Did Darwin undercut all Paley-style arguments?
November 30, 2010 — 9:30

Author: Alexander Pruss  Category: Existence of God  Tags: , , , ,   Comments: 68

Classic Paley-style design arguments go like this: There is some complex biological feature C which is such that

  1. God would have good reason to produce C, and
  2. C is extremely unlikely to occur through a random combination of elements.

It is concluded that probably God produced C, and hence probably God exists. The standard story is that Darwin undercut Paley-style arguments by providing a plausible explanation that does not involve God.

I shall suggest that the story is not so simple, and that, in fact, a very powerful Paley-style design argument may continue to go through.

The reason I say “suggest” reather than “argue” is that my argument is based on a crucial simplifying assumption. I shall assume a physics with a classical Hamiltonian dynamics satisfying Liouville’s Theorem. (To some readers this may already give a lot of my game away.) The justification is two-fold. First, for aught that we know, the correct dynamics of the world, whether deterministic or not, is such as to support some analogue of Liouville’s Theorem. Second, Darwin’s work appears to be consistent with classical mechanics, and was developed when classical mechanics was king. Thus, if Darwin’s work refutes classic Paley-style design arguments, this refutation should be consistent with classical mechanics.

Now, begin by posing this question: The standard story claims that Darwin naturalistically explained the explanandum of a Paley-style argument in a way that undercut that arguments–what is that explanandum?

Here are three options for the explanandum of a Paley-style argument, where t1 is the present:

  1. C occurs at t1
  2. C occurs at some time or other
  3. C occurs as soon as it does.

The most obvious option seems to be (3). Here is the watch upon the heath, and we wonder why there is here and now a watch upon the heath. But if (3) is the explanandum, then we have a serious problem for the Darwinian alternative to the design hypothesis. The Darwinian alternative is supposed to go something like this. We grant that it is “astronomically unlikely” (I’ll use that loose phrase for something like 10−30 or lower) that a random combination of elements should immediately produce C. In other words, we grant that it is astronomically unlikely that a random state of the universe should be such as to exemplify C. But we claim that the state of the world at t1 wasn’t produced randomly from scratch—it evolved, by means of variation and natural selection, from an earlier simpler state at t0. And this evolutionary story makes C more likely.

Except it doesn’t. Let S be the set of all possible physical states of the universe. Let C1 be the subset of S at which C is exhibited. Let C0 be the subset of S consisting of all the states s which have the property that according to the laws, if s occurs, then t1t0 units of time later C will be exhibited. Then because in classical mechanics we have two-way deterministic laws (so that not only do earlier states determine later ones, but later ones determine earlier ones) only, there is a one-to-one correspondence between C0 and C1. Intuitively, then, if it was astronomically unlikely that the state of the world at t1 should be in C1, it will be astronomically unlikely that the state of the world at t0 should be in C0. But if it is just as astronomically unlikely that the universe should be in C0 as that it should be in C1, then the Darwinian explanation hasn’t accomplished anything to undercut the design argument. So far this isn’t my own argument—I once came across a paper, which I did not note down the author of, in some journal from the 1950s or 1960s, perhaps the Review of Metaphysics, that made this argument. I wrongly dismissed the argument as uninteresting until I got to thinking about it again recently.

My initial reason for rejecting the argument was two-fold. First, the argument assumed determinism. Second, the argument, if my memory of it is accurate, had a serious hole. The mere existence of a one-to-one correspondence between possible states of the universe at t0 and at t1 only shows that the cardinalities of C0 and C1 are equal, not that their probabilities are equal (any non-zero-length interval of real numbers has the same cardinality, but in general given a probability measure they will not all have the same probability).

But in regard to the assumption of determinism, see my opening remarks. And in regard to the hole, Liouville’s Theorem exactly plugs that. Liouville’s theorem says that the evolution of a system governed by Hamiltonian mechanics—and classical systems will be like that—preserves volume in phase space (i.e., in the phase of all states of the system). And volume in phase space seems exactly the right measure of probability—at least, that’s what the classical statistical dynamics assumes. (There are some technical worries about infinite volumes, but perhaps one can do some limiting procedure in my argments.) Consequently, we learn from Liouville’s Theorem that the one-to-one correspondence between C0 and C1 preserves probability, and hence we can correctly conclude that the probability of C0 is astronomically low given that the probability of C1 is astronomically low. In other words, probabilistically, C0 is just as remarkable as C1.

Trent Dougherty gave me this vivid illustration of the point. Imagine Laplace’s demon, who knowing the state of the universe at one time immediately sees what state the universe must have at all other times. We look at the universe at t1 and exclaim: “By golly, we have C. How unlikely!” And when we look at the universe at t0—at which time we may have only the simplest life forms or even no life forms on earth—we find nothing remarkable. But Laplace’s demon could look at the universe at t0 and exclaim: “By golly, this universe is such that it will exhibit C in t1t0 units of time. How unlikely!”

I am not disputing that Darwinian evolution may provide a correct explanation of (3). But it does not provide a probability-raising explanation of (3), and to challenge a design argument based on (3) it would need to provide a probability-raising explanation of (3).

What about (4)? Maybe the reason why Darwinism couldn’t provide a probability-raising probability of (3) was because of (3)’s reference to a particular time. But if the explanandum is (4), maybe we can indeed get probability-raising.

However, without accounting for Darwinism, in our classical setting we can say that the physical probability of (4) is one. For classical mechanics turns out to be ergodic. From “almost all” (this is a precise term in measure theory: a property holds of almost all points in a space provided that the set of points of which it doesn’t hold has measure zero; for instance, almost all real numbers are irrational, if we are working with Lebesgue measure) starting points, we will visit arbitrary small neighborhoods of all points infinitely often. Now the kinds of features C that Paley-style arguments are run on have non-zero tolerances—in other words, if s is the present state of the universe, not only is C exhibited in s, but there will be a small neighborhood of s at all points of which C is exhibited. (If C is the existence of human-type brains, then any world whose particles are sufficiently close in position and momentum to those of our world will also have human-type brains, albeit just slightly differently shaped.) It follows from ergodicity that from almost all starting points the system will eventually produce C, and will even do so infinitely often, and hence the physical probability of (4) is one, without taking any account of evolutionary theory.

Thus, a design argument based on (4) is indeed undercut. However it is not undercut by evolutionary theory, but simply by the underlying classical mechanics.

This leaves (5). This may be the best bet for what evolutionary theorists should say in respect of the explanation of C. It is a puzzling fact that complex features like C should occur so soon after the beginning of the universe. We are less than 14 billion years from the Big Bang. This isn’t really all that long. Darwin famously talked of countless ages for evolution to work in. But if (5) is the explanandum that the evolutionary theory explains, then the talk of countless ages should be de-emphasized. (If an age is 1000 years, then 14 billion years is not at all a countless number of ages—if I counted the ages, counting out one age each second, 12 hours a day, I would be done in less than 11 months.) Ergodicity all but guaranteed, in an appropriate classical setting, that C would occur. But the wonder of evolutionary theory is that C occurred so quickly. Now, there is a fly in the ointment here: I doubt that the mathematics of evolutionary theory is yet sufficiently advanced to be able to pre
dict that the processes of variation and selection are fast enough to be at all likely to produce C in the amount of time available. But where one cannot prove, one may sometimes reasonably speculate, and I am happy to grant that evolutionary theory may well give a good probability-raising explanation of (5). But (5) need not be the design theorist’s explanandum. And if it’s not, then evolutionary theory’s success in respect of (5)—impressive as it is scientifically—is not relevant to the design argument.

So far I’ve looked at how the three explananda (3)-(5) do given evolutionary theory, on my assumption of classical mechanics. We have seen that in cases (4) and (5), we may well be able to give good probability-raising naturalistic explanations—though, interestingly, in case (4) we can do this without any mention of evolutionary theory. So these are not promising candidates for a design argument. But (3) is. So let me now give such an argument.

Suppose C is the existence of contingent intelligent beings. Let t1 be the present time. Given the discussion of (3), we see that evolution does not raise the probability of C occurring at t1 beyond the presumably astronomically small probability that it would occur at t1 by a completely chance coming-together of elements. I shall also assume that we have only one universe, and it is not so incredibly large that as to make C better than astronomically unlikely. (On multiverse theories, or theories with a very large universe, we get (3) with high probability, but again without evolutionary theory playing much of a role.) Give our assumptions, the conditional probability that C occurs at t1 astronomically small on naturalism. But God is responsive to reasons, and hence at any given time, if God exists, it is not very unlikely that he has created intelligent beings that exist at that time. Thus, the conditional probability that C occurs at t1 given theism is not very low. If theism and naturalism are our only hypotheses, this gives very strong confirmation to theism.

Let’s assign some numbers. Suppose the probability of C occurring completely at random at t1 given naturalism is 10−30. The probability of a state at t0 that evolves into a state that exhibits C at t1 is also 10−30. So, P(C at t0|naturalism)=10−30. Now the probability that God would have created intelligent beings that exist at t1 is surely at least 10−9. Granted, we may worry that God might take a long time to prepare the universe for intelligent beings. But God also has good reason to ensure that there always are intelligent creatures, or that they be there as soon as possible. I don’t know how to evaluate these probabilities but one in a billion is very conservative. So P(C at t0|theism)=10−9, say. Suppose that theism and naturalism are our only options, so P(naturalism)=1−P(theism), and suppose that the prior probability of theism is one a trillion: P(theism)=10−12 (this is crazy, of course, given the explanatory power of theism). We can now plug the numbers into Bayes’ theorem and get, to a very good approximation, P(theism|C at t0)=0.999999999. And how much more could one want from an inductive argument?

Of course, this argument neglects three important factors: (a) multiverse hypothesis; (b) giant universe hypothesis; and (c) non-classical mechanics. Note that (a) and (b) are not Darwinian in nature. And while (c) might make Darwinian explanations of (3) be probability-raising, that this is so would need to be argued for. One might, for instance, think that the kinds of statistical results that Liouville’s Theorem yields are likely to hold at least approximately for the time-evolution of macroscopic objects.

Let me add that the argument is partly inspired by reflection on an unpublished multiverse-based argument by Mike Rota.

Comments:
  • Ted Poston

    Alex,
    There’s a lot to chew on here. Could you say why you think Darwinian theory should be consistent with deterministic mechanics (or Hamiltonian mechanics)? As I understand it, you’re pointing out that on some views the complexity of the universe is constant. (Thus, Trent’s nice illustration). It would seem to me that Darwinian theory is inconsistent with that claim.

