A firestorm of controversy has been unleashed by the recent Uncommon Descent post, Economist John Maynard Keynes understood ID? (June 13, 2013), which claimed that whatever his merits may have been as an economist, John Maynard Keynes (pictured above) at least displayed an admirable grasp of the case for Intelligent Design, which he succinctly summarized in his classic work, A Treatise on Probability. No attempt was made to paint the man as an Intelligent Design sympathizer, and it was subsequently pointed out by Mark Frank that he was an atheist. Over at the Skeptical Zone, the author of the original Uncommon Descent post on Keynes was reproached in a post by KeithS for not including a follow-up quote from the very next page of John Maynard Keynes’ book, in which Keynes, while acknowledging that the argument from design strengthened the case for a Designer, pointed out that the argument was inconclusive, as we have no information on the prior probability of the Designer’s existence:
Thus we cannot measure the probability of the conscious agent’s existence after the event, unless we can measure its probability before the event… No conclusion, therefore, which is worth having, can be based on the argument from design alone; like induction, this type of argument can only strengthen the probability of conclusions, for which there is something to be said on other grounds. We cannot say, for example, that the human eye is due to design more probably than not, unless we have some reason, apart from the nature of its construction, for suspecting conscious workmanship.
Dr. Elizabeth Liddle, in a comment attached to the Uncommon Descent post, laid out the reasoning on both sides with admirable clarity, following up with a comment of her own:
Note the reasoning:
From Denyse’s extract:
X is an event of low probability given non-design.
If we’d assumed a Designer X occurred we might have predicted X.
From keiths’ extract:
But unless we estimated the probability of the Designer before X occurred we cannot estimate the increased probability of a Designer after X occurred.
Therefore X alone is insufficient to infer a Designer.
So, yes, JMK understood ID, but it seems he understood it well enough to see the flaw in it.
The two flaws in Keynes’ reasoning
I have two comments I’d like to make on Keynes’ reasoning in the quote reproduced by KeithS. First, even if we don’t know the antecedent or prior probability of a Designer’s existence but suspect that it is very very low, Bayes’ theorem can still be used to show how low a prior probability the evidence for design can overcome. Second, since the prior probability of a Designer’s existence must be at least 1 in 10^120 (which is the number of events that could have occurred during the history of the observable universe), it therefore follows that if good enough scientific evidence is found for a Designer, it is possible in principle to demonstrate that a Designer does indeed exist, after all.
On the first point, I’d like to quote a passage from a post by the philosopher Lydia McGrew, titled, The odds form of Bayes’s Theorem [Updated] (January 6, 2011). In a much-commented-on 2007 paper, The Argument from Miracles: A Cumulative Case for the Resurrection of Jesus of Nazareth, she and her husband, Dr. Timothy McGrew had examined the evidence for the claim (let’s call it claim R) that Jesus of Nazareth rose from the dead around 33 A.D., and concluded that there was sufficient evidence for the resurrection (R) to overcome even an incredibly low prior probability of 1 in 10^40. In the passage below, she addresses the frequently heard atheist objection that if we don’t know the prior probability of an extraordinary claim (e.g. the claim that the Resurrection occurred, or that there is a Designer of Nature), then we can’t say anything meaningful about the posterior probability of this claim, even if it is well-supported by confirming evidence:
I understand that the current atheist meme on this, which shows a rather striking lack of understanding of probability, is to say that if one does not argue for a particular prior probability for some proposition, one literally can say nothing meaningful about the confirmation provided by evidence beyond the statement that there is some confirmation or other.
This is flatly false, as both the second of the quotations above from the paper and my rather detailed explanation to Luke M. show.
Let me try to lay this out, step by step, for those who are interested:
The odds form of Bayes’s Theorem works like multiplying a fraction by a fraction–a fairly simple mathematical operation we all learned to do in grammar school (hopefully).
The first fraction is the ratio of the prior probabilities. So, let’s take an example. Suppose that, to begin with (that is, before you get some specific evidence) some proposition H is ten times less probable than its negation. The odds are ten to one against it. Then the ratio of the prior probabilities is
Now, the second fraction we’re going to multiply is the ratio of the likelihoods. So, for our simple example, suppose that the evidence is ten times more probable if H is true than if H is false. The evidence favors H by odds of 10/1. Then the ratio of the likelihoods (which is also called a Bayes factor) is
If you multiply
1/10 x 10/1
The odds form of Bayes’s Theorem says that the ratio of the posterior probabilities equals the ratio of the priors times the ratio of the likelihoods. What this means is that in this imaginary case, after taking that evidence into account, the probability that the event happened is equal to the probability that it didn’t: what we would call colloquially 50/50. (You’ll notice that the ratio 50/50 has the same value as the ratio 10/10. In this case, that’s no accident.)
