Another Way to Detect Design?

Below is a three part lecture series entitled �Another Way to Detect Design� which contains William Dembski's response to Fitelson, Stephens, and Sober whose article "How Not to Detect Design" ran on Metanexus:Views (2001.09.14, 2001.09.21, and 2001.09.28). These lectures were first made available online at Metanexus: The Online Forum on Religion and Science  This is from three keynote lectures delivered October 5-6, 2001 at the Society of Christian Philosopher's meeting at the University of Colorado, Boulder.

William A. Dembski

Lecture 1 - Another Way to Detect Design?

1. Overview of the Design Inference

Darwin began his Origin of Species with the commonsense recognition that artificial selection in animal and plant breeding experiments is capable of directing organismal variation. A design-theoretic research program likewise begins with a commonsense recognition, in this case that humans draw design inferences routinely in ordinary life, explaining some things in terms of blind, undirected causes and other things in terms of intelligence or design. For instance, archeologists attribute rock formations in one case to erosion and in another to design -- as with the megaliths at Stonehenge.

Having massaged our intuitions, Darwin next formalized and extended our commonsense understanding of artificial selection. Specifically, Darwin proposed natural selection as a general mechanism to account for how organismal variation gets channeled in the production of new species. Similarly, a design-theoretic research program next formalizes and extends our commonsense understanding of design inferences so that they can be rigorously applied in scientific investigation. My codification of design inferences as an extension of Fisherian hypothesis testing provides one such formalization. At the heart of my codification is the notion of specified complexity, which is a statistical and complexity-theoretic concept. An object, event, or structure exhibits specified complexity if it matches a highly improbable, independently given pattern.

At the molecular level, erectile dysfunction drugs act in a similar way to antiviral drugs, this is an application of the theory of evolution in our lives.

Think of the signal that convinced the radio astronomers in the movie Contact that they had found an extraterrestrial intelligence. The signal was a long sequence of prime numbers. On account of its length the signal was complex and could not be assimilated to any natural regularity. And yet on account of its arithmetic properties it matched an objective, independently given pattern. The signal was thus both complex and specified. What's more, the combination of complexity and specification convincingly pointed those astronomers to an extraterrestrial intelligence. Design theorists contend that specified complexity is a reliable indicator of design, is instantiated in certain (though by no means all) biological structures, and lies beyond the remit of nature to generate it.

To say that specified complexity lies beyond the remit of nature to generate it is not to say that naturally occurring systems cannot exhibit specified complexity or that natural processes cannot serve as a conduit for specified complexity. Naturally occurring systems can exhibit specified complexity and nature operating unassisted can take preexisting specified complexity and shuffle it around. But that is not the point. The point is whether nature (conceived as a closed system of blind, unbroken natural causes) can generate specified complexity in the sense of originating it when previously there was none. Take, for instance, a D�rer woodcut. It arose by mechanically impressing an inked woodblock on paper. The D�rer woodcut exhibits specified complexity. But the mechanical application of ink to paper via a woodblock does not account for that specified complexity in the woodcut. The specified complexity in the woodcut must be referred back to the specified complexity in the woodblock which in turn must be referred back to the designing activity of D�rer himself (in this case deliberately chiseling the woodblock). Specified complexity's causal chains end not with nature but with a designing intelligence.

To employ specified complexity as a criterion for detecting design remains controversial. The philosophy of science community, wedded as it is to a Bayesian (or more generally likelihood) approach to probabilities, is still not convinced that my account of specified complexity is even coherent. The Darwinian community, convinced that the Darwinian mechanism can do all the design work in biology, regards specified complexity as an unexpected vindication of Darwinism -- that's just what the Darwinian mechanism does, we are told, to wit, generate specified complexity. On the other hand, mathematicians and statisticians have tended to be more generous toward my work and to regard it as an interesting contribution to the study of randomness. Perhaps the best reception of my work has come from engineers and the defense industry looking for ways to apply specified complexity in pattern matching (for instance, I've even been approached on behalf of DARPA to assist in developing techniques for tracking terrorists). The final verdict is not in. Indeed, the discussion has barely begun. In this talk I will address the concern that specified complexity is not even a coherent probabilistic notion. In my next talk I will show that the Darwinian mechanism is incapable of doing the design work that biologists routinely attribute to it.

Detecting design by means of specified complexity constitutes a straightforward extension of Fisherian significance testing. In Fisher's approach to significance testing, a chance hypothesis is eliminated provided an event falls within a prespecified rejection region and provided that rejection region has small probability with respect to the chance hypothesis under consideration. The picture here is of an arrow landing in the target. Provided the target is small enough, chance cannot plausibly explain the arrow hitting the target. Of course, the target must be given independently of the arrow's trajectory. Movable targets that can be adjusted after the arrow has landed will not do (one can't, for instance, paint a target around the arrow after it has landed).

In extending Fisher's approach to hypothesis testing, the design inference generalizes the types of rejection regions capable of eliminating chance. In Fisher's approach, to eliminate chance because an event falls within a rejection region, that rejection region must be identified prior to the occurrence of the event. This is to avoid the familiar problem known among statisticians as "data snooping" or "cherry picking," in which a pattern is imposed on an event after the fact. Requiring the rejection region to be set prior to the occurrence of an event safeguards against attributing patterns to the event that are factitious and that do not properly preclude its occurrence by chance.