    November 30, 2010 — 12:44
  • David Warwick

    “on some views the complexity of the universe is constant … It would seem to me that Darwinian theory is inconsistent with that claim.”
    This is something creationists say a lot, for example:
    http://www.icr.org/article/evolution-not-based-natural-laws/
    Here’s how the New Scientist deals with it:
    http://www.newscientist.com/article/dn13720-evolution-myths-evolution-violates-the-second-law-of-thermodynamics.html
    For evolution to occur on Earth without violating the laws of thermodynamics, there would have to be some enormous external energy source nearby, one that poured, say, light and heat and radiation over the planet. It would look like a giant glowing ball in the sky and would have shone for billions of years.

    November 30, 2010 — 13:02
  • Roberto Valenzuela

    Big flaw in the argument: the inductive probably of evolution producing intelligent creatures (granting that problematic term for the moment) C at t1 is 1. Until we observe other ecosystems on similar planets that have *not* developed intelligent life with similar starting conditions, there is simply no ground for supposing that the probability of “intelligent creatures” evolving over two billion years or so in a carbon-based ecosystem is “low,” particularly given the demonstrably high survival value intelligence confers. How on earth would such a conclusion as to probability be reached, with an observable set of just one member (the earth)? All we have is our existence, as well as extremely solid evidence of universal common ancestry. It would be a totally unjustified inference from the available data to assume a low probability of intelligent life developing on Earth-like planets.
    I also smell some dirty laundry in the use of the term “random,” particularly given the argument is premised on determinism and therefore is premised on the non-existence of actual randomness. There thus seems to be an equivocation: “Random” seems here used in a sense suggesting a mathematical variable approach, when by the terms of the argument all can “random” can possibly mean is simply “without conscious direction.”
    Finally: Explanatory power of theism?! Really? πŸ˜› When theism starts making testable, falsifiable predictions, THEN it has explanatory power. As it stands, theism has exactly the explanatory power of Last Thursdayism: that is to say, it has total and unfalsifiable explanatory power, and therefore utterly lacks explanatory power. To say theism has immense explanatory power is simply to commit bad philosophy of science.

    November 30, 2010 — 13:54
  • Roberto Valenzuela

    Also, as a quick followup, if, as in classical theism, God is ineffable and wholly Other, supposing that God DEFINITELY HAS (rather than MIGHT SPECULATIVELY HAVE) good reasons for doing X seems… eh, let’s say somewhere between utterly undemonstrable without special pleading on the one hand, and hideously arrogant on the other.
    Supposing it’s even coherent to say a hypothesized God has reasons, of course. Timelessness, eternity, omniscience, and ineffability kinda cluster together to make a term like “God has reasons” terribly and irrationally anthropomorphic and likely meaningless in any actual sense.

    November 30, 2010 — 14:05
  • a. The relevant probability is the probability that a completely from-scratch randomly produced (with respect to something like the microcanonical ensemble measure) state of the universe would exemplify C. It is not the probability that the universe would evolve to exemplify C. Intuitively, the probability is low. If it weren’t low, then we wouldn’t need the Darwinian story to undercut the design argument.
    b. I said nothing about entropy. I haven’t even said much about complexity–I said that the biological feature C is “complex”, but the only work that does in the argument is that it is a feature that it is unlikely to get from scratch. I am sceptical about Ted’s point that on a deterministic picture we get constant complexity. The issue is that complexity can be defined in terms of higher-level natural properties, and the property of exemplifying C is more natural than the property of being such that C will be exemplified in t1-t0 units of time.
    c. Everything I loosely say about randomness can be replaced with rigorous claims about probability with an appropriate measure on the phase space, such as the microcanonical ensemble measure.
    d. I actually think evolutionary theory is compatible with Hamiltonian mechanics, as long as we do not take evolutionary theory to offer probability-raising explanations of explananda like (3). If it offers non-probability-raising explanations of (3), or doesn’t offer explanations of (3) at all, then it’s fine.
    e. As far as I know it an open question whether something like Hamiltonian mechanics is or is not a sufficiently good approximation to the correct mechanics for the purposes of the argument. We know it’s a sufficiently good approximation for thermodynamic processes within a certain range of conditions.
    f. As for extreme unlikeliness, the point is not that unlikely events don’t happen. They of course do. (It may even be the case that events with zero probability happen. Whether they do or not roughly depends on whether we live in a discrete or continuous world.) The point, rather, is that in good Bayesian fashion we need to compare hypotheses. If on the naturalistic hypothesis something has probability 10^-30 and on the theistic hypothesis it has probability 10^-9, then this is massively powerful incremental evidence for theism over naturalism by Bayes’ theorem, and as long as theism didn’t start off as too unlikely, it becomes very likely after the argument.

    November 30, 2010 — 14:37
  • David Warwick

    “The relevant probability is the probability that a completely from-scratch randomly produced (with respect to something like the microcanonical ensemble measure) state of the universe would exemplify C.”
    By ‘exemplify C’, you have to mean only ‘get to the same result’ – ending up with Paley’s watch on a hillside, say – because obviously the paths evolution and creation would take to deliver the watch there would be radically different.
    Think of it in terms of a walk. Someone walks from point A to point B, a mile across some countryside. In another, identical, universe, the same person makes the same journey. The odds that they can both reach point B are good. The odds that both *perfectly* reproduce every single step, so that there is absolutely no difference between them is astronomical.
    If we ran evolution again, we wouldn’t get an identical result. We know that from experimental data on identical colonies of bacteria in identical conditions. Many mutations are random. We would, though, reach many common destinations. We know that lots of creatures independently evolved eyes, for example.
    The odds for two species evolving eyes are good. The odds for evolving *exactly the same* eyes are astronomical.

    November 30, 2010 — 15:58
  • David Warwick

    “If on the naturalistic hypothesis something has probability 10^-30 and on the theistic hypothesis it has probability 10^-9, then this is massively powerful incremental evidence for theism over naturalism”
    It depends what the ‘something’ is.
    Say it’s ‘a single mutation in a single bacterium’.
    And there are two options: a completely random one in 10^-30 chance it will happen each time a new bacterium is born; a one in a billion chance God once created one as a single event …
    … well, there are 5×10^30 bacteria on Earth, so the odds are there are five mutated bacteria right at this moment, and they’ve been around for four billion years, so there will have been countless examples (about a trillion, in fact). But there’s still only a one in a billion chance there’s ever been a created one.

    November 30, 2010 — 16:23
  • Gregory Lewis

    Alexander:
    Couldn’t one just accept C1 and C0 have the same probability, but then use that to adjust up one’s ‘intuitive’ assignment of C1? An evolutionary story ‘funnels’ traces through time such that many more worlds exhibit C at t1. Or, another way of putting it: the darwinian story gives reason to think the possibility that a world at t0 without C will remain not C when it reaches t1.
    Apologies if I’m missing something basic.

    November 30, 2010 — 18:10
  • Billy McDoniel

    I’ll admit to not being able to follow a lot of the technical stuff, but it seems to me that that this same argument ought to show that gravity is not a probability-raising explanation for why matter tends to occur in such dense clumps.
    The fact that matter occurs in very dense clumps in our universe would appear to be very unlikely, if what is meant by “a completely chance coming-together of elements” is something like just randomly choosing spatial coordinates for each atom. But gravity explains this, in a probability-raising way, by showing that, in fact, almost any initial distribution of matter will clump. What a theory of gravity allows us to do is to go back and correct ourselves – we now understand that clumping /isn’t/ an unlikely sort of thing to see. Does this seem right?

    November 30, 2010 — 18:41
  • Mr Warwick:
    The “something” is a proposition, say “That at t1, there is intelligent life somewhere in the universe.”
    Gregory:
    That’s a neat move. I am not sure it’s plausible. Plausibly, the vast majority of possible configurations of particles are just way too messy to contain highly structured life, maybe apart from an isolated Boltzmann brain (and we can stipulate that the intelligent life that C talks of isn’t isolated). Most of them won’t even contain stars or planets. Remember that the kinds of probabilities I am talking about are “Humean”: all possible particle positions and momenta (maybe subject to a total energy constraint or something like that) are equally likely.
    Ted:
    One more thought on why take Darwinism to be compatible with Hamiltonian mechanics. Suppose it’s not. Then that is a very interesting result. It means that physicists need to pay more attention to evolutionary biology than they do, since evolutionary biology places strong constraints on fundamental physics, namely that it cannot satisfy any sufficiently close analogue of Liouville’s theorem. It also means that as soon as evolutionary biology became a well-confirmed science, we had a pretty decent argument for abandoning classical physics. This does not seem all that plausible, since it seems plausible that evolutionary theory is multiply realizable in terms of different possible underlying dynamical bases.

    November 30, 2010 — 19:01
  • That’s a very nice point about gravity. I really don’t know enough physics to know what to say, but let me speculate. But if I say something embarrassingly naive about the physics, remember that while I am a mathematician I am not a physicist.
    The gravitational explanation introduces a new fundamental force and so it changes the Hamiltonian. The probability density on the phase space defined by the microcanonical ensemble is defined for a fixed total energy level. Now, when the particles are clumped together, their gravitational energy is low, which permits them to have a wider range of variation in momenta, and hence a large proportion of the states will exhibit such clumping. So we can give a kind of non-dynamic probabilistic explanation of clumping, simply in terms of energy levels and the like.
    The evolutionary explanation does not introduce a new fundamental force into the story. It introduces a new story, but one that involves the old forces. It is far from clear that a similar kind of non-dynamic probabilistic explanation of, say, intelligence can be given, one showing that in fact the states involving intelligence are likely to occur from scratch given the laws of physics.
    One issue is that it does not appear clear that the kinds of complexities that we’re trying to explain have the kinds of energy implications that clumping does in the gravitational case–ones allowing a greater variation in momenta within the same total energy.

    November 30, 2010 — 19:52
  • “By ‘exemplify C’, you have to mean only ‘get to the same result’ – ending up with Paley’s watch on a hillside, say – because obviously the paths evolution and creation would take to deliver the watch there would be radically different.”
    If C is intelligent life, by “exemplify C” I mean be a state of the universe containing intelligent life of some sort somewhere (however that state might have arisen).
    To run the argument, C needs to be chosen in such a way that the probability of C on theism is significantly higher than the probability of C on the microcanonical ensemble measure. To do that, I would want C to be a feature that embodies the sort of value that a perfectly good being would be not unlikely to want to promote–say, intelligence–and that is unlikely to be exhibited in a random state of the universe.
    In particular, I don’t want C to be too specific (e.g., “intelligent life just like Alvin Plantinga”), since then both the probability of C on theism and the probability of C on the microcanonical ensemble measure are going to be astronomically small. (I suspect it’s still going to be larger on theism, and so the argument might still work, but it may be harder to get reliable intuitions when one is comparing such tiny quantities.)
    Intelligent life is a nice example.

