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Applying Bayes’ Theorem to Biological Design

Jonathan McLatchie
Mega Millions
Photo: Mega Millions billboard, by Tony Webster from Minneapolis, Minnesota, United States / CC BY (

In a post yesterday, I asked how we can apply the mathematical tool of Bayes’ Theorem to the case for biological design. See, “A Bayesian Approach to Intelligent Design.” 

I propose that we construct the argument as follows: Given the hypothesis that living systems are the result of design, it is not extremely unlikely that biological systems would be rich in digitally encoded information content and irreducibly complex machinery (given that we know from experience with human agents that they often generate information and produce irreducibly complex contraptions). On the other hand, it is incredibly unlikely that such information-rich systems and irreducibly complex machinery could have arisen by an unguided natural process involving chance and physical necessity. Therefore, given that we in fact find such systems to be abundant in living cells, we may take the presence of such features as strong confirmatory evidence for the hypothesis of design over non-design.

God of the Gaps?

Does such an argument commit a God-of-the-gaps fallacy? Not at all. Considering why can, in fact, be quite instructive for understanding the nature of Bayesian inferences. As Lydia McGrew explains in her paper in the journal Philo, it is easy to conceive of a scenario where we know the likelihood on the hypothesis of chance is very low, but nonetheless we do not have evidence for the likelihood on the hypothesis of design being higher. For instance, suppose we were to find a small cloud of hydrogen molecules floating in interstellar space in which the molecules were not dispersing. Without sufficient mass for the cloud to be held together by gravity, such an observation would be an anomaly given our present understanding of physics. However, even though such an observation would be seemingly improbable on the hypothesis of natural law, there would be no reason to think that the hypothesis of design is a better explanation. After all, there is no independent reason to think that a designer would likely cause a small cloud of hydrogen molecules to clump together.

McGrew further points out that it would be quite a different story if, in the distant future, we were able to capture high resolution images of Alpha Centauri (the closest star after the sun) and discover that a Volkswagen Beetle was orbiting a planet there. In that case, the probability of a Volkswagen Beetle being there would be much, much higher on the hypothesis of design than on its falsehood.

A Consideration of Prior Probability

No discussion of Bayes’ Theorem can be complete without a consideration of the prior probability. Prior probability relates to the intrinsic plausibility of a proposition before the evidence is considered. Normally the prior probability will be somewhere between zero and one. A prior probability of one means that the conclusion is certain. For instance, the fact that two added to two is equal to four has a prior probability of one. It is definitionally true. A prior probability of zero, conversely, means that the hypothesis entails some sort of logical contradiction (such as the concept of a married bachelor) and thus cannot be overcome by any amount of evidence.

Priors can be established on the basis of past information. For example, suppose we want to know the odds that a particular individual won last week’s Mega Millions jackpot in the United States. The prior probability would be set at 1 in 302.6 million since those are the odds that any individual lottery participant, chosen at random, would win the Mega Millions jackpot. That is a low prior probability, but it could be overcome if the supposed winner were to subsequently quit his job and start routinely investing in private jets, sports cars, and expensive vacations. Perhaps he could even show us his bank statement, or the documentary evidence of his winnings. 

Those different pieces of evidence, taken together, would stack up to provide powerful confirmatory evidence sufficient to overcome a very small prior probability to yield a high posterior probability that the individual did indeed win the Mega Millions jackpot. In other situations, setting an objective prior is more tricky, and in those cases priors may be determined by a more subjective assessment. In my own arguments, I tend to set the prior probability generously low, to err on the side of caution. In the case of ID, however, one could argue that the prior probability of design is raised significantly by the evidence of cosmic fine-tuning.

Structuring the argument in the way I have proposed above in fact helps us to address some popular objections to intelligent design. Tomorrow, I will explain how.