Sunday, June 07, 2015

Fine tuning and probability

Luke Barnes criticizes this version of Ikeda and Jefferys' paper, "The Anthropic Principle Does Not Support Supernaturalism." (I usually link to this version; I assume the content is identical.) Barnes' post is five years old, but it's still be referenced by some people, so I guess it's still alive enough to be worth rebutting. In his criticism, Barnes runs afoul of some of probability's conceptual problems.

In general, probability is very philosophically problematic. Definitely with the frequentist interpretation, but also with the Bayesian interpretation, using probability requires us to adopt an ontological commitment to the existence of unknowable things: frequentism requires us to talk about experiments not performed, Bayesianism requires us to talk precisely about what we don't know. It is philosophically respectable to reject probability entirely: the past is fixed and certain, the future is determined by the present, and it is incoherent to measure our ignorance. However, if you're going to use probability to make inferences, you have to bite all the philosophical bullets that probability requires.

To briefly recap, the Fine Tuning Argument (FTA) says that, given relatively unproblematic assumptions about the laws of physics at the most general level, the probability is very low that the (apparently) arbitrary constants of the laws of physics, i.e. those constants whose values cannot be determined theoretically and must be determined observationally, are such that life can exist. We human beings apparently got ridiculously lucky when the universe formed almost perfectly set up for life to evolve. The Weak Anthropic Principle (WAP) rebuts the FTA: if the universe were not "fine tuned" for life, we would not be around to observe otherwise; of course we observe that the universe is "fine tuned." Barnes counter-argues that if we are required to condition on the result (life exists), then probabilistic arguments are generally useless. Barnes is correct: if we are required in principle to condition a probabilistic argument on the result, then probabilistic arguments are useless. However, he is not correct that Ikeda and Jeffries argue that we are required in principle to condition on the result.

We have to make additional assumptions to make probability work. First, we have to be conceptually able to "observe" both success or failures. If we cannot in principle observe failures, then we cannot make any inference at all about the probability of the successes we observe. This is a trick that "psychics" use: they show the hits but hide the misses. Second, we have to be conceptually able to describe success before we actually observe it. In a large probability space, every actual event has a very low probability. Shuffle a deck of cards and then look at it: before you shuffled it, the probability that the deck would end up in exactly that order is $1/{52!}≈1.24×10^{-68}$.

The difference between the FTA and Barnes' example is that in the FTA, we cannot in principle, even conceptually, observe a universe that does not have life in it. In contrast, I personally could in principle have observed Magneto and his grandson being killed by the shrapnel. Furthermore, even though the grandson could not have actually observed that outcome, he could conceptually have "observed" the alternative outcome, e.g. by observing that other people actually died.

Ikeda and Jeffries invert the FTA. Instead of asking the probability of naturalism, they ask the probability of God existing. We first assume first that if God does not exist, then life will exist only in a life-friendly universe. Life existing entails life friendliness $P(F|~G&L)=1$. We don't have to condition on L, but if we do, then if $G$ is false then $F$ must be true.

We then consider two alternative hypotheses. The first hypothesis is that if God1 exists, then He would have created a life-friendly universe, If that is the hypothesized God, then observing life-friendly universe with life in it (our only actual observation) does not distinguish between the existence and non-existence of God. The second hypothesis is that if God2 exists, then He would have created life, and might have created life in a non-life-friendly universe. In this case, Ikeda and Jeffries correctly argue that observing life in a life-friendly universe lowers (slightly) the probability that God2 exists (in the same sense that observing a non-black non-crow raises the probability slightly that all crows are black).

We don't have to condition on life existing. However, we're worse off. We could not conceptually have predicted before observing any universe that life would exist in it. The only reason we have to assume that if God exists, He would have created life is just that we are in fact alive. We are "predicting" the random order of the deck after we've seen it. (Positing indirect attributes of God that entail His creating life just move the problem around.) Just the hypothesis that if God exists, he would have created anything we actually see begs the question: it assumes what we are setting out to "prove." Plantinga would call that an adequate argument, but Plantinga is a doofus who doesn't understand modal logic or probability.

In short, the Fine Tuning Argument for the existence of God is dead. It either provides evidence against the existence of God, or it fails to satisfy the requirements to even make a probabilistic argument in the first place.

14 comments:

  1. I'm on record as having disagreed with Ikeda and Jefferys, and I would say my point of disagreement here is it matters whether you could, in principle observe the ~L outcome. Thus to me the Magneto example is analogous and I'd rather not bite that bullet.

    However, I completely agree with your second to last paragraph, which to me is a more important disanalogy to the Magneto example. We have every reason to believe that Magneto would want to protect his grandchild, even before observing him do so. In contrast, the only reason we have to think God would create life is because (if we believe in God) we saw them do just that.

    But is this the argument used by Ikeda and Jefferys? The "neutral" priors they suggest are P(N|L) = P(~N|L). I suppose that this implies that God is just as likely to create a world with life in it as are natural causes. So perhaps Ikeda and Jefferys have been making this very argument all along, and now I find I agree with it.

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    1. Typo correction: it does not matter whether you could, in principle observe the ~L outcome.

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    2. I suppose that this implies that God is just as likely to create a world with life in it as are natural causes.

      Actually, that statement would be expressed as $P(L|N) = P(L|~N)$.

