A simple design argument
December 1, 2010 — 16:35

Author: Alexander Pruss  Category: Existence of God  Tags: , , , ,   Comments: 43
  1. P(the universe has low entropy | naturalism) is extremely tiny.
  2. P(the universe has low entropy | theism) is not very small.
  3. The universe has low entropy.
  4. Therefore, the low entropy of the universe strongly confirms theism over naturalism.

Low-entropy states have low probability. So, (1) is true. The universe, at the Big Bang, had a very surprisingly low entropy. It still has a low entropy, though the entropy has gone up. So, (3) is true. What about (2)? This follows from the fact that there is significant value in a world that has low entropy and given theism God is not unlikely to produce what is significantly valuable. At least locally low entropy is needed for the existence of life, and we need uniformity between our local area and the rest of the universe if we are to have scientific knowledge of the universe, and such knowledge is valuable. So (2) is true. The rest is Bayes.

When I gave him the argument, Dan Johnson made the point to me that this appears to be a species of fine-tuning argument and that a good way to explore the argument is to see how standard objections to standard fine-tuning arguments fare against this one. So let’s do that.

I. “There is a multiverse, and because it’s so big, it’s likely that in one of its universes there is life. That kind of a universe is going to be fine-tuned, and we only observe universes like that, since only universes like that have an observer.” This doesn’t apply to the entropy argument, however, because globally low entropy isn’t needed for the existence of an observer like me. All that’s needed is locally low entropy. What we’d expect to see, on the multiverse hypothesis, is a locally low entropy universe with a big mess outside a very small area–like the size of my brain. (This is the Boltzmann brain problem>)

II. “You can’t use as evidence anything that is entailed by the existence of observers.” While this sort of a principle has been argued for, surely it’s false. If we’re choosing between two evolutionary theories, both of them fitting the data, both equally simple, but one of them making it likely that observers would evolve and the other making it unlikely, we should choose the one that makes it likely. But I can grant the principle, because my evidence–the low entropy of the universe–is not entailed by the existence of observers. All that the existence of observers implies (and even that isn’t perhaps an entailment) is locally low entropy. Notice that my responses to Objections I and II show a way in which the argument differs from typical fine-tuning arguments, because while we expect constants in the laws of nature to stay, well, constant throughout a universe, not so for entropy.

III. “It’s a law of nature that the value of the constants–or in this case of the universe’s entropy–is exactly as it is.” The law of nature suggestion is more plausible in the case of some fundamental constant like the mass of the electron than it is in the case of a continually changing non-fundamental quantity like total entropy which is a function of more fundamental microphysical properties. Nonetheless, the suggestion that the initial low entropy of the universe is a law of nature has been made in the philosophy of sceince literature. Suppose the suggestion is true. Now consider this point. There is a large number–indeed, an infinite number–of possible laws about the initial values of non-fundamental quantities, many of which are incompatible with the low initial entropy. The law that the initial entropy is low is only one among many competing incompatible laws. The probability given naturalism of initially low entropy being the law is going to be low, too. (Note that this response can also be given in the case of standard fine-tuning arguments.)

IV. “The value of the constant–or of the initially low entropy–does not require an explanation.” That suggestion has also been made in the philosophy of science literature in the entropy case. But the suggestion is irrelevant to the argument, since none of the premises in the argument say anything about explanation. The point is purely Bayesian.

Comments:
  • David Warwick

    “The universe, at the Big Bang, had a very surprisingly low entropy. It still has a low entropy, though the entropy has gone up.”
    I don’t really understand what ‘surprisingly low entropy’ means in this context. ‘Entropy’ is the energy that’s not available for work. At the Big Bang, we’d expect all of the energy to be available. We’d expect entropy to increase as that energy is spent forming things, and that’s what we observe.
    Immediately after you’ve poured a cup of coffee, it’s at its hottest. It gradually cools down. That doesn’t have any implications for naturalism versus theism.
    Unless you mean the rate of entropy is lower than it ‘ought’ to be. In which case … is it? If so, I’d look for a problem with a model before I looked for a problem with naturalism. If a book purporting to explain something and reality don’t match up, it’s not usually reality that’s got it wrong.
    “At least locally low entropy is needed for the existence of life,”
    Yes.
    “and we need uniformity between our local area and the rest of the universe if we are to have scientific knowledge of the universe”
    Misunderstanding. If I boil a kettle of water next to a equal sized pot of cold water, I have drawn energy (from the fuel ultimately used to heat the kettle, probably in the nearest power station) into one vessel of water, not the other. Locally, the two vessels of water are in different entropy states.
    Uniformity means the same things act in the same way *in the same conditions*. If I’d boiled the *other* vessel of water in the same kettle, it would have acted in exactly the same way as the one I did boil. If it hadn’t, it would point to some different level of impurities in the water.
    Water will act the same way in the same conditions even if it’s water on Mars, water from Andromeda or whatever. That’s all uniformity means. It’s a slightly circular argument – water acts like water, something that doesn’t act like water isn’t water.