Okay, now, suppose, on the other hand, that the second fraction, the ratio of the likelihoods, is
1000/1. That is, the evidence is 1000 times more probable if H is true than if H is false. So the evidence favors H by odds of 1000 to 1.
Then, the ratio of the posteriors is
1/10 x 1000/1 = 1000/10 = 100/1,
which means that after taking that evidence into account (evidence that is a thousand times more probable if H is true than if it is false), we should think of the event itself as a hundred times more probable than its negation.
See how this works?
What this amounts to is that if we can argue for a high Bayes factor (that second fraction), even if we don’t say what the prior odds are, we can say something very significant–namely, how low of a prior probability this evidence can overcome. That is exactly what we say in the second quotation from our paper that I gave above. It is exactly what I explain to Luke M. We say that we have argued for “a weight of evidence that would be sufficient to overcome a prior probability (or rather improbability) of 10^–40 for R and leave us with a posterior probability in excess of 0.9999.”
In our paper, we concentrate on the Bayes factor. The Bayes factor shows the direction of the evidence and measures its force. We argue that it is staggeringly high in favor of R for the evidence we adduce. Naturally, the skeptics will not be likely to agree with us on that. My point here and now, however, is that neither in the paper nor in my interview was there a mistake about probability, any insignificance or triviality in our intended conclusion, nor any deception. We are clear that we are not specifying a prior probability (to do so and to argue for it in any detail would require us to evaluate all the other evidence for and against the existence of God, since that is highly relevant to the prior probability of the resurrection, which obviously would lie beyond the scope of a single paper). Nonetheless, what we do argue is, if we are successful, of great epistemic significance concerning the resurrection, because it means that this evidence is so good that it can overcome even an incredibly low prior probability.
I trust that this is now cleared up.
As a follow-up to Lydia McGrew’s argument, I would claim that the prior probability of the existence of a Designer of Nature cannot plausibly be lower than 1 in 10^120. Notice how I’m framing the hypothesis here: I’m not saying the Designer is omnibenevolent, so arguments from the evil in the world will count as naught against this hypothesis. Likewise, I’m not claiming that the Designer personally planned the design of each and every life-form, so alleged instances of poor design in Nature are also irrelevant to the claim I’m making. My sole claim is that a Designer exists, and that some features of the natural world were planned by this Designer. The negation of this hypothesis is that no features of the natural world were designed.
Now, a skeptic might argue that we don’t need a design explanation for law-governed occurrences: the laws themselves are enough. I think this line of reasoning is grossly mistaken: laws by themselves don’t explain anything. I would also argue that laws can only be properly understood as normative or prescriptive statements, which in turn implies the existence of a Great Prescriber or Lawmaker. But let us leave that aside, and suppose that the objector is correct. Even if we allow that every occurrence which is observed to conform to scientific laws counts as evidence against the likelihood of there being a Designer of Nature, we can still show that the prior probability of a Designer’s existence is at least 1 in 10^120, or 1 with 120 zeroes after it. That’s the number of events calculated to have occurred by Dr. Seth Lloyd of MIT in his 2001 article, Computational capacity of the universe. If every successive law-governed event weakens belief in a Designer, then on a naive view (which is, after all, what we mean by a prior probability), the occurrence of 10^120 such events would reduce our estimate of the prior probability of the Designer’s existence to 1 in 10^120.
In a recent post of mine, titled, The Edge of Evolution, I quoted from a 2011 paper by Dr. Branko Kozulic, Proteins and Genes, Singletons and Species, which argued that the appearance of hundreds of unique proteins and genes that characterize each species is an event beyond the reach of chance. For the purposes of brevity, I’ll just quote from his conclusion:
If just 200 unique proteins are present in each species, the probability of their simultaneous appearance is one against at least 10^4,000. [The] Probabilistic resources of our universe are much, much smaller; they allow for a maximum of 10^149 events  and thus could account for a one-time simultaneous appearance of at most 7 unique proteins. The alternative, a sequential appearance of singletons, would require that the descendants of one family live through hundreds of “macromolecular miracles” to become a new species – again a scenario of exceedingly low probability. Therefore, now one can say that each species is a result of a Biological Big Bang; to reserve that term just for the first living organism  is not justified anymore. This view about species differs sharply from the predominant one according to which speciation is caused by reproductive isolation of two populations [159, 160] mediated by difficult to find speciation genes [161-163]. (p. 21)
Evolutionary biologists of earlier generations have not anticipated [164, 165] the challenge that singletons pose to contemporary biologists. By discovering millions of unique genes biologists have run into brick walls similar to those hit by physicists with the discovery of quantum phenomena. The predominant viewpoint in biology has become untenable: we are witnessing a scientific revolution of unprecedented proportions. (p. 21)
I conclude that the evidence for Intelligent Design is more than enough to overcome any obstacles posed by skeptics, and that disbelief in the existence of such a Designer is not only philosophically but scientifically irrational, whatever Keynes himself may have thought.