    November 30, 2010 — 20:57
  • Heath White

    I am out of my depth in this conversation, but it does seem that–unlike eyes–intelligence of our sort has evolved exactly once, which in turn indicates that such intelligence is fairly difficult for evolution to come up with.
    That is, prima facie, the probability of intelligent life is quite low on naturalism, and rather higher on theism.

    November 30, 2010 — 23:01
  • David Warwick

    “Intelligent life is a nice example.”
    The problem is that we’re missing two crucial data points: we don’t even have a ballpark figure of intelligent species in the universe and we don’t know the number of gods.
    If the number of gods has always been less than one, then the theist case is disproved.
    We know that intelligence evolved at least once on Earth, in the common ancestor of humans and the now-extinct intelligent hominids. We know that once intelligence evolved, intelligent species branched off (so that, for example, Neanderthal and homo sapiens brains independently grew larger and more complex).
    We also know that evolution often independently finds the same ‘solutions’ to problems – there’s lots of parallel evolution of eyes, wings and so on.
    So ‘eyes’ might be a better example. ‘What use is half an eye?’ was a question often asked by Darwin’s critics, the eye is an extremely complicated structure. And we know that eyes are common, that they evolved independently a number of times, using different methods.
    The implication of your argument seems to be that if we discovered intelligent life was abundant in the universe, that would damage the theist case. I’m not sure that follows – the case for a unique ‘in my image’ theism would suffer, but modern churches have said there could be intelligent life on other planets. The Vatican said so last year, and the Book of Mormon states it. If there were lots of intelligent species, I imagine theists would go ‘look at all the intelligent species God created, proof he desires intelligence’

    December 1, 2010 — 7:22
  • My formulation of the argument was not as clear as it could be, no doubt in part because I wasn’t as clear on the argument as I am now, thanks to the comments. Moreover, the structure of my post was not to argue for the existence of God–that was thrown in at end of the post as a corollary–but to argue that, given classical mechanics, Darwinian theory wasn’t the game-changer that it was thought to be.
    But if I am to focus in on the design argument I gave, let me go like this. What I will say is basically the same argument, but it is refined in some ways.
    The argument needs to substantiate two claims:
    A. P(C occurs at t1 | theism) is not very small–it’s at least one in a billion.
    B. P(C occurs at t1 | naturalism) is very small, much smaller than one in a billion.
    Given A and B, it follows that the fact that C occurs at t1 is significant evidence for theism over naturalism, by Bayes’ theorem.
    Let C be the existence of a natural kind containing a large number of intelligent beings (if you want to be definite, make “large number” be “at least a million”) and let t1 be the present. We know that C is in fact exemplified at t1. That is the fact I am working with. We do not know how many times over C is exemplified at t1–for all that we know, it is exemplified on a very large number of planets–but that is irrelevant to my argument. We have some estimates for what proportion of earth’s history C has been exemplified, but those estimates are irrelevant to my point.
    Now, P(C is exemplified at t1 | theism) is not ridiculously low. In my original argument I said it’s at least one a billion, and that sure seems very conservative–it is probably at least 0.01, and may be as high as 1/2. That takes care of point A.
    That leaves point B. Now, many of us have an intuition that if you take as many particles as the universe contains, and arrange them completely randomly, you’re all but certain not to get C. It is this intuition that Paley was trading on. The Darwinian answer to Paley can be seen as making this dialectical move: “Sure, if you want to get C all at once by randomly arranging particles, you’re not going to have any luck. But that’s not how it happened. Rather, over countless ages, the processes of variation and selection led to C, because C exhibits certain selective advantages. And so while it was unlikely to get C all at once, it was not at all unlikely that we would get C through, say, a billion years of evolution.” In other words, the Darwinian grants:
    B1. The probability of arranging particles randomly in such a way that they exhibit C is ridiculously small
    but denies that B follows from B1. And it is here that I bring in Liouville’s theorem which shows that in the context of classical mechanics and the natural phase-space measures (more on those later), the claim that you increase the probability of C by giving it, say, a billion years to evolve rather than randomly arranging particles all at once is incoherent. For, according to Liouville’s theorem, probabilities are conserved. So given B1, which the Darwinian answer to the design argument grants, I get B (on my assumption of classicality, which is one of the two main weaknesses of the argument, the other being the denial of a multiverse / giant universe).
    We can be more precise about the argument for B in a way that shows its structure, at the expense of greater technicality. For a fixed total number N of particles and total energy E, we can define a very natural microcanonical ensemble measure (mem) on the set of states with N and E. [Feel free to skip this part in brackets, and remember I am not a physicist so don’t laugh if I get the details wrong. Assuming for simplicity (and we can no doubt drop this assumption without much difficulty) that all particles are alike, we can describe any state of the universe by a sequence of 6N numbers: to describe any particle we need three numbers to describe the position and three numbers to describe the momentum. (If there are additional degrees of freedom, like spin, we can complicate the picture.) We thus have a 6N-dimensional phase-space, but the constraint that the total energy is E constrains us to a (6N-1)-dimensional hypersurface. We can then define a natural measure on that hypersurface, derived from the standard Lebesgue measure on 6N-dimensional space. This is mem.]
    Let t0 be a time before there was any life in the universe. Continue fixing the number of particles and total energy (this fixing is a complicating factor that I will ignore). Let C0 be the set of states of the universe that have the property that after t1-t0 units of time, C will be exhibited. Let C1 be the set of states of the universe that exhibit C. A reasonable estimate for P(C at t1 | naturalism), and in light of evolutionary theory, is given by mem(C0).
    However, Liouville’s Theorem tells us that mem(C0)=mem(C1). But mem(C1) is ridiculously small according to the intuition behind B1, which the Darwinist objector to the design argument grants. Hence, so is mem(C0), we get to conclude B, as desired.
    We can also give an intuitive argument for why mem(C1) is small. Take any state that exhibits C. The existence of intelligent life, as far as we can tell, is very sensitive to rearrangements of particles that have little effect on the total energy. In other words, intuitively, for any point in phase-space that exhibits C, there are many systems in the vicinity with somewhat different particle positions and/or momenta that do not exhibit C. There is a fragility about C. Therefore, if you’re randomly assigning positions and momenta to particles, subject to the total-energy constraint, the vast majority of the arrangements aren’t going to exhibit C, unless you’re dealing with a multiverse or an extremely large universe (in which cases you don’t need Darwinian theory to explain C’s being exhibited).
    Now, more than one commenter suggested that the question of how much intelligent life there is in the universe is relevant to the argument. Well, let’s try for an extreme case. We discover that, say, 10% of the stars in all galaxies contain planets that have species with intelligent life with at least a million members. This helps the arguments. Let C* be the feature of there being species with intelligent life with at least a million members around 10% of the stars in all galaxies. P(C* at t1 | theism) is lower than P(C at t1 | theism), but not much lower, since it is not very unlikely that God would want there to be a lot of intelligent life. On the other hand, if we let C1* be the set of states that exhibit C*, mem(C1*) is going to be much, much smaller than mem(C). So the argument would improve.
    Of course, in such a case it would be tempting to say: “The fact that intelligent life is so common gives us reason to think that the evolution of intelligent life is probable.” But I think that would be mistaken. Given atheism, that intelligent life is so common would give one reason to think the evolution of intelligent life is probable. But only given atheism. The intuitions about mem(C1) and random particle arrangements would continue to apply.

    December 1, 2010 — 9:18
  • David Warwick

    “Given atheism, that intelligent life is so common would give one reason to think the evolution of intelligent life is probable. But only given atheism.”
    I think it comes down to this being a scientific issue, one with predictive power.
    Christianity, even in its modern non-literalist forms, has man subject to a *special* creation by God and that we are unusual. Christ was incarnated *once*, not once on Earth, once on Vulcan, once on Alderaan. The prediction it makes is that life is notably rare, and the very strong implication is that we are the only intelligent life.
    Modern science takes a more materialistic approach – chemicals operating in the same conditions operate in the same way everywhere in the universe. An ‘earthlike’ planet might well produce life, and ‘earthlike’ is a pretty broad category. Study of extremophiles on Earth shows that life can exist in acids, volcanic vents, miles under the sea (all this life has DNA, too, which is very, very strongly suggestive that evolution is true).
    The theist prediction is ‘life is rare’, the scientific prediction would be ‘it is common’.
    So if NASA scientists announced tomorrow that evidence of life had been found on Titan, a planet that’s not *much* like Earth (we couldn’t live there), but one that we can literally see from our backyards with a $20 telescope, or Mars, or Rhea or on a comet … life would seem to be extremely common.
    Life is obviously a pre-requisite of intelligent life. Intelligent life can only evolve from primitive life. If primitive life is abundant across the universe, the chances that intelligent life has evolved in many places dramatically increases.
    So the case for *theism* doesn’t change. The evidence for the sort of theism claims we’re used to ‘god thinks human beings are special!’ does.
    The argument that theists never make, and it’s interesting although not all that surprising that they don’t, is that God might have specially created intelligent life … just not here on Earth. Just because we’re the products of evolution it doesn’t follow that *every* instance of life / intelligent life is.

    December 1, 2010 — 10:50
  • Alexander, your argument (in both forms) manages to completely miss the point of the Darwinian response to Paley.
    Gregory said this already, but let me make it a little more explicit. Paley’s argument is that, because C_1 contains complex biological phenomenon C, it has a (intuitively) low probability. Evolution says that all states in C_1 arise from a state in C_0. Now, none of the states in C_0 contain complex biological phenomenon C, so C_0 need not be a situation of low probability. It is not, certainly, subject to Paley’s argument.
    Then, by Liouville’s theorem, C_1 has the same probability as C_0, and therefore C_1 need not be of small probability, either.
    I don’t think your answer to Gregory addresses this. The question of the absolute probability of C_0 in the space of all possible configurations is not really the one we are talking about. Rather, Paley is saying something about the probability of (stars, planets and so forth, PLUS intelligent life) as compared to the probability of (stars, planets and so forth).
    Here’s an analogy: Take a look at the following picture and ask yourself if it’s evidence of an intelligent or a natural force at work:
    http://newsimg.bbc.co.uk/media/images/38703000/jpg/_38703439_arc300.jpg
    Made up your mind? OK, then read this article:
    http://news.bbc.co.uk/2/hi/science/nature/2665675.stm
    Personally, I think that if I were to stumble upon that landscape without any previous knowledge of it, I would have been certain that some person or group of people had been running around creating those patterns. But, once I know that there is a possible explanation for the phenomenon in terms of natural forces, the intelligent designer is no longer an attractive hypothesis.
    Since the rock circles are equally subject to Liouville’s theorem, I don’t think that your argument works here. Nor does it work in the case of evolution.