      I think I&J assert that $P(F|~N&L) < P(F|N&L)$, iow $P(F|~N&L)<1$

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    3. In other words, there is a nonzero probability that God would create life in a world without life-friendly physics.

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    4. You're right, I stand corrected about the math.

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  2. Suppose I have two experiments. In the first one, behind a screen, I flip a fair coin with regular frequency, and call out "heads" when I get heads, and remain silent if I get tails. In the other experiment, I sit behind a screen and call out "heads" after waiting an exponentially distributed random amount of time. Because you cannot in principle ever observe tails, you cannot, given the appropriate frequency in the first matching the exponential distribution in the second, distinguish between the two experiments. Hence you have to be able, in principle, to be able to observe all the potential outcomes to make an inference.

    Even if the Magneto example is analogous to I&J, so what? It's just a bad experiment to determine if grandpa really is Magneto. I can design bad experiments that will fail to prove even the most mundane truths.

    We have to condition on L, not because we generally have to condition on the result of any experiment, but because we've restricted the sample space to only hits.

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  3. If we were a priori committed to the idea that a creator God would probably create life, and that a naturalistic world would probably not create life, then the restricted sample space doesn't matter, because you don't need a single sample. You would simply conclude that most universes with life in them have creator Gods, observations be damned.

    That a priori assumption is fundamental to the FTA as most people understand it. But I&J, rather than questioning that assumption explicitly, imply that the assumption is incorrect and proceed to criticize an entirely different FTA. I&J's argument is correct, but incomplete because it doesn't address the common a priori assumption.

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    1. As I recall, I argued at your site that I&J didn't consider that argument because it obviously begs the question and is not really worth rebutting.

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    2. Yes that is acceptable to me. We all rebut the parts that we personally deem most important.

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  4. What's your take on Jonathan Weisberg's argument from Divine Indifference? He seems to be making the same points.

    http://www.utm.utoronto.ca/~weisber3/new/Research_files/TAfDI.pdf

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    1. Weisberg's argument looks good. It's a clever technique introducing strictness/laxness.

      Note that his argument also depends on conditioning on life existing.

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  5. 1. And, part 1 of my critique? I state that the second part is just a few case studies, rather than a definitive critique. https://letterstonature.wordpress.com/2010/10/26/terms-and-conditions-a-fine-tuned-critique-of-ikeda-and-jeffreys-part-1/

    2. "philosophically respectable to reject probability entirely". And so, to reject the vast majority of data analysis in the sciences today? The physical sciences are largely Bayesian these days: https://letterstonature.wordpress.com/2015/03/11/a-beginners-guide-to-cosmological-speculation/

    3. "The Weak Anthropic Principle (WAP) rebuts the FTA". I know of no scientist that has defended this response to fine-tuning. "If observers, then an observer permitting universe" cannot answer "why an observer permitting universe at all?". Why do you think we're all talking about the multiverse if the answer is as simple as WAP?

    4. "First, we have to be conceptually able to "observe" both success or failures. If we cannot in principle observe failures, then we cannot make any inference at all about the probability of the successes we observe." So, modern cosmology is impossible? We can only observe one cosmic microwave background, so there cannot be observations of both success and failure.

    5. If we only need to imagine observing a life-prohibiting universe, then could conceptually observe failure by simulating these other universes and noting that they are life-prohibiting, or even (science fiction style) creating them in the laboratory.

    6. Applying this "observe both success or failure" principle to the Magneto case, you haven't avoided the conclusion that the survivors cannot conclude that Grandpa is Magneto. Only a bystander could reach that conclusion, which seems wrong.

    7. "We don't have to condition on life existing." You do if you're a Bayesian. Hence, part 1 of my critique.

    8. "The first hypothesis is that if God1 exists, then He would have created a life-friendly universe, If that is the hypothesized God, then observing life-friendly universe with life in it (our only actual observation) does not distinguish between the existence and non-existence of God."

    a) If X then Y.
    b) If not-X, then almost certainly not Y.
    c) Therefore, Y is evidence for X over not-X

    Exercise: prove, using Bayes's theorem.

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  6. Hi Luke! Thanks for coming over.

    1, 7. The comment that prompted my investigation linked to your part 2, so that's what I looked at. I'll be happy to look at part 1 as time permits.

    2. Philosophers are highly weird. What can I say?

    3. That's Ikeda and Jeffries' position. I think it's sound for the reasons they say. If your part 1 addresses that argument, then I'll get to it when I reply to part 1.

    4-5. Can you expand on these points? I'm not sure where you're going there.

    6. Magneto is a bad experiment for people who can only observe success.

    7. see 1.

    8. P(F|N&L) = 1. P(F|G1&L) = 1. Therefore, given L, F, does not distinguish between N and G. If we're going to use Bayes theorem, we have to have some reason to posit some definite prior probability for G1. Given that God can do literally anything, the space of all possible gods (of which G1 is a subset), is larger than the space of all natural universes that have life.

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  7. I would say, as a physicist, that the WAP is totally a serious candidate explanation for fine-tuning. Have you ever heard of the Boltzmann brain problem? The only reason it's a problem is that it appears to refute certain anthropic principles. Cosmologists argue over ways around the Boltzmann problem, which would only make sense if they took anthropic principles seriously.

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