    December 2, 2010 — 6:55
  • Mr Warwick:
    “At the Big Bang, we’d expect all of the energy to be available. We’d expect entropy to increase as that energy is spent forming things, and that’s what we observe.”
    It is widely accepted by cosmologists and philosophers of science–many of them not theists–that the lowness of the initial entropy of the universe is a surprising fact. (Try googling big bang and low entropy.) Here are two ways to see that it’s a surprising fact.
    1. Most of the universe states in phase space are pretty close to equilibrium. (That’s not unrelated to the fact that systems that run over a long time tend to spend most of their time in equilibrium.) Here, the “most” isn’t cardinality but measure. So if there is no intelligence behind the selection of the initial state of the universe, it seems more likely that it would be a state close to equilibrium.
    2. The fundamental laws of nature, as far as we can tell, are time-reversal symmetric. In a classical setting, this means that if you take all the particles and flip their momenta, you’re going to get a system that reverses its path. (In a quantum setting, you also need to reverse charge and parity to get the symmetry, and you don’t necessarily get a reversal of the path, but apparently you still have a symmetry.) This, of course, makes the Second Law of Thermodynamics very puzzling, since the Second Law says that we get an increase in entropy with time. Yet if we reverse all the momenta of the particles we now have, we will get a system that obeys all the fundamental laws of nature and yet where the entropy goes down. (The puzzle is more subtle in a quantum setting.) So the puzzle is that the fundamental laws are symmetric in respect of time-reversal, but the behavior of the universe is asymmetric. A widely-accepted solution to the puzzle is that the asymmetry comes from the fact that the universe happens to start in a state of improbably low entropy. In other words, the asymmetry in behavior comes not from an asymmetry in the laws, but an asymmetry in the boundary conditions.

    December 2, 2010 — 8:26
  • By the way, Penrose estimates the probability of the initial state at 1/10^(10^123). See this paper by Callender for some background on the issue. Callender himself takes the tack that I labeled “IV”–he argues that no explanation is needed.

    December 2, 2010 — 8:36
  • I’m not sure about your treatment of the multiverse objection. The salience of the multiverse for these retooled Paley arguments is not that we should expect to find ourselves in a universe with observers, but that any conceivable combination of fundamental laws and constants is expected. You seem to be saying, in your I, that the multiverse objection does not apply (incorrectly), which is the only thing that enables you to say III, and since both fail, I think the objection stands.
    In short, it begs the question against the multiverse objection for you to say that any set of initial conditions whatsoever has a high or low probability. Since this is sufficient to defeat the argument, I won’t trouble myself with pointing out that you’ve gone to know lengths to show that your premise 2 is true, or that this universe has this mysterious property called “value” in some abundance.

    December 2, 2010 — 9:20
  • “Low-entropy states have low probability.”
    This is false. The ice cube in my freezer has low entropy, relative to that of an equal amount of water in a glass on my counter. But the ice cube is does not have low probability – I make them all the time. The reason it is false it that there is a dynamical process that removes heat from the freezer and puts the ice cube into a low entropy state (with high probability).
    “By the way, Penrose estimates the probability of the initial state at 1/10^(10^123).”
    Penrose estimates this probability assuming the initial state of the Big Bang was chosen at random from all possible starting configurations. WAS the initial state chosen at random from all possible starting configurations? We don’t know. Possibly there was some dynamical process in the pre-Big Bang universe that drove this local region into a low entropy state. Until we have a reliable theory of the pre-Big Bang universe, arguments about the probability of that initial state are meaningless.