    December 1, 2010 — 12:30
  • David Warwick

    “The Darwinian answer to Paley can be seen as making this dialectical move: “Sure, if you want to get C”
    Evolution isn’t set up to get you to C. It doesn’t have ‘final cause’ in mind. The giraffe doesn’t *intend* its neck to get longer so that its great-grandchildren can reach the high branches.
    After the fact, we can account how we got to C via evolution.
    If we want a system to deliver intelligent life, evolution is a terrible way to achieve it. If we want a system that allows the best strategies to emerge and survive in a diverse, complex and changing environment, using only the resources available, evolution’s brilliant.
    So the Darwinian response is ‘I can’t promise you C, but I can promise you something that, by definition, has found a good way to pass on its genes. And intelligence works as a strategy for us, so there’s reason to think it would work for some other species’.

    December 1, 2010 — 13:21
  • Mr Warwick:
    Theism is something like the doctrine that there is a perfectly good, all-knowing, all-powerful creator. Theism, as such, says nothing about the human race being special. Moreover, theism makes it not unlikely that there should be a variety of species of intelligent beings.
    Now, Judaism and Christianity do say that on earth, humanity is special. But both Judaism and Christianity also hold that there are large numbers of intelligent beings who are not human, namely angels. Christianity holds that Jesus became a human being. Christianity is agnostic on the question whether there is intelligent life outside earth. If there is intelligent life outside earth, God may or may not have become incarnate as one of them. Aquinas is explicit that God could have become incarnate as two human beings; by the same token, he could have become incarnate as a human and as a member of some other species.
    Robert:
    Thanks for these really neat picture. If I just look at the picture, it looks like a particularly dense field of impact craters, with some important differences: the insides are very level, there are no overlapping circles, all the circles are in close proximity, and the range of diameters is smaller than in the case of the lunar craters that I see more often (compare this photo). I clicked too fast to the article, so I am not a good subject for your experiment. And on reflection, cell-like or bubble-like arrangements are pretty common in nature.
    But the point remains. What am I to make of the really nice geological explanation.
    I think a couple of moves are available to me. The simplest may be this. Sure, we have a scientific explanation here. By Liouville’s Theorem, it is an explanation in terms of an unlikely earlier state. That does not make the explanation vacuous, unilluminating or uninteresting, just as my argument does not make the Darwinian story vacuous, unilluminating or uninteresting. It just makes the explanation not be probability-raising. Specifically, in this case, I strongly suspect that the feature is in some remote way a result of the low initial entropy of the universe. (This might be true in the Darwinian case as well.) But the low initial entropy of the universe is an extremely low probability feature.
    The second move is that the level of complexity and fragility in this arrangement is nowhere near that in the human brain. You can do all sorts of rearrangements of the matter in this picture, and it’ll still exemplify the elegant pattern. But human brains stop working much more easily when you rearrange their matter. So in this case, it is easier to bite the bullet and say that the analogue to C1 isn’t as improbable as we initially thought.
    “Now, none of the states in C_0 contain complex biological phenomenon C, so C_0 need not be a situation of low probability.”
    I don’t see this. C_0 exemplifies a pretty neat feature: it is such that in exactly t_1-t_0 units of time, C will result. The low-probability intuition should apply just as much to C_0.
    Here’s an analogy. Take this image. Seemingly, this is unremarkable, not improbable, etc. But now observe that if we apply a DES-CBC decryption algorithm to it (or, more precisely, to a decomposition of it into an rgb888 row-by-row bitstream) with password “pass”, we get this, which is certainly remarkable. The right lesson to learn from this is not that the second image isn’t remarkable and improbable, but that the first is. It sure looks like a mess, but while most things that look like a mess also turn into a mess when you apply DES-CBC with password “pass” to them, this one has the special property that it doesn’t turn into a mess, but it turns into a photograph of a Mughal-period painting of an archery competition (I took the photo at one of the Smithsonian Museums, a couple of years back).
    In other words, I think we’re deceived when we are unimpressed by C_0, assuming the classical setting and all that.

    December 1, 2010 — 16:34
  • “Evolution isn’t set up to get you to C. It doesn’t have ‘final cause’ in mind.”
    But that’s far from clear. Of course, you could argue that evolution didn’t exclusively get you to C, it got you to many other things including C (insects, animals, plants, etc. in addition to intelligent life). But that’s of no problem to the theist.
    Perhaps evolution is biased, either due to extrinsic factors (like Simon Conway Morris or, oddly enough, Richard Dawkins suggest – that evolution produces certain results reliably due to inevitable cycles or constant selection pressures/niches available on the landscape) or intrinsic factors (mutationist views where the variation drives a large or majority portion of the evolutionary development, with certain variations being more likely, which in turn imparts direction in another way). This before getting into the options available to an omniscient and omnipotent, or even “merely tremendously smart” being.
    I wonder if the naturalist isn’t stuck in a dilemma where they’re practically committed to insisting A) The chance that claims X would obtain is tremendously low given naturalism and far higher given theism, and B) Nevertheless it did. Forever stuck with believing in spite of the odds.

    December 1, 2010 — 20:25
  • David Warwick

    “I wonder if the naturalist isn’t stuck in a dilemma”
    No, because I don’t buy the basic premise that you can stick a number on whether evolution of intelligent life is ‘more likely’ than the existence of a creator God who creates intelligent life. Not when we don’t know how much intelligent life there is or how many gods there are.
    As I say, if, looking back, the odds of a random mutation in a bacterium that brings us ‘one step closer’ to intelligent life are one in a thousand, million, billion, trillion, that means five bacteria on Earth right now are ‘stepping in the right direction’. It means, given four billion years of bacterial evolution and a ten minute average generation, that bacteria have taken a trillion steps towards intelligence.
    If the odds that God created intelligent life in a single act of creation are a billion to one, the odds remain a billion to one.
    But the nonillion-to-one, billion-to-one numbers are made up, there’s no way to come up with those values.

    December 2, 2010 — 9:46
  • Alexander, I still feel like you’re missing the point.
    Paley’s argument is that it’s highly unlikely that the watch could have come about by natural processes, because of the precise arrangement of the parts, etc. Surely, if we show HOW the watch could have come about by natural processes, that undercuts his argument.
    Here’s the point about the photo: According to your argument, a very special-looking end result can only have arisen from some very special starting conditions. But the sorting theory shows that, given any starting arrangement of rock whatsoever, we will ALWAYS end up with circular patterns like these. That is, our intuition says C_1 has low probability. But our intuition is wrong: C_0 has probability one, and therefore so does C_1.
    In other words, what the Darwinian argument tells you is that C_0 is vastly larger than your intuition would tell you if you only considered C_1. This is where the probability-raising comes in, not in the dynamics of going from t_0 to t_1.

    December 2, 2010 — 9:49
  • David Warwick

    Another way to think about this is a thought experiment about predictive value:
    Organic chemistry predicts that life should exist on more planets than intelligent life, simply because intelligent life requires more time to develop.
    If ‘God has good reason’ to produce intelligent life, we’d expect intelligent life to exist … well, everywhere possible. On every planet where there is life. Or, at the very least, that the ratio of life : intelligent life was heavily skewed towards the development of intelligence.
    Let’s confine our sample size to our solar system, now.
    There are about ten planets ‘like’ Earth in our solar system, including some of the moons – rocky ones with some sort of atmosphere and the sort of elements and heat sources that might sustain some sort of life as we know it.
    So, let’s plug in the numbers: 10% of planets are known to contain life (just the Earth) 100% of the planets known to contain life contain intelligent life.
    It’s extremely unlikely, but not impossible, that without intervention 100% of known lifebearing planets would have intelligent life.
    That result doesn’t contradict the scientific model, it does represent a result right at one end of its spectrum; it fits perfectly with the theist prediction.
    If, hypothetically, they announced they’d discovered primitive life on Titan this afternoon, then the figures would be:
    20% of suitable planets have life, 50% of planets with life have intelligent life.
    This swings it far more towards the existing scientific model than the existing theistic one.
    Say five planets were found to, or to have had, primitive life, but only Earth has intelligent life. That would be 50% have life, 10% intelligent life. Our solar system would not look like a place God had designed to create C.
    The scientific model predicts a tendency to finding primitive life elsewhere in the solar syatem. The theistic model, as currently stated, requires us not to. Were primitive life to be discovered on Titan, the theist model would go from ‘God has good reason to produce intelligent life wherever life is possible’, to ‘… but other, unknown, reasons not to in some circumstances’.

    December 2, 2010 — 10:27
  • David Warwick

    “before getting into the options available to an omniscient and omnipotent, or even “merely tremendously smart” being.”
    There are options open to human designers that nature hasn’t exercised.
    If, say, airplane designers come up with comfortable, light seats, the designers of trains, cars and so on can use that design. That tends to be how technology works – innovations in one field have implications for others.
    The natural world simply doesn’t do that. Humans don’t get the latest bird or fish technology installed. Cats are good at turning fat they eat into muscle, humans are terrible at it. Someone designing a human would probably stick some cat technology in there to fix that.
    The core problem with the Paley argument is that we *don’t* look designed. There are all sorts of things about the human body that a ‘tremendous smart’ designer would change. Any camera designer who came up with the human eye would be fired.

