a lot of systems that are explicitly not designed (for example, the stock market) are very chaotic and extremely hard to model accurately.
I still don't see why you would think order of a kind comprehensible to humans in the universe is evidence it was designed by a much smarter entity.
I'm trying to use it as evidence that it was designed at all.
Would it's being designed by a Matrix Lord of non-superhuman intelligence help your case?
It would certainly explain the observations that I am using as evidence.
Did you mean to say "can not" in that sentence ?
No, I did not.
I'm not sure I understand your argument, then. If intelligence can arise from "arbitrary randomness", then a universe that contains intelligence is evidence neither for nor against a creator deity, once you take the anthropic principle into account.
Yes, intelligence can arise from arbitrary randomness; I'm not using intelligence as evidence of an intelligent Creator. Using intelligence as an indicator of anything falls foul of anthropic principles.
My argument is that a universe that's as straightforward, as comprehensible in its natural laws, as our universe seems about as unlikely as tossing a coin ten thousand times and getting an exact alternating pattern of heads and tails (HTHTHTHTHTHT...), or a lottery draw that consists of the numbers 1, 2, 3, 4, 5, 6 in that order.
Isn't this just the anthropic principle in action ? Mathematically speaking, the probability of "123456" is exactly the same as that of "632415" or any other sequence. We humans only think that "123456" is special because we especially enjoy monotonically increasing numbers.
I'm not sure. The anthropic principle is arguing from the existence of an intelligent observer; I'm arguing from the existence of an orderly universe. I don't think that the existence of an orderly universe is necessarily highly correlated with the existence of an intelligent observer. Unfortunately, lacking a large number of universes to compare with each other, I have no proof of that.
Yes. I do not claim that the existence of an orderly universe is undeniable proof of the existence of God; I simply claim that it is evidence which suggests that the universe is planned, and therefore that there is (or was) a Planner.
Consider the lottery example; there are a vast number of sequences that could be generated. Such as (35, 3, 19, 45, 15, 8). All are equally probable, in a fair lottery. However, in a biased, unfair lottery, in which the result is predetermined by an intelligent agent, the sort of patterns that might appeal to an intelligent agent (e.g. 1, 2, 3, 4, 5, 6) are more likely to turn up. So P(bias|(1, 2, 3, 4, 5, 6)) > P(bias|(35, 3, 19, 45, 15, 8)).