    December 2, 2010 — 10:04
  • Teapot:
    “it begs the question against the multiverse objection for you to say that any set of initial conditions whatsoever has a high or low probability”
    Make it a dilemma, then. Either the multiverse is or is not compatible with the assignment of probabilities to states.
    If it is compatible with the assignment of probabilities to states, then what I said is correct.
    If it is not compatible with the assignment of probabilities to states, then the multiverse hypothesis undercuts all science, since all scientific prediction requires the assignment of probabilities to states.
    Dr Oerter:
    The ice cube is not a complete system. It has a high conditional probability on certain assumptions, such as that there is a person with certain desires, a fridge, etc. But the state that it has a high conditional probability on is itself an unlikely state.
    “Until we have a reliable theory of the pre-Big Bang universe, arguments about the probability of that initial state are meaningless.”
    There I disagree. We’re looking, fairly intuitively, at the probability of a low entropy universe given naturalism. Think about it in terms of two toy models.
    First model. You’re told that there is exactly one microscopic red dot on the tenth page of your copy of Dirac’s PQM. You have no information about what process, if any, placed the dot, except that you’re told that no intelligent agent did so. The pages are, let us suppose 20cm x 30cm in dimensions. You are now given a multiple choice quiz by a rich tycoon who also doesn’t know where the dot is, and who just made up the quiz on the spot for his perverse amusement:
    1. The dot is in a circle of radius 3 cm centered on a point 5 cm down from the top and 4 cm from the left.
    2. The dot is in a 20 cm x 5 cm rectangle at the bottom of the page.
    3. Neither of the above.
    After you answer the quiz, you and the tycoon will go and check with a microscope where the dot is. If you got the right answer, you get a million dollars. Otherwise, you are killed. What should you say?
    Second model. You somehow find out that the universe (or your portion of it) consists of N particles, each with six degrees of freedom, and total energy E, and that the universe hasn’t been produced by any agential process. You don’t know whether or not the universe exhibits some macroscopic feature F, and you want to figure out the probability, because the tycoon from the first story is going to ask you if you think the universe exhibits F, and then he’ll fund an experiment to check. If you got it right, he’ll give you a million, and if not, he’ll kill you. What should you do? Well, following the method of model 1, you’re going to compute the Lebesgue measure in phase-space, restricted to the hypersurface with total energy E. If that turns out to be more than a half of the total measure of the hypersurface, you’ll say “Yes”, and if it’s less than half, you’ll say “No”, and if it’s half it really doesn’t matter what you say–maybe you can just flip a coin.
    But of course the second model is basically what Penrose is up to.
    I actually think we need to do something a little different. We need to ask the intuitive, and alas not exactly quantifiable, question of what theories and laws we would think are likely if naturalism is true. And my intuition is this. Given naturalism, we don’t expect a bias in favor of valuable states. Given theism, we do expect a bias in favor of valuable states. Since valuable states are apt to have low entropy, theism predicts lower entropy than naturalism does.

    December 2, 2010 — 11:26
  • David Warwick

    “Given naturalism, we don’t expect a bias in favor of valuable states. Given theism, we do expect a bias in favor of valuable states. Since valuable states are apt to have low entropy, theism predicts lower entropy than naturalism does.”
    Like Teapot, I think ‘value’ is too imprecise a word. If it’s used in a theistic context, it becomes entirely circular. God builds the universe to match his desires, the universe matches the desires of God.
    If C is ‘intelligent life’, the argument is ‘we expect a universe favorable to the creation of intelligent life’. Our observation of the universe is that it’s a sphere nearly a hundred billion light years in diameter, it’s fourteen billion years old and there’s precisely one planet we know of which has had intelligent life for … a million years? If Yahweh has set the universe up to build worshipers for himself, then we can get that down to, say, four thousand years.
    The thing is … to me, that sounds like a terribly inefficient way to go about things. It might actually be the fastest possible way to get from ‘nothing’ to ‘Catholics’. There’s just no way of knowing. Again, the theistic argument is circular – God did it this way, so it must have been the best way.
    Instinctively it isn’t. Intelligent dinosaurs could have evolved. There were mass extinctions that represented hundred million year setbacks to the development of life on Earth.
    What we see is a very big universe with very rare, extremely slow-to-form areas where life might evolve. We see the universe naturalism predicts.

    December 2, 2010 — 12:15
  • Personally, I don’t see anything imprecise about “value”. Now there are some naturalists who think that no states of affairs are objectively valuable, but there are plenty of naturalists who think you can naturalize value. If you can’t have value given naturalism, then we have a very simple argument against naturalism. Kindness is objectively valuable; if naturalism is true, nothing is objectively valuable; hence, naturalism is false.
    As for efficiency, we have little evidence for the claim that intelligent life is rare.
    And as for time, 14 billion years from the beginning of the universe is actually pretty quick. The sun is probably only a third generation star.