    December 2, 2010 — 10:41
  • Robert:
    In the rock case the outcome does arise from a very special set of initial conditions. The sorting story presupposes the existence of bunches of solid-state stuff, sitting on a boundary between solid and gaseous/liquid stuff, with a certain size of gravitational influence in the direction of the solid stuff. This is a very special set of conditions, exemplified in a very, very small area of spacetime–namely, on the surfaces of planets of particular composition of a particular size. Most of the matter in the universe, or even in the Solar System, is not like that. πŸ™‚ It could very well be, thus, that the surprisingly outcome here is one of the fruits of the surprisingly low initial entropy of the universe.
    On the Darwinian side, we have a conflict between two intuitions. We first have the intuition that C_1 is very unlikely. But then by reflecting on Darwin, we are led to the intuition that C_1 is likely to evolve from a large variety of initial starting points.
    One thought I have about this is that when we reflect on Darwinian mechanisms, this makes us think that it is more likely that we’ll get C_1 from some random arrangement than from scratch. Thought experiment. Ask a biologist which of the following two methods is a better way of generating intelligent life.
    Method 1: Take a large bunch particles of total energy E, randomly set their momenta and positions subject to the total energy condition, and be done with it.
    Method 2: Do the same as in Method 1, but wait some pre-specified length of time (say, 14 billion years) “to allow evolutionary processes to take place.”
    I bet that the biologist will think that Method 2 is by far the better method for generating intelligent life. But Liouville’s Theorem tells us that, in the classical realm, the two methods have exactly the same likelihood of success. If I am right, then the biological intuition that we are tempted to use to support the claim that C_1 isn’t as improbable as it seemed is in fact mistaken–for it is an intuition that evolutionary methods are probability-raising in a way in which they are not.
    So, in our conflict between the intuition that we’re unlikely to get C_1 from scratch but likely to get C_1 from some earlier likely state, we have good reason to think that the latter intuition is the less plausible one.
    Another relevant point is this. What is likely on evolutionary grounds is not that we’ll have intelligent life precisely at t_1, but that we’ll get intelligent life at some time or other, or that we’ll get it in not-too-long a time. But theism predicts intelligent life at t1 (since it predicts finite intelligent life–though not necessarily intelligent material life–at most times).
    A final point (for now). Suppose that somehow, justifiably or not, biologists came to the belief that in fact the universe is only 10,000 years old. Then I think the biologists would no longer think that the design argument has been trumped by Darwinian considerations. Very, very few biologists would say: “Ah, the Darwinian story has shown us that in fact the likelihood of getting intelligence from scratch is rather higher than we thought, so it’s not at all unlikely that the universe came into existence 10,000 years ago, fully formed, with all the species there.”

    December 2, 2010 — 11:54
  • David Warwick

    “Suppose that somehow, justifiably or not, biologists came to the belief that in fact the universe is only 10,000 years old. Then I think the biologists would no longer think that the design argument has been trumped by Darwinian considerations.”
    You are right.
    The problem being is that it’s the *exact* opposite of what happened. The universe is immeasurably older and larger than any previous model. We used to think it was a young, small universe. It isn’t.
    If the universe is a few thousand years old, the case for the Bible is immensely strengthened, the case for pretty much every branch of all modern science is completely demolished.
    Which is why creationists spend so much time on the creation. They understand that the opposite is also true – that if the universe formed blindly, over billions of years, if we are the descendants of bacteria, fish, shrews and monkeys, sharing their DNA and other biological features … then there is no case for the Bible. There was no Fall, there was no seven day creation, in the beginning wasn’t the word. The creationists *get* that in a way that a lot of more sophisticated Christian thinkers just don’t.

    December 2, 2010 — 12:27
  • “If the universe is a few thousand years old, the case for the Bible is immensely strengthened, the case for pretty much every branch of all modern science is completely demolished.”
    Notice, though, that in the classical setting, the probability of getting a fully-formed universe a few thousand years ago as a random combination of particles is exactly the same as the probability getting whatever initial state the universe in fact had at its beginning. So in the classical setting, it would be mistaken to think that it would strengthen the design argument to think the world was only 10,000 years old.
    Personally, I find the sharing of DNA to be a part of the kind of orderliness of the universe that we would expect given theism. It is plausible, given theism, that objects should fall into a hierarchy of natural kinds, because their so doing is aesthetically valuable. (This relates to one of the neat things about theism. Theism allows one to say that the same kinds of “simplicity, beauty and elegance” considerations that guide scientists–especially physicists–in their choice between theories were in play in deciding which world was to come into existence.)

    December 2, 2010 — 13:27
  • David Warwick

    “in the classical setting”
    I don’t really understand this point. Darwin was informed by the work of people like James Hutton, who’d demonstrated that the Earth was far older than had been thought. He expressly says that the Earth has to be very old for natural selection to work.
    It doesn’t strengthen the design argument if the world is only 10,000 years old. It does hole evolution below the waterline, though, and if that’s out of the way, the only game in town is some form of guided process.
    As for ‘simplicity’, a system is more simple than the same system but with an omniscient being overseeing it and bringing supernatural force to bear on it when he feels it’s needed.
    God isn’t necessary. And once God isn’t necessary, many of the traditional proofs requiring a necessary being can be discounted.

    December 2, 2010 — 20:56
  • “It doesn’t strengthen the design argument if the world is only 10,000 years old. It does hole evolution below the waterline, though, and if that’s out of the way, the only game in town is some form of guided process.”
    On the 10,000 year hypothesis, why couldn’t the naturalist just say: “Well, the world just came into existence, for no reason at all, 10000 years ago, full of humans, tigers, mice, oak trees, and all the other nifty stuff we’ve got”? My suggestion is that the reason she couldn’t say that is that it would be ridiculously improbable for that to happen. I get the impression you agree.
    But now Liouville’s theorem shows that in a classical setting (i.e., the setting of the classical physics that was king in Darwin’s time) the probability of getting a universe with random parameters having humans, tigers, mice and oak trees is exactly equal to the probability of getting a universe with random parameters that has the property that in exactly thirteen billion years it will evolve humans, tigers, mice and oak trees. In other words, you don’t get any probability increase of the nifty stuff by moving back in time. In both the 10000 year scenario and our actual history of the world, the naturalist just has to bite the bullet and say that the universe came into existence with an unlikely set of parameters. And then the naturalist has to do something to get out of the apparent consequences of Bayes’ theorem.

    December 3, 2010 — 8:29
  • David Warwick

    “My suggestion is that the reason she couldn’t say that is that it would be ridiculously improbable for that to happen.”
    I *sort* of agree.
    Here’s the thing: the whole point of evolution is it *can* start at ‘random’. I think you’re seeing it like a slot machine, where you pull the lever and all the atoms randomly end up as oak trees and mice and so on.
    That could, I suppose, have happened. The probability of it defies ‘astronomical’. You’d have to make up a new number, it’s 10^billions, at the very least. It’s Heart of Gold territory, so let’s call it a one in zaphodillion chance.
    But there is a chance. If we take multiverse theory at its most literal, there are a zaphodillion universes, and that has to be one of them, so there’s a one in a zaphodillion chance we live in it.
    But …
    Natural selection produces a mechanism by which a random selection of building blocks can become oak trees. And it *can* only work gradually. Some biologists talk about ‘punctuated equilibria’ where there’s some amazing period of rapid development … but the Cambrian explosion, say, lasted ten million years (and ten million years ago many of the most common modern species weren’t around in a recognizable form – ants, horses, hippos, kangaroos, people). ‘Rapid’ in those terms doesn’t mean ‘10,000 years’.
    Evolution *needs* time. It’s a ‘hold’ button for that slot machine. When patterns emerge, they stick, you don’t completely randomize.
    How many times, statistically, do you have to flip 100 coins and they all come up tails? It’s that number again: about that one-in-nonillion chance (10^30).
    Now … have the rule that whenever you get tails, you can save those and only have to throw the ones that came up heads again. Statistically, you get 50 the first time, 25 the second, 12.5, 6.25, 3.12, 1.06 … you should, statistically, have 100 tails in six or seven throws. Versus a thousand, million, billion, trillion throws for ‘random’.
    So it’s *not* about the starting conditions. Given a planet with the ‘building blocks of life’ (and we learned yesterday that arsenic can be a building block of life) and natural selection, we can get to something incredibly complex in much, much shorter time than randomness.
    We *could* be in a universe where particles fell into place 10,000 years ago so that 11,000 light years away a star that looks like it’s billions of years old formed. Not just that, but from there to here, there’s a 1000 light year complete trail of photons that randomly fell so that, when observed from Earth, they exactly simulate that star.
    It’s staggeringly unlikely. That said, it’s probably *less* likely that a powerful extra-universal being would have any motivation for engineering that situation.
    Modern science depends on an old Earth and (older, obviously) universe. We’ve observed things we think are 12 billion light years away. If the universe is 10,000 years old, the list of things we’d have to be misunderstanding to be that wrong would be a very long one.

    December 3, 2010 — 9:22
  • “Natural selection produces a mechanism by which a random selection of building blocks can become oak trees.”
    That’s the kind of thing I thought two weeks ago–i.e., before I came up with the Liouville’s Theorem based argument. πŸ™‚
    But given classical mechanics, there is a one-to-one correspondence between those states of the universe in which there are oak trees, and those states of the universe which have the property that they will produce oak trees in a billion years. And I learned from Liouville’s Theorem (and it’s kind of embarrassing that I hadn’t known the theorem earlier) that this one-to-one correspondence preserves probabilities–the set of states that contain oak trees and the set of states that will produce oak trees in a billion years have exactly the same probability. That is very counterintuitive!
    Of course, it could be that things are different given quantum mechanics. But they might different in either direction–in a way that favors the design argument and in a way that disfavors it.
    “Modern science depends on an old Earth and (older, obviously) universe. We’ve observed things we think are 12 billion light years away. If the universe is 10,000 years old, the list of things we’d have to be misunderstanding to be that wrong would be a very long one.”
    No disagreement there.

    December 3, 2010 — 10:02
  • David Warwick

    “But given classical mechanics, there is a one-to-one correspondence between those states of the universe in which there are oak trees, and those states of the universe which have the property that they will produce oak trees in a billion years”
    We don’t use ‘classical mechanics’ any more, and if what you say is true, that would be a very good reason not to. Darwin didn’t think he lived on a young Earth, or that evolution could exist on one. Theories of entropy were developed while he was writing. Evolution is not a product of ‘classical mechanics’. You can’t have random mutation and a perfect Newtonian clockwork. Classical mechanics is not a given.
    As I understand it, the crucial difference here is between ‘is’ and ‘might’. We could start out with a million identical Earths and natural selection and end up with no Earths with oak trees or a million Earths with oak trees.
    All one million Earths have natural selection, as that’s a given. So the presence or absence of oak trees has no bearing on that.
    What theism demands is knowledge of the future at that point. Either via an omniscient being, ‘final cause’ or the simple chronological chauvinism of being in the present.
    It’s a very difficult mindset to get out of. It’s basically impossible for the theist, because if there is an omniscient being, the result is known. If that being has a divine purpose, there are final causes.
    ‘What are the odds that a giraffe just evolved?’ – staggeringly small. We have giraffes, though, so it happened.
    What are the odds that out of all the cars that have ever been built, *yours* is the one you own?

