Intelligent design and mathematical statistics: a troubledalliancePeter OlofssonReceived: 28 February 2007 / Accepted: 4 June 2007 / Published online: 7 August 2007! Springer Science+Business Media B.V. 2007Abstract The explanatory filter is a proposed method to detect design in nature with theaim of refuting Darwinian evolution. The explanatory filter borrows its logical structurefrom the theory of statistical hypothesis testing but we argue that, when viewed within thiscontext, the filter runs into serious trouble in any interesting biological application. Al-though the explanatory filter has been extensively criticized from many angles, we presentthe first rigorous criticism based on the theory of mathematical statistics.Keywords Intelligent design ! Evolution ! Mathematical statistics ! Hypothesis testingIntroductionA classic creationist argument against Darwinian evolution is that it is as likely as atornado in a junkyard creating a Boeing 747. In recent years, the criticism has becomemore measured, coming not from young-earth creationists but from proponents of Intel-ligent Design (ID). The main claim of the ID proponents is that some biological phe-nomena are impossible to adequately explain without referring to design. The perhaps mostprominent representative for the ID movement is biochemist Michael Behe whose 1996book Darwin’s Black Box (Behe 1996) presents challenges to Darwinian evolution basedon irreducibly complex biochemical systems. A system is irreducibly complex if it consistsof several different parts that are such that if any of them is removed, the system loses itsfunction altogether. The favorite biological example is the bacterial flagellum, the little‘‘outboard motor’’ that some bacteria are equipped with and to which we will return later.Behe’s point is that Darwinian evolution cannot account for the emergence of irreduciblycomplex systems as all the parts need to be in place at once. Other than that, Behe seems toP. Olofsson (&)Mathematics Department, Trinity University, One Trinity Place, San Antonio, TX 78212-7200, USAe-mail: [email protected] Philos (2008) 23:545–553DOI 10.1007/s10539-007-9078-6accept most of the accounts of Darwinian evolution. His claims in Darwin’s Black Boxhave been thoroughly opposed, one of the most prominent critics being biologist KennethMiller (2000, 2004).Whether the arguments against Darwinian evolution are based on tornadoes in junk-yards or bacteria, the key concept for evolution critics is improbability. Since mathematics,probability, and statistics are highly developed disciplines, and are well established asindispensable scientific tools, it is only natural that evolution criticism has turned math-ematical, trying to establish objective criteria to rule out chance explanations. The chiefadvocate for this approach is William Dembski whose ideas are described in his books TheDesign Inference (Dembski 1998) and No Free Lunch (Dembski 2002), and also in variouspostings on his own website (http://www.designinference.com).In The Design Inference, Dembski introduces the explanatory filter as a generic methodto eliminate chance explanations and infer design. Inspired by principles from statisticalhypothesis testing, the explanatory filter aims at ruling out chance explanations of observedphenomena based on calculating their probabilities and argues that these probabilities areso small that chance is all but impossible. The filter is further discussed in No Free Lunchalthough in much less detail as the focus is this book is on mathematical complexity theoryand the alleged failure of evolutionary algorithms (the title refers to a class of mathematicaltheorems that say, in essence, that in the absence of knowledge of the location of a target,nothing can beat blind search).Dembski’s oeuvre has been attacked from many different angles. He has had to endurecriticism from biologists, philosophers, and mathematicians and the criticism spans therange from accusations of quasi-philosophy to discovery of arithmetic errors. Much of thecriticism has been aimed at Dembski’s forages into mathematical complexity theory andoptimization theory, most notably by Jeffrey Shallit and Wesley Elsberry (Elsberry andShallit 2003, 2004; Shallit 2002). An admirably short and surgically precise criticism ofDembski’s use of the no-free-lunch theorems is presented by Ha¨ggstro¨m ( 2007).The explanatory filter from The Design Inference has also been extensively criticized,perhaps most notably by philosopher Elliot Sober whose articles (Fitelson et al. 1999;Sober 2002, 2004), amongst many other things, criticize its purely eliminative nature,advocating instead that sound scientific practice require that conclusions are based oncomparative reasoning. Perhaps a chance hypothesis confers a small probability on theevidence, but how do we know that a design hypothesis does not confer an even smallerprobability? As the strategy of the ID movement is to try to discredit Darwinian evolutionwithout offering any substantive alternative theory, the question is not easily answered. InNo Free Lunch, Dembski argues against Sober that elimination is indeed a legitimatescientific principle. As an example, Dembski offers the hypothesis that the moon is madeof cheese which he claims could be rejected without suggesting an alternative lunarmaterial. The filter has also been criticized by Mark Perakh (2003, 2005) and by severalothers, for example on the websites http://www.talkreason.org and http://www.pandas-thumb.org.However, there has not yet been published a criticism of the filter from the vantage pointof mathematical statistics. It is clear from Dembski’s writings that his main source ofinspiration for the explanatory filter is the theory of statistical hypothesis testing and amathematical statistician immediately recognizes it as such. We shall see that, from thisparticular angle, even if the filter is put in the most benevolent light, it runs into serioustrouble when it comes to biological applications. The filter will be described in the nextsection; thereafter we will outline how it relates to statistical hypothesis testing and finallyaddress its weaknesses.546 P. Olofsson123The explanatory filterDembski’s flowchart description of the explanatory filter differs slightly between TheDesign Inference and No Free Lunch, but the basic structure is the same. An event isobserved and it must be decided whether it is attributable to