    December 2, 2010 — 12:25
  • David Warwick

    “Kindness is objectively valuable”
    I met a convicted child molester at the bus stop yesterday, he said he was a bit short of cash, and he needed a dollar for his bus fare to the local school. He was clearly in a worse off state than me, and I could spare the dollar. So I did the objectively kind thing.

    December 2, 2010 — 12:48
  • You mean, you called the police? ๐Ÿ™‚ That’s the objectively kind thing to do. (Not a kind thing to lead people into temptation.)

    December 2, 2010 — 13:21
  • David Warwick

    I think we’re straying!
    I don’t think the universe, taken as a whole, is structurally designed to ‘value kindness’. If we were anywhere in the universe we know of apart from some regions of the land surface of this planet, we wouldn’t live long enough to be kind.

    December 2, 2010 — 13:28
  • Adito

    Premise 1 is true so far as I can tell but premise 2 is implausible. There is no particular reason for God to value anything and therefore the chances of him valuing everything he needs to for premise 2 to work is as small as the chance of the universe existing on premise 1. It will stay implausible unless a theist can show that the brute facts that determined Gods nature are “less brutish” then the facts that determined the universes nature on naturalism. I don’t see any reason to believe something like that so I don’t think this argument gets us anywhere.

    December 2, 2010 — 23:33
  • More or less by definition, God is an all-knowing, all-powerful and perfectly good being. An all-knowing being knows what is good. A perfectly good being values what all and only what he knows to be good. Therefore, if God exists, he values everything that is good.

    December 3, 2010 — 8:45
  • Kraig

    I have a question about whether conditional probability is the right sort of probability, in this case, to get you from your premises to your conclusion. P(I will dunk at the gym tonight|I am short) is very low. But if I get to the gym tonight, and the goals have been lowered, the probabilities change drastically. Probability is non-monotonic.
    In regards to the origins of the universe, it seems to me that there are a great many mysterious and unknown and perhaps unknowable factors. This makes the assignment of conditional probability highly uncertain, given that there are so many truths about the origins of the universe such that, were we to learn them, the probabilities involved in these premises might change drastically. Or, maybe there are no such truths. But we just have no idea.

    December 3, 2010 — 9:00
  • Kraig

    Actually, I think what I said was wrong. Perhaps the fact that there are a great many unknown about the origins of the universe does not make the assignment of the relevant conditional probability uncertain, but it does make it highly uncertain whether or not the relevant conditional probability tells us anything at all about the relevant objective probability.

    December 3, 2010 — 10:42
  • Adito99

    “More or less by definition, God is an all-knowing, all-powerful and perfectly good being.”
    Right, and why is He that way rather than some other way? Eventually you’ll have to conclude that there are simply brute facts about His nature. Since only a very finely tuned nature would lead Him to create a finely tuned universe why is the universe more likely under theism?

    December 4, 2010 — 2:38
  • “Eventually you’ll have to conclude that there are simply brute facts about His nature.”
    Maybe, though (a) they would be metaphysically necessary truths, and (b) they could be very simple brute facts. For instance, Aquinas thinks he can derive bunches of God’s attributes from his being pure actuality. Anselm thinks he can derive bunches of God’s attributes from his being that than which a greater cannot be conceived. Swinburne thinks he can do it from omniscience and omnipotence.

    December 4, 2010 — 8:10
  • David Warwick

    “For instance, Aquinas thinks he can derive bunches of God’s attributes from his being pure actuality.”
    This is part of my point. If God *isn’t* necessary to explain the origin of the universe or life or intelligent life, then a lot of these traditional proofs can be discounted.

    December 4, 2010 — 8:38
  • I don’t see anything in the Aquinas point to support the claim that positing God isn’t explanatorily necessary.

    December 4, 2010 — 13:02
  • Adito99

    “(a) they would be metaphysically necessary truths, and (b) they could be very simple brute facts”
    I don’t think this helps unless we also have some idea of what a atheistic brute fact could be. For one thing, why is it that simplicity and necessity cannot apply to it as well? And again, only a very particular nature could lead him to create human beings in a universe that’s exactly the size of ours with exactly the attributes it has. You don’t get a planet weighing 6E+24 kilograms populated by humans who you value from the properties of omniscience and omnipotence.