    December 3, 2010 — 11:00
  • “You can’t have random mutation and a perfect Newtonian clockwork. ”
    Sure, but evolution doesn’t require strictly random mutation. For instance, when one uses an evolutionary algorithm, one doesn’t need to use a genuine random number generator–one just needs a good-enough deterministic pseudorandom number generator. What evolution needs is, basically, a lack of a correlation between mutation and fitness. And one can have that in deterministic systems.
    Note also that there are deterministic versions of quantum mechanics which are empirically equivalent to ordinary quantum mechanics (I am thinking of Bohmian mechanics). This means that if evolution cannot possibly empirically work under determinism, it will also not be able to work empirically given quantum mechanics. This is not enough to show that my argument works given quantum mechanics, because not every deterministic theory satisfies Liouville’s Theorem. What happens to the argument given quantum mechanics is an open question.

    December 3, 2010 — 11:55
  • “In the rock case the outcome does arise from a very special set of initial conditions. The sorting story presupposes the existence of bunches of solid-state stuff, sitting on a boundary between solid and gaseous/liquid stuff, with a certain size of gravitational influence in the direction of the solid stuff. This is a very special set of conditions, exemplified in a very, very small area of spacetime–namely, on the surfaces of planets of particular composition of a particular size. Most of the matter in the universe, or even in the Solar System, is not like that. πŸ™‚ It could very well be, thus, that the surprisingly outcome here is one of the fruits of the surprisingly low initial entropy of the universe.”
    By this move you have made your argument completely irrelevant to Paley’s design argument. By this reasoning, Paley should have been equally surprised to pick up a rock instead of a watch. You have, in effect, switched from a design argument to an argument from contingency.
    The point of the rock argument is not to examine why there are rocks, but why they are patterned. It is the pattern, after all, that is in need of explanation. I wouldn’t be at all surprised to go to the tundra and come across a field that looks like a random jumble of rocks. I am surprised because the rocks look like they have been sorted by size and arranged in circular patterns of roughly equal size. I know that this can happen by intelligent intervention. But, if I have never before encountered sorted patterned rock formations, I do not expect it to happen by natural means.
    The relevant probability is not the probability that there are rocks at all, but the probability that the rocks would be found in a sorted state, compared to the probability that they would be found in an unsorted state.
    But if I KNOW there is a natural process that can result in sorting, then the naturalistic hypothesis becomes more likely, compared to the intelligent design hypothesis.

    December 4, 2010 — 11:25
  • Joshua Rasmussen

    Interesting argument. It reminds me of the following thought experiment. Suppose I see a seemingly random configuration of rocks rolling off a cliff. The rocks fall into a surprising pattern that looks like the English sentence, “I was designed.” Now suppose that all of this is recorded on video. After analyzing this video, a certain team of scientists determines that the resulting configuration is a probable result of the initial configuration of rocks falling. Of course, the initial configuration is seemingly random (not the sort of thing that a designer might likely set up). But given its result, it seems that we have grounds for thinking that the initial configuration was designed to produce the resulting configuration. It would be a mistake to suppose that the resulting configuration wasn’t a result of design just because it was a probable outcome of a seemingly random configuration of rocks.
    You see the analogy with evolution. Suppose that given evolutionary theory, my brain’s existing at t is a not so improbable outcome of seemingly random configurations of elements on Earth 4.3 billion years ago. Would my present brain then be less likely a result of design given evolutionary theory than without it? If not, then why shouldn’t the team’s analysis of the video of rocks equally undercut an inference to design of their resulting configuration?

    December 4, 2010 — 12:07
  • Robert:
    I think one of the ways progress is made in philosophy is that we find new things to be puzzled and surprised by. Paley wasn’t surprised by rocks, but if he knew just how unlikely the initial conditions of the universe would need to be for there to be rocks, he’d be surprised.
    But it may well be that we should be less surprised by rocks than we initially are by their arrangement. In that case, I grant the point–the non-agential hypothesis is better off once one finds the story about self-arrangement, and especially if we have computer models with fairly realistic physics that show that a large variety of initial conditions leads to the same outcome. Note that we don’t have an analogue to the latter point in the biological case.
    I think that the intelligent life case is more recalcitrant than the rock case. For one, the probability that an omnipotent, omniscient and perfectly good being would want to make intelligent life is significantly higher than the probability that such a being would want to make this kind of a pretty arrangement of rocks, because intelligent life is much more valuable than this kind of a pretty arrangement of rocks. So the theistic explanation confers more probability on the intelligent life hypothesis. Nonetheless, I think the rock arrangement does give rise to a theistic argument from beauty, just a weaker one. (In fact, this is a species of my entropic argument.)
    Also, note that in both the rock and intelligent life cases we can think like this. We have two situations, C0 and C1, and we initially think that C1 is very unlikely to obtain at random “from scratch” (i.e., by a random arrangement of all the degrees of freedom subject to a total energy constraint) while C0 is not unlikely to obtain at random “from scratch.” Then from Liouville’s Theorem and the fact that the configurations in C0 are what gives rise to the configurations in C1, we learn that P(C0)=P(C1), and hence that our earlier views were implausible. We now have three options:
    1. Revise our estimate of P(C1) to make it as high as our earlier estimate of P(C0).
    2. Revise our estimate of P(C0) to make it as low as our earlier estimate of P(C1).
    3. Revise both estimates, lowering our estimate of P(C0) and raising our estimate of P(C1).
    After this, our probability of P(C0) will equal that of P(C1).
    In the rock case, option 1 is not so crazy. We already know that equilibrium states in various cases involve bubble-like phenomena, and it’s not so surprising that here we would have something like that. Moreover, we have good computer models showing that the underlying physics is likely to result in such sorting in a way that is insensitive to initial conditions.
    In the intelligent life case, option 1 seems pretty crazy. It still seems very plausible, even after the Darwinian story has been given, that if you randomly assign values to all the degrees of freedom subject to a total energy constraint, you’re not at all likely to get instant intelligent life. This probabilistic claim remains plausible even if you further conditionalize your probabilities on the existence of stars and planets.

    December 4, 2010 — 13:01
  • Josh:
    I think the difference between the case you give and the rock sorting case that Robert gives is that in the rock sorting case we have reason (grounded in computer simulations) to think that a very significant proportion of the initial rock configurations will give rise to the formations in N years (for some fixed N). In your story, there isn’t a similar result.
    What if we add such a result to your story? Then things get really interesting, don’t they? It is a really surprising fact that the laws of nature are such as to transform random initial rock configurations into “I am designed”. I wonder if a similar point can’t be made on the intelligent life side.

    December 4, 2010 — 13:08
  • While my point that Darwin hasn’t undercut design arguments stands, there is a serious flaw in the argument I gave, which has not been noticed in the above discussion.
    Here’s the flaw. Assume intelligent life supervenes on arrangement of matter. As a dualist, I think this assumption is false, but my design argument shouldn’t depend on dualism (Paley’s doesn’t, after all). In my discussion of option (4) in the original post, I noted that in the classical setting ergodicity by itself yields the claim that almost surely (i.e., with probability one) intelligent life will occur at some time or other. That’s why my explanandum is (5) rather than (4): Why is there intelligent life at t1? But this opens my argument to a very serious objection. I have granted (assuming materialism) that we’re going to get intelligent life at some time or other. Now, if t1 were a randomly chosen time, and we observed that there is intelligent life at t1, then we could use the fact that there is intelligent life at t1 as evidence. But the method by which I came up with t1 was biased–I, who am an intelligent being, chose a time at which I already knew there are intelligent beings, namely the present. So on its face we have here a case of selection bias, akin to that which earlier this fall I was exposing in Rowe’s argument from evil.
    Now, I actually think that the argument can perhaps be saved, but only at the expense of controversial epistemology. One method for saving the argument might require thirding in Sleeping Beauty. But all of this is tricky.
    Happily, my entropic argument in my more recent post is only weakly affected by the problem. Taking the selection bias seriously account probably just involves conditionalizing on locally-low entropy in both the naturalistic and theistic probabilities, but the global argument remains.

    December 4, 2010 — 14:05
  • David Warwick

    “It is a really surprising fact”
    An ‘argument from personal incredulity’ isn’t a good one.
    The falling rocks thing is not an analogy for evolution, just as a cloud that looks like a whale isn’t a whale, just as cutting open a fruit and it looking a bit like the symbol for ‘Allah’ isn’t proof of Allah’s existence.
    If, over the, say, two and a half thousand years we’ve had the Latin alphabet, rocks had fallen in a way that resembled a single letter, and each instance had been carefully stored in a great hall somewhere and now there were enough to say ‘this was designed’ … well, that wouldn’t be staggeringly unremarkable. That’s more of an analogy for evolution.
    The whole point about evolution is that it builds on success. If something works, it’s saved so it can work again.
    ‘Intelligence’, however we define it, did not suddenly, distinctly and uniquely appear in homo sapiens. I don’t think anyone would argue that dolphins, chimps, dogs and cats have some semblance of intelligence, and they’re all mammals, but their common ancestor was a long time ago, and all four groups seem to have seen brain sizes increase since that divergence.

    December 4, 2010 — 14:55
  • David Warwick

    “So on its face we have here a case of selection bias”
    Indeed. Taking the *very* limited information we have, in any randomly picked year, based on the universe so far, there’s about a one in 280000 chance of t1 including intelligent life.

    December 4, 2010 — 16:22
  • Actually, 1/280000 is surprisingly high, I think, but that’s matter for another argument. πŸ™‚ Let me express my thanks to all of you for pressing me on different points. Interestingly, where I think the argument has a problem is not any of the things that have been mentioned. And it is interesting that Darwin has nothing to do with the problem with argument.
    I think I’ll close this discussion, unless someone has a good way out of the selection-bias issue.

    December 4, 2010 — 18:40
  • Joshua Rasmussen

    Alex, I’m not convinced your argument has that flaw. I’ll start with an analogy. I observe two people playing poker and watch one of them lay down a royal flush twelve times in a row. I suspect he’s cheating (and to be sure I quickly run a Baysean argument in my head: yeah, definitely cheating). Now suppose I accept Lewis’s theory of possible worlds and so believe that there are infinitely many pairs of poker players. So, infinitely many people get twelve royal flushes by chance. This doesn’t undercut my suspicion because I understand that for any given pair in which one gets twelve royal flushes, it is more likely that that sequence is a result of cheating than by chance. The point: this is true even if there’s selection bias. Suppose I get out my modal telescope and I search for a poker game where someone gets twelve royal flushes. Any given such game I find is more likely a result of cheating than chance.
    I don’t see why the same cannot be said for your argument. I pick a time in which C exists. Now suppose that without an evolutionary history, C’s existing at t is ridiculously unlikely on naturalism (and not nearly so unlikely on theism). Then given Liouville’s Theorem, C’s existing at t is just as unlikely on naturalism given an evolutionary history. Suppose all of that is true. Then why should it matter whether I selected t at random or whether I got out my selection “telescope” to find a t that contains C? I don’t see that it matters. There might be a flaw in your argument, but I’m not seeing that it has to do with selection bias.