    December 4, 2010 — 13:25
  • “only a very particular nature could lead him to create human beings in a universe that’s exactly the size of ours with exactly the attributes it has”
    Right. That’s why I am not asking for an explanation why there are human beings in a universe that’s exactly the size of ours with exactly the attributes it has. Rather, I am asking for an explanation of why entropy is low, or why there is intelligent life, or something like that.
    Now, granted, if the naturalist comes up with some equally simple brute hypothesis that has relevant similar consequences to the theistic one, then that will damage the argument. But the mere possibility that there is such an alternate hypothesis is beside the point. In science, we don’t worry about the fact that there might be a simple alternate hypothesis that fits the same data. We only start worrying once that hypothesis has been given.

    December 4, 2010 — 13:52
  • David Warwick

    “if the naturalist comes up with some equally simple brute hypothesis”
    ‘The simplest explanation for the total absence of evidence for gods is a total absence of gods’.

    December 4, 2010 — 17:57
  • Adito

    “I am asking for an explanation of why entropy is low, or why there is intelligent life, or something like that.”
    Don’t they go together? For any given thing that exists in a universe designed by God it can only exist because He wanted it that way. If all God wanted was intelligent life or low entropy (or both) then there are far simpler sets of affairs he could have actualized than the one we have.
    “In science, we don’t worry about the fact that there might be a simple alternate hypothesis that fits the same data.”
    How about we consider the multiverse such a brute fact? I know there are good objections to the theory but I don’t think they’re any stronger than the in principle objections against a God.

    December 4, 2010 — 23:37
  • “How about we consider the multiverse such a brute fact?”
    A multiverse doesn’t challenge this argument. See Objection I in my post.
    Moreover, for a multiverse to do any explaining, you need to say more about the multiverse. Here’s a multiverse theory, after all: “There are infinitely many universes, all of them exactly alike.” You need to specify how many universes there are and what laws of nature they obey. You don’t need to specify in exhaustive detail. Just enough detail for the explanatory tasks at hand. The same point holds in the God case–we only need to specify enough detail for the explanatory tasks at hand. We can specify the theistic hypothesis in enough detail for the explanatory tasks at hand fairly simply–“there is an all-knowing, all-powerful and perfectly good being” or maybe just “there is a perfect being”.
    Can we do that with the multiverse hypothesis? Could be. But it’s important to be clear on what would need to be done.
    Also, some of the simpler multiverse hypotheses are more logically problematic. For instance, Lewis’s hypothesis that all metaphysically possible universes exist or Tegmark’s hypothesis that all coherent mathematical structures are exemplified. Those are elegantly simple, but the price is that there are a lot of arguments against them. Typical scientific multiverse hypotheses arise from fairly complex inflationary or string theories.
    Note, also, that the multiverse hypothesis is compatible with theism, and indeed is moderately likely on theism. My five-year-old speculated a couple of days ago that every moment of time a new universe is created. (I don’t think I talked to him about multiverse hypotheses.)

    December 5, 2010 — 8:55
  • David Warwick

    “My five-year-old speculated a couple of days ago that every moment of time a new universe is created.”
    Tell him if he can find a way to prove that, he’ll go a long way in life.

    December 5, 2010 — 9:34
  • David Warwick

    The multiverse thing doesn’t address the issue in hand, which is why C happens *to us*. Yes, if you toss a coin it can come up heads or tails. Yes, multiverse theories say both happen. Yes, theism says God could make it either (but not both).
    Why is it heads *here*?

    December 5, 2010 — 9:38
  • Alex,
    (1) I’m late to the show, but: Given a commonsensical understanding of “strongly confirms,” this argument appears to be a non-sequitur.
    Consider: I just told a random number generator to give me a random integer between 1 and 1,000,000,000. It gave me 262,818,318.
    The probability of this event, on the hypothesis that this was truly random, is 0.0000001%.
    It is much higher on the hypothesis that the alleged “random number generator” temporarily came under control of a demon whose favorite number is 262,818,318.
    Commonsensically, though, we don’t want to say that this strongly confirms the demon hypothesis.
    (2) One of your arguments for your premise (1) can be easily modified into an argument that the prior probability of theism is very low. You write:
    “There is a large number–indeed, an infinite number–of possible laws about the initial values of non-fundamental quantities, many of which are incompatible with the low initial entropy. The law that the initial entropy is low is only one among many competing incompatible laws. The probability given naturalism of initially low entropy being the law is going to be low, too.”
    Similarly, one might argue:
    “There is a large number–indeed, an infinite number–of possible supernatural beings who might have been in control of the initial values of non-fundamental qualities, many of whom would have done things incompatible with the low initial entropy. The supernatural being who wants the initial entropy to be low because he is omnibenevolent is only one among many competing incompatible beings. Therefore, the prior probability of that specific being existing is going to be low, too.”

    December 5, 2010 — 20:25
  • If we’re going to have any hope of doing science, we need to privilege simpler hypotheses and give them higher priors. Now, let’s grant that there is an infinite number of supernatural being hypotheses, each of them with a different set of values. For instance, Sam values universes that has a moderate but not too high entropy, and that either contains pigs and no bats, or frogs but not toads. Now, most of these beings are going to have a value/desire set that cannot be described very simply. Sam is in fact going to be among the simpler of the hypotheses. But some of the beings are going to have a value set that can be described in a particularly simple way.
    Here are a couple of the supernatural agent value sets that have a particularly simple and elegant description:
    – A1 values nothing.
    – A2 values every state of affairs equally.
    – A3 values every state of affairs proportionately to its objective value.
    – A4 values every state of affairs in inverse proportion to its objective value.
    Supernatural-being hypotheses with such simple descriptions of their value sets will have higher prior probabilities, for the same kind of reason for which the hypothesis that there is an attractive force between two objects inversely proportional to the square of the distance and the product of the masses is to be preferred to the hypothesis that there is an attractive force between any two objects inversely proportional to the square of the distance and the product of the masses unless the two objects are sapphire icosahedra weighing between one and two hundred pounds in which case the force is repulsive. (Both hypotheses fit our observations equally well, since, I assume, no sapphire icosahedra of that mass have been observed.)
    Moreover, among these supernatural-being value-set hypotheses, those will have the highest probability which can be most neatly integrated into a larger story about what this supernatural being is like. For instance, of the above beings, A2 and A4 each has subjective values that do not match the objective values. This means that either their knowledge is limited or that they suffer from some sort of akratic limitation on its rationality. But if the being’s knowledge is limited, we need to specify the way in which the knowledge is limited, and that adds complexity. And if the being suffers from a limitation on its rationality, we need to specify the way in which its rationality is limited, and that adds complexity.
    A1 may have an elegant simplicity, on the other hand, but it is likely to be incompatible with being an agent (except in potentia).
    But A3, and A3 alone, is compatible with the simple hypothesis that the being is fully rational and all-knowing.
    So while there are lots of weird supernatural-being hypotheses, we should prefer the simpler ones.
    How do we precisely define the complexity of a hypothesis? I have no idea. But a first approximation to the complexity of a hypothesis is the length of the description of the hypothesis in a non-gerrymandered language. And we had better have some such way of measuring the complexity of a hypothesis, or modern science has no way of getting off the ground. (Without a measure of complexity there is no reason to prefer the Copernican theory to the Ptolemaic one. In fact, if you add enough epicycles you can get predictions better than those on Newtonian mechanics, because you can even simulate relativistic corrections with epicycles.)

    December 5, 2010 — 21:32
  • David Warwick

    “So while there are lots of weird supernatural-being hypotheses, we should prefer the simpler ones.”
    Well, OK.
    Given that coin tosses are all controlled by the gods:
    There are two warring beings, Headius and Tailius, both perfectly matched, who spar every time someone tosses a coin and the result of the coin toss depends on who wins that fight?
    Is that more complicated or at variance with what we observe than the Christian hypothesis that the process is guided by an omnipotent being who allows it to be random, while knowing the result, while also somehow not violating quantum theory, who also created the universe, created man in his image and sent his only son to Earth to redeem our sins, and monitoring every particle in the universe?
    In days gone by, the world looked extremely capricious. Gods were the very best explanation for earthquakes and plagues and why coins ended up the way they did.
    Given science, God gets in the way. He makes it *harder* to explain things. The hypothesis that he guides evolution while makes it look unguided, that he controls apparent randomness while making it look random … it’s just the old simulation argument. We are living in a simulation of the world we think we’re living in, one designed to fool us that it behaves the way we observe.
    Given that ‘simple is best’, if the scientific model works without God, then ‘scientific model’ is, by definition, more simple than ‘scientific model + God’.

    December 6, 2010 — 9:23
  • The Headius/Tailius hypothesis is a fairly simple hypothesis, but it doesn’t explain much–only coin tosses.
    As for whether God gets in the way of science, that’s matter for another discussion. I will just briefly say that only on the theistic hypothesis is it reasonable to think that more elegant physical hypotheses are more likely to be true, and without that assumption science cannot be done. But obviously that is a big discussion, and many philosophers of science disagree.