    December 4, 2010 — 19:11
  • Joshua Rasmussen

    David,
    The whole point about evolution is that it builds on success. If something works, it’s saved so it can work again.
    Perhaps this is another way of suggesting that the existence of C at t is a not so improbable outcome of seemingly random configurations of elements on Earth 4.3 billion years ago. (Same goes for your analogy of evolution.) I don’t see, however, that this suggestion undercuts a Paley-style argument if Liouville’s Theorem is true. Of course, one might consider recalculating the probabilities once one is convinced that C at t was a non-improbable result of a seemingly random configuration (but I’m sympathetic with what Alex says about that in his last note to Robert…)

    December 4, 2010 — 19:40
  • David Warwick

    “one might consider recalculating the probabilities”
    This is the problem. The argument from finding a pocket watch just there on a hillside is that something *that happened* was impossible. When science suggests that, if anything, the problem is that we haven’t found more of them.
    We know that DNA exists. We know that it is in all living creatures and nothing but living creatures. We know that it is a material which could incrementally adapt and account for all known living creatures, including us, if there was enough time. We know there was enough time, and that given DNA, given evolution, there simply isn’t anything that we observe that can’t be accounted for, including many, many design flaws that a schoolchild with a felt tip wouldn’t include in a creature he designed.
    Given that, the argument ‘God did it’ is extremely sparse. Because ‘it’ doesn’t mean ‘created life’ any more, it means ‘created life *in a manner resembling, but not actually, literally the only known entirely consistent atheistic method of creating life as we observe it*’.
    The theist accepts, on the basis of no evidence, God expending vast resources creating a faked up, deceptive universe that *looks* from a wealth of evidence like an elegant, atheistic one. There are reasons why God might do that, they are not ‘simple’ ones.

    December 5, 2010 — 6:40
  • Mr Warwick:
    The standard answer to why God would have chosen this circuitous method is that there is a value in nature’s being deeply involved in the production of complexity, a value akin to that of free will.
    Josh:
    One difference between the card case and the intelligent life case is that on the theism hypothesis all cases of intelligent life are the result of divine design while on the naturalism hypothesis none of them are. In the card case, the specific games are independent.
    Consider this analogy. Suppose microscopes haven’t been invented yet, and we don’t yet have a germ theory of disease.
    Hypothesis 1. All living things are big enough to be seen with the naked eye.
    Hypothesis 2. Some living things are small enough to be invisible to the naked eye and some are large enough to be visible to the naked eye.
    I now observe Fred the cricket. Does that give me support for (1)?
    I don’t know if the analogy is a good one.

    December 5, 2010 — 8:20
  • My selection-bias objection to the argument failed to take into account the refinement to the argument that I made in a comment: “Let C be the existence of a natural kind containing a large number of intelligent beings … and let t1 be the present.”
    Ergodicity plus supervenience makes it almost certain that intelligent beings will exist. But at most times at which there is an intelligent being, this will be a lonely intelligent being, not a member of a natural kind containing a large number of intelligent beings.

    December 5, 2010 — 8:44
  • David Warwick

    “The standard answer to why God would have chosen this circuitous method is that there is a value in nature’s being deeply involved in the production of complexity, a value akin to that of free will.”
    Indeed … but it’s not a very satisfying argument, is it? It’s not an explanation, for one thing, just a restatement of the core argument ‘given God, everything that happens is God’s will’.
    Also, in terms of intelligent life … we have to pick one. Given God, he either created conditions in which intelligent life might arise at random, or he created conditions / tipped the balance in favor of a universe in which intelligent life would emerge. If the former, that’s just God creating materialism.

    December 5, 2010 — 9:21
  • David Warwick

    “But at most times at which there is an intelligent being, this will be a lonely intelligent being, not a member of a natural kind containing a large number of intelligent beings.”
    No.
    Pandas are complex and rare. Panda theologians with a belief that they hold a special place in the universe would probably value ‘being a panda’ and imagine that God thinks the same. They would point out that seven billion animals are intelligent, but there are only a few thousand instances of ‘being a panda’. Evolution tells us that pandas actually took longer to evolve than intelligent beings.
    If C is ‘being a panda’, it does not follow – it is in fact absurd – to suggest that most universes containing C will contain one lonely panda.

    December 5, 2010 — 9:48
  • Joshua Rasmussen

    Alex,
    There is a sense in which specific times can be considered independent. I’ll explain with a different analogy. Suppose you appear on a desert and your background knowledge is this: (i) it’s infinite in all directions, and (ii) there are no other non-divine intelligent agents there. You see little bugs randomly carving lines in the sand. You walk a while and then come across a carving that forms the sentence, “this is designed by an intelligent being.” Now you can reason as follows: “for any given square mile of sand, the probability that there be that sort of carving given naturalism is lower than the probability that there be that sort of carving given theism. Therefore, this carving provides evidence for theism.” That seems true even if we stipulate that given theism, all such “message”-like carvings are from divine design and that given naturalism they are all by the bugs. (The evidence would be defeated, of course, if I could somehow examine the entire desert and discover that the distribution of such carvings is as would be expected by chance.)
    As to your analogy, I’d say that observing Fred doesn’t support Hypothesis 1 because Fred’s existence doesn’t seem more likely on Hypothesis 1 than it is on the negation of Hypothesis 1.
    Although I’m not convinced that there’s a serious selection effect flaw, I do think your entropy argument is better. I think there’s too much of a pull to think that if Darwinian evolution makes it not too unlikely that C1 results from C0 and C0 doesn’t seem entirely unlikely, then given Liouville’s Theorem, we can conclude that C1 isn’t entirely unlikely on naturalism after all (despite initial appearances).

    December 5, 2010 — 14:48
  • misternullasalus

    “The theist accepts, on the basis of no evidence, God expending vast resources creating a faked up, deceptive universe that *looks* from a wealth of evidence like an elegant, atheistic one.”
    First, the theist has plenty of evidence to call on – ranging from revelation to philosophical arguments to design observations to more. You may reject all of these, but saying there’s “no evidence” is just nonsense.
    Second, the universe does not even look like an “elegant, atheistic one”. I think you’re confusing a personal ability to look at the universe and imagine no God exists with the universe actually looking atheistic – they’re not the same thing. I say the universe looks like an elegant, theistic one. What’s the evidence against my view? Quantum entanglement? Regular planetary orbits? Dark matter?
    Finally, atheism is entirely compatible with a tremendous number of other ways life could appear – evolution is simply not mandated in any way. Again, I think you confuse the fact that evolution has in some quarters been worked into a popular atheist apologetic (specifically against YECs) with “this is exactly what we should expect if atheism is true”. It simply isn’t. At best it’s one thing that’s possible given atheism, but A) so are a variety of other ways, and B) it’s also possible given theism. I accept evolution, and to me the entire process absolutely screams design and intelligence, “flaws” and all.

    December 5, 2010 — 17:06
  • “If C is ‘being a panda’, it does not follow – it is in fact absurd – to suggest that most universes containing C will contain one lonely panda.”
    Pandas are improbable. Most states, where “most” is understood in the microcanonical ensemble measure, will not contain any of them. A very small proportion will contain at least one such unlikely beast. A small proportion of these will contain at least two. Etc.
    Compare this. In very few poker games does at least one royal flush appear. In only a very small proportion of those games will at least two royal flushes appear. Etc.
    “It’s not an explanation, for one thing, just a restatement of the core argument ‘given God, everything that happens is God’s will’.”
    The theistic position is that the probability of a world is approximately proportional to its objective value. It does appear to be of objective value to have a world of biological development, just as moral growth within the individual, as opposed to individuals coming on the scene already fully virtuous, appears to be of objective value. It is important to stress here that I do not define objective value in terms of what God wills (just as I do not define mathematical truth in terms of what God wills).

    December 5, 2010 — 20:24
  • Josh:
    I think the selection bias thing can be gotten around, but it is not an easy matter. The thing really is a version of Sleeping Beauty. Here’s one way to see it. Suppose that there is no God, and that at the beginning of existence there is a coin flip. If it’s heads, then there will be about a million observers at each given time (with each observer having a standard 75 year lifetime) over a period of 1000 years at some point in the future, and no observers at any other time. If it’s tails, then there will be about a million observers (with the same observer lifetimes) over a period of 2000 years at some point in the future, and no observers at any other time. The observers in both cases are basically the same, they do not have any records as to how long there have been observers in existence or how long it is since the beginning of the universe, and there is no other evidence of the coin flip. (The case needs some cleanup, but you can see how it works.)
    We now try to figure out if the coin landed tails. Well, this really is very much like Sleeping Beauty. We are first pulled towards 1/2, because of the following homely argument: “In both cases, we’d expect to observe observers, and that’s what we observe, so we have no data.”
    But we are also pulled towards 2/3 by arguments like: “If tails, there are twice as many times at which there are observers, so by noting that there are now observers, we get confirmation of tails.”
    If one takes thirding to be the right thing to say in SB, then we should say in this case as well that we have confirmation of tails. But the claim that thirding is right, even though I think it is right, is controversial. And if thirding isn’t right, then my argument without the modification of C isn’t right, either.
    Here is an interesting-looking relevant paper I haven’t read yet.

    December 5, 2010 — 20:44
  • David Warwick

    “I accept evolution, and to me the entire process absolutely screams design and intelligence”
    I’ll make one point: the theist-who-accepts-science viewpoint used to be – in 1800, say – predicated on the idea that a god was absolutely necessary in some way. And scientists accepted God for the same reason – the world looked designed, there had to be a prime mover, man was set apart from the animals, there hadn’t been enough time for natural processes to create animals. God was there, actively guiding things, and that was evident because there was no better model.
    By ‘evidence’ I mean scientific evidence. Repeatable, falsifiable, testable. ‘God is involved in evolution’, ‘God created the universe’, ‘if you pray to God you’ll get cured’ … those are scientific claims, and so subject to scientific scrutiny. (The theist response at this point is usually something like ‘string theory and multiverses’. Yes, but the untestability of those is a huge *problem* with those theories, not something to celebrate. Or ‘you can’t test faith in a lab’ … which, of course, is what spoonbenders say about their abilities – and whenever they are tested in a lab, hidden cameras show them sneakily bending spoons with their hands). If God affects evolution, the whole point is that you *could* test it in a lab, and the whole basis of Christian belief in 1800 was that God *was* scientific, *was* subject to these processes, and that was the most compelling evidence for him.
    If you can take evolution on Earth and point to the places where we can see God affecting specific events, or demonstrate how evolution differs from the computer models that perfectly replicate what we observe without factoring in God; or tell astronomers where to point the Hubble to see the parting of the waters; or show exactly which prayer pleases God enough to cure cancer, please do, and I’ll happily withdraw my objection. And, if that’s not incentive enough, you’ll win at least three Nobel Prizes.