    December 6, 2010 — 9:43
  • Alex,
    I take it you were responding to my point (2) – maybe what you said could be part of a response to (1), but I don’t think you’ve said enough on that score yet.
    Taking your point that way: if you take simplicity, and not just number of alternatives, into account, I think we can show that the probability of initial low entropy on naturalism is not so low as the argument in your initial post suggests.
    For example, consider a multiverse hypothesis where it’s a law of nature that every time a new universe is birthed, it has minimal entropy. It seems to me that that hypothesis is obviously simpler that one where it’s a law of nature that all universes start out with 32.17% of initial entropy.
    At a more basic level, I think it would be utterly unsurprising if there were a good physical reason why the initial entropy of our universe was so low.

    December 6, 2010 — 16:36
  • M.

    What about (2)? This follows from the fact that there is significant value in a world that has low entropy and given theism God is not unlikely to produce what is significantly valuable.
    But that doesn’t follow, unless the only feasible way for God to actualize valuable things (namely, life) is through a low-entropy universe. If God should prefer life in the form of disembodied souls, then P(low entropy universe|theism) is also tiny. I think Jonathan Weisberg makes this point in a paper I’ve seen posted here a while ago.

    December 6, 2010 — 17:48
  • Chris:
    But our universe doesn’t start with minimal entropy. The early universe is pretty uniform, but if my memory of what I’ve heard from physicists is right, it’s not perfectly uniform. And that’s important, because the non-uniformity gives rise to clumping of a sort needed to form galaxies.
    M.:
    Disembodied souls have value. But so do enmattered souls, and the value of enmattered souls is different, not strictly less. And a world containing both disembodied and enmattered souls has even more value than a world containing just one of the two.

    December 6, 2010 — 22:52
  • M.

    Disembodied souls have value. But so do enmattered souls, and the value of enmattered souls is different, not strictly less. And a world containing both disembodied and enmattered souls has even more value than a world containing just one of the two.
    I think the claim expressed in this last sentence needs to be argued for, especially if we’re talking about objective value here. But disembodied souls were just an illustration. If you prefer, replace “disembodied souls” with “enmattered souls in a universe whose physics does not require fine-tuning for life to exist within it,” or even “enmattered souls in an life-hostile universe miraculously sustained by divine volition.”

    December 7, 2010 — 0:34
  • David Warwick

    “A multiverse doesn’t challenge this argument.”
    Catholicism talks of ‘the unique and altogether singular event of the Incarnation of the Son of God’.
    Given a ‘flipped coin’ model of the multiverse (popularly: every time I flip a coin, one universe is created where it lands heads, another universe is created where it landed tails).
    We know the Roman soldiers drew lots for Christ’s clothing before the Crucifixion.
    So:
    1. At the foot of the Cross, Marcus and Quintus go through a fair process where they draw lots, with an equal chance of Marcus winning.
    2. At the moment Marcus draws the straw, two universes are created: one where he wins, one where he loses.
    3. As the universes are otherwise identical, there are two Crucifixions.

    December 7, 2010 — 10:04
  • I don’t think flipped-coin-type multiverse theories are plausible, for reasons independent of theism. I think any multiverse theory of that sort will create insuperable problems for probability theory. (Imagine a quantum system that has probability 1/pi of branching one way and probability 1-(1/pi) of branching another way. Nothing absurd about such a system. But these irrational-number probabilities cannot be modeled by means of proportions of branch universes.)
    An example of the kind of multiverse theory I find somewhat plausible are inflationary theories on which universes bud off from other universes.

    December 7, 2010 — 11:07
  • M.:
    Sure, there are things to be filled in. But it still seems pretty plausible that if you list all the obviously valuable and simply-describable scenarios at some high level of generality, some scenario involving intelligent beings in a low-entropy universe will be somewhere in your top million or so scenarios, and maybe even in your top ten scenarios. ๐Ÿ™‚ And that’s all we need.

    December 7, 2010 — 11:11
  • M.