    December 6, 2010 — 7:08
  • Joshua Rasmussen

    Alex, I track what you are saying.

    December 6, 2010 — 7:29
  • “or demonstrate how evolution differs from the computer models that perfectly replicate what we observe without factoring in God”
    The “perfectly” is an overstatement. While we have computer models of evolutionary scenarios, they are vastly oversimplified. (Nonetheless, they’re suggestive and interesting.)
    But more importantly, even if they were much better, the computer models would have to have a starting point. Let’s suppose they start with the conditions of the earth four billion years ago, and then exactly predict what species exist now. (That would imply either determinism or a radical Simon Conway Morris style evolutionary theory that is constrained to particular outcomes. But bracket that worry.) Is it true the computer models perfectly replicate what we observe without factoring in God? Not exactly. For it could well be that the relevant conditions of the earth four billion years ago are extremely unlikely on naturalism and much more likely on theism. (E.g., entropy, fine-tuning, etc.)

    December 6, 2010 — 7:30
  • David Warwick

    “Pandas are improbable. Most states, where “most” is understood in the microcanonical ensemble measure, will not contain any of them. A very small proportion will contain at least one such unlikely beast. A small proportion of these will contain at least two. Etc.”
    This would be true in an infinite multiverse, where every atom was arranged randomly.
    Neither the theist or atheist evolutionary biologist thinks we live in that multiverse … or that if we do, there’s little useful discussion to be had. The universe would look the way it does because we live in universe nine trillion three hundred and seven, not because of God or any natural process.
    But there’s an important observation here.
    It is, sadly, very plausible that an Earth very like ours that operates atheistically would have one panda in it. But there’s only one way that could happen, and that would be that all the other pandas died.
    The atheistic position is not that pandas come from atoms drifting together aimlessly until they create a panda, the atheist position is that pandas come from other pandas.

    December 6, 2010 — 7:39
  • David Warwick

    “The theistic position is that the probability of a world is approximately proportional to its objective value. It does appear to be of objective value to have a world of biological development, just as moral growth within the individual, as opposed to individuals coming on the scene already fully virtuous, appears to be of objective value.”
    But this is my point. That’s a process of inference, and it’s circular logic.
    Given the multiverse in its most popularly-expressed form.
    I decide I’ll kill my wife if a coin comes up heads. I flip a fair coin in two otherwise perfectly identical parallel universes. One comes up heads, the other tails.
    The atheistic explanation: this is a perfect expression of what we would expect. While both universes could have come up heads or tails, the probability was equal that it would be heads or tails. What happened can be fully and easily accounted for. There is a category error in linking the purely mechanical coin toss to the ethical decision.
    The theistic position is that *both* results reflect God’s will. As that’s absurd, the position shifts to ‘God values my free will’. As it takes less than a second to realize that the issue here is not my free will, it’s that my wife is shortly going to lose her capacity for free will, it shifts again to ‘God set up the game knowing that this was a possibility’. Which means God’s set up a game with a 50% chance of a murder at the end of it … at which point any attempts to infer human morality go out the window. So it shifts again a little bit ‘God trusts us to get on with this sort of thing ourself’.
    The only useful theistic position is that God has a fixed view about the fate of my wife. In a theistic *multiverse*, let alone universe, the result would always come up tails (we assume, given that God doesn’t like murder). Otherwise ‘the divine will’ is just synonymous with ‘chance’.

    December 6, 2010 — 8:01
  • “As it takes less than a second to realize that the issue here is not my free will, it’s that my wife is shortly going to lose her capacity for free will”
    Why not say that both values matter–the value of your choosing freely and the value of your wife’s life both need to be considered?

    December 6, 2010 — 8:42
  • David Warwick

    “Is it true the computer models perfectly replicate what we observe without factoring in God?”
    As a variable, yes it would be. There are two theistic models – he ‘set the machine in motion’ and ‘he adjusts the machine from time to time’.
    We can come up with atheistic ways in which the machine was set in motion (the machine being either ‘the universe’, ‘life’ or ‘man’, although I don’t think anyone serious argues for ‘man’ as special creation now – perhaps ‘intelligence’ represents a wrinkle on that). But we can’t really get past the issue that an absence of evidence isn’t evidence of absence.
    The ‘he adjusts’ model, though … yes, that’s precisely something that can be observed. Universe/life/man are traditionally seen as three events that *couldn’t* have happened without God. They were conscious, willed acts of creation.
    At the crude level, we ought to be able to see the graph bending where God intervenes or the suddenly introduction of an entirely new factor. We don’t.

    December 6, 2010 — 9:39
  • David Warwick

    “Why not say that both values matter–the value of your choosing freely and the value of your wife’s life both need to be considered?”
    Given God, if the result *can* be heads or tails, God values my free will over my wife’s life. Even if it comes up tails.
    That’s the only sensible inference, I think. If God is making a broader or more long term point, it’s an obscure one – this is not, routinely, how people come to a decision to murder someone, so it doesn’t really help as an instructive moment. If he wants my wife to join him in Heaven, then he’s only giving himself a 50% chance of that.
    There could, of course, be all sorts of indirect consequences – he knows that the sound of the gunshot will wake a hundred nuns next door, they’ll realize the convent’s on fire and evacuate in time. But that’s not part of *my* decision, it’s nothing to do with free will and introducing that factor marks a huge shift of goalposts.
    I think the bottom line is that I think if God meant it as a teaching moment, the moral lesson would be evident.
    But that’s my opinion. I’ll turn it around: what would you need to be convinced that this was an atheistic process? Would there need to be an atheistic universe? In which case, what would demonstrate that to you?

    December 6, 2010 — 9:59
  • “what would you need to be convinced that this was an atheistic process?”
    Because I think Catholicism is almost certainly true if theism is true, a disproof of Catholicism would be evidence against theism. And Catholicism makes some empirically testable predictions, such as that in matters of faith and morals no pope will ever ex cathedra teach a falsehood and no ecumenical council will definitively teach a falsehood. In particular, it follows that there will never be any definitive papal or conciliar teachings on matters of faith or morals that contradict other such teachings.
    However, notice that the entropic argument is incredibly strong. The kind of probability it confers on theism is not likely to be shaken by all sorts of evils and the like. And I additionally think there are good deductive arguments for the existence of God, especially the cosmological argument, which arguments are largely independent of the precise content of the universe.

    December 6, 2010 — 13:08
  • anon

    Alex,
    “… Catholicism is almost certainly true if theism is true…”
    Are there any books or journal articles that make the case for this claim that you would recommend?

    December 6, 2010 — 14:49
  • Turning to a different issue, we should ask whether this is even a situation to which Liouville’s theorem plausibly applies. Even in the classical context that you’ve chosen, it is by no means true that all systems can be described by a Hamiltonian. If we are thinking about the earth as our system, I think it is more plausibly modeled as a driven, damped system.
    In this sort of system, probability-increasing dynamics is very common. These systems have attractors, and after a long time the system is very likely to be found close to an attractor.
    I think it is a bit disingenuous to cherry-pick the part of classical mechanics that gives you the result you want, while ignoring other possibilities.

    December 7, 2010 — 3:58
  • David Warwick

    “And Catholicism makes some empirically testable predictions, such as that in matters of faith and morals no pope will ever ex cathedra teach a falsehood”
    ‘Falsehood’ meaning … something we know now to be false? Or merely something someone at the time had no way of knowing was not true? And you would consider such truths to be eternal, ie: what’s infallibly true in 1000 will be in 2000 and 3000? And that any statement the Vatican states to be ex cathedra will eternally remain ex cathedra, and neither you nor anyone else can declare that statement to be null and void?
    Ordinatio Sacerdotalis, is (as I’m sure you know) a 1994 statement stated to be infallible, in which the Pope said “We declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgment is to be definitively held by all the Church’s faithful”.
    So the instant you learned that a single woman priest had been ordained, you would easily and irrevocably accept the statement ‘No gods have nor will ever exist, all Catholic doctrine is false’?

    December 7, 2010 — 6:45
  • Dr Oerter:
    The system I was thinking of wasn’t the earth but the universe as a whole. Do you think a similar non-Hamiltonian probability-increasing dynamics might be plausibly true of the universe as a whole?
    anon:
    That was just an off-the-cuff remark about my assessment of my own conditional probabilities and my knowledge of the apologetic arguments. I think the apologetic arguments for Christianity, and for Catholicism, become much stronger once one accepts the existence of God.

    December 7, 2010 — 10:50
  • We’re getting off-topic, so I’ll be brief. Ordinatio Sacerdotalis isn’t an exercise of papal infallibility. Pope John Paul II was very clear about this. The content of it, however, is almost certainly an infallible part of the Tradition. Notice, though, that the content of it isn’t that the ordination of women is impossible. It is that the Church lacks the authority to ordain women. There are two ways that could be true. The Church could have the ability but not the authority to ordain women. Or the Church could have neither the ability nor the authority.

    December 7, 2010 — 10:59
  • “The system I was thinking of wasn’t the earth but the universe as a whole. Do you think a similar non-Hamiltonian probability-increasing dynamics might be plausibly true of the universe as a whole?”
    I don’t think you would have found any physicist in Darwin’s day who would have thought that. And if you’re talking about today, yes, many physicists probably believe that there is some sort of universal Hamiltonian (that we do not yet know), but it would definitely be a quantum Hamiltonian they had in mind, not a classical one.
    But there is a problem with taking “the universe” as your system. The phase space for the universe is infinite. And a fixed-energy slice of that phase space is still infinite. So you have no way of normalizing your probabilities: ANY finite chunk of that phase space is “astronomically unlikely” compared to the whole phase space.

    December 8, 2010 — 10:07
  • The universe might turn out to be closed. Might we not have a normalizable phase space then? And if it’s not closed, maybe we can reasonably hope to be able to do some sort of finite approximation, or close up the universe at a distance four billion light-years away from us (which is all that we care about for evolutionary purposes), and then estimate our probabilities.
    Or perhaps there is a large enough chunk of the universe such that we do not think that external influences are important for evolutionary processes. For instance, maybe what happens outside our Local Supercluster doesn’t really matter much for the four billion years of evolution of life on earth.

    December 8, 2010 — 14:40