    Maybe low-entropy universes are among the simplest value-permitting scenarios. But for this to matter, 1. we must suppose that God prefers simpler laws over more complex ones, and 2. the simplicity of low-entropy universes must be such that it makes them all-things-considered God’s favorite among all possible kinds of value-permitting universes. For suppose there are two sets of physical laws of equivalent value (insofar as they both permit the same sorts of valuable states of affairs), but God slightly prefers one to the other. What’s the probability that God implements the less-preferred laws? I’d say close to nil. What would possess him to violate his own preferences in this instance?
    Now that I think about it, it seems like your stance may commit you to the almost Leibnizian position that ours is a maximally simple value-permitting universe.

    December 7, 2010 — 11:36
  • God’s preferences are in line with the objective values. Elegant laws are, in respect of their aesthetic qualities, objectively better than messy laws. Hence God prefers them in respect of their elegance. But messy laws can exhibit non-aesthetic values. So we can’t say with any certainty that God will create a world with elegant laws. My intuition is that what we should expect God to bring it about that either the world has maximal simplicity (and that’s a world where God is the only being) or it has incredible diversity (and that’s some sort of a multiverse) or it balances a fair amount of diversity with a fair amount simplicity (and that’s probably what we get). It doesn’t seem crazy to assign probability 1/3 to each of these. But if you think I’m missing some major options, the argument is not affected if I assign 1/100000000 to each of these options, and add some “small” number (relative to numbers like 10^(10^123)) of other options.
    I actually think that if we have worlds w1 and w2 such that w2 is in every respect better than w1, and it’s up to God to choose between them (as opposed to its being up to our free will), then God is certain not to actualize w1. But this does not lead to a Leibnizian conclusion because I deny that there is a single world that is best in every respect.

    December 7, 2010 — 12:14
  • M.

    I suspect many of us are going to have to get off the train once we start enlisting objective aesthetic values into the argument. Ignoring that caveat, though, I’m still having trouble. Since you think simplicity is itself a thing God values, let’s distinguish between simplicity-value and creature-value. Simplicity-value is just the value of having simple laws; while creature-value is the sort of good possessed by universes, simple or complicated, which permit intelligent life to exist and flourish. The more “robust” the flourishing, the more creature-value is present. I grant that there is no single world simultaneously best in both simplicity-value and creature-value. But perhaps there is a world which is better than the actual one in both respects. For instance, perhaps intelligent life could have existed/flourished in a universe just like ours, but with even more uniform initial conditions. In that case, it seems we should expect God to have created that universe and not ours. So it seems you’re still committed to the somewhat Leibnizian claim that, among all the universes that support creature-value commensurable with ours, there are none simpler than ours.
    Maybe you’d want to deny that there is a set of maximally simple universes relative to our level of creature-value?

    December 7, 2010 — 14:12
  • There is nothing wrong with objective aesthetic values.
    Simplicity of law and of arrangement of matter also gives you a non-aesthetic value–it makes it easier for intelligent beings to know stuff.
    “So it seems you’re still committed to the somewhat Leibnizian claim that, among all the universes that support creature-value commensurable with ours, there are none simpler than ours.”
    I think any world other than ours is worse than ours in respect of some value. Simplicity-value and creature-value are not be the only two values, however.
    Actually, because God exists necessarily, I am committed to the view that there is no pair of worlds w1 and w2 such that w1 is in every respect worse than w2.

    December 7, 2010 — 14:29
  • David Warwick

    “An example of the kind of multiverse theory I find somewhat plausible are inflationary theories on which universes bud off from other universes.”
    I agree about ‘flipped coin’ multiverses. If I’m really ‘creating’ a universe by flipping a coin, then … where’s that energy needed to create *a whole universe* coming from? What’s the minimum standard of a ‘choice’?
    But if you accept that our universe budded from another, what’s the problem with low entropy? It drew as much energy as it did from the parent universe.

    December 7, 2010 — 21:30
  • Enigman

    If we’re going to have any hope of doing science, we need to privilege simpler hypotheses and give them higher priors.
    We also need to privilege more complex hypotheses, similarly. This is often over-looked, and I don’t know why. Recall doing science at school, or your reading of the history of science. Scientists look at the world and discover what it’s like. Now, they don’t add unnecessary complications to their theories. But that isn’t to say that they make them as simple as possible. Similarly, they don’t unnecessarily simplify their theories (except for introductory pedagologic reasons). A complex curve will go through all the observation-points, but be unlikely. It’s likely that there were some mistakes. But a straight line is not always the right sort of curve. The scientist looks at the dots and sees what sort of shape they are. However complicated it is, that’s what she sees. (There is of course a limit to humanly perceptible complexity, but that’s not a deliberate privileging.)

    December 14, 2010 — 8:27