This safeguard, however, is unduly restrictive. In cryptography, for instance, a pattern that breaks a cryptosystem (known as a cryptographic key) is identified after the fact (i.e., after one has listened in and recorded an enemy communication). Nonetheless, once the key is discovered, there is no doubt that the intercepted communication was not random but rather a message with semantic content and therefore designed. In contrast to statistics, which always identifies its patterns before an experiment is performed, cryptanalysis must discover its patterns after the fact. In both instances, however, the patterns are suitable for inferring design. Patterns suitable for inferring design I call specifications. A full account of specifications can be found in my book The Design Inference as well as in my forthcoming book No Free Lunch. Suffice it to say, specifications constitute a straightforward generalization of Fisher's rejection regions.

2. Design by Comparison

By employing rejection regions, the design inference takes an eliminative approach to detecting design. But design detection can also be approached comparatively. In their review for Philosophy of Science of my book The Design Inference, Branden Fitelson, Christopher Stephens, and Elliott Sober argue that my eliminative approach to detecting design is defective and offer an alternative comparative approach that they regard as superior.[1] According to them, if design is to pass scientific muster, it must be able to generate predictions about observables.[2] By contrast, they see my approach as establishing the plausibility of design "merely by criticizing alternatives."[3]

Sober's critique of my work on design did not end with this review. In his 1999 presidential address to the American Philosophical Association, Sober presented a paper titled "Testability."[4] In the first half of that paper he laid out what he regards as the proper approach for testing scientific hypotheses, namely, a comparative, likelihood approach in which hypotheses are confirmed to the degree that they render observations probable. In the second half of that paper he showed how the approach I develop for detecting design in The Design Inference diverges from this likelihood approach. Sober concluded that my approach to detecting renders design untestable and therefore unscientific.

The likelihood approach that Sober and his colleagues advocate was familiar to me before I wrote The Design Inference. I found that approach to detecting design inadequate then and I still do. Sober's likelihood approach is a comparative approach to detecting design. In that approach all hypotheses are treated as chance hypotheses in the sense that they confer probabilities on states of affairs.[5] Thus, in a competition between a design hypothesis and other hypotheses, design is confirmed by determining whether and the degree to which the design hypothesis confers greater probability than the others on a given state of affairs.

The likelihood approach of Sober and colleagues has a crucial place in Bayesian decision theory. The likelihood approach is concerned with the relative degree to which hypotheses confirm states of affairs as measured by likelihood ratios. Bayesian decision theory, in addition, focuses on how prior probabilities attached to those hypotheses recalibrate the likelihood ratios and thereby reapportion our belief in those hypotheses. Briefly, likelihoods measure strength of evidence irrespective of background knowledge. Bayesianism also factors in our background knowledge and thus characterizes not just strength of evidence but also degree of conviction.

Sober's likelihood approach parallels his preferred model of scientific explanation, known as inference to the best explanation (IBE), in which a "best explanation" always presupposes at least two competing explanations.[6] Inference to the best explanation eliminates hypotheses not by eliminating them individually but by setting them against each other and determining which comes out on top. But why should eliminating a chance hypothesis always require additional chance hypotheses that compete with it? Certainly this is not a requirement for eliminating hypotheses generally. Consider the following hypothesis: "The moon is made of cheese." One does not need additional hypotheses (e.g., "The moon is a great ball of nylon") to eliminate the moon-is-made-of-cheese hypothesis. There are plenty of hypotheses that we eliminate in isolation, and for which additional competing hypotheses do nothing to assist in eliminating them. Indeed, often with scientific problems we are fortunate if we can offer even a single hypothesis as a proposed solution (How many alternatives were there to Newtonian mechanics when Newton proposed it?). What's more, a proposed solution may be so poor and unacceptable that it can rightly be eliminated without proposing an alternative. It is not a requirement of logic that eliminating a hypothesis means superseding it.

But is there something special about chance hypotheses? Sober advocates a likelihood approach to evaluating chance hypotheses according to which a hypothesis is confirmed to the degree that it confers increasing probability on a known state of affairs. Unlike Fisher's approach, the likelihood approach has no need for significance levels or small probabilities. What matters is the relative assignment of probabilities, not their absolute value. Also, unlike Fisher's approach (which is purely eliminative, eliminating a chance hypothesis without accepting another), the likelihood approach focuses on finding a hypothesis that confers maximum probability, thus making the elimination of hypotheses always a by-product of finding a better hypothesis. But there are problems with the likelihood approach, problems that severely limit its scope and prevent it from becoming the universal instrument for adjudicating among chance hypotheses that Sober intends. Indeed, the likelihood approach is necessarily parasitic on Fisher's approach and can properly adjudicate only among hypotheses that Fisher's approach has thus far failed to eliminate.

To see this, consider the supposed improvement that a likelihood analysis brings to one of my key examples for motivating the design inference, namely, the "Caputo case." Nicholas Caputo, a county clerk from New Jersey was charged with cheating -- before the New Jersey Supreme Court no less -- because he gave the preferred ballot line to Democrats over Republicans 40 out of 41 times (the improbability here is that of flipping a fair coin 41 times and getting 40 heads). I give a detailed analysis of the Caputo case in The Design Inference and extend the analysis in my forthcoming book No Free Lunch. For now, however, I want to focus on Sober's analysis. Here it is -- in full detail:

There is a straightforward reason for thinking that the observed outcomes favor Design over Chance. If Caputo had allowed his political allegiance to guide his arrangement of ballots, you would expect Democrats to be listed first on all or almost all of the ballots. However, if Caputo did the equivalent of tossing a fair coin, the outcome he obtained would be very surprising.[7]

Such an analysis does not go far enough. To see this, take Caputo's actual ballot line selection and call that event E. E consists of 41 selections of Democrats and Republicans in some particular sequence with Democrats outnumbering Republicans 40 to 1 (say twenty-two Democrats, followed by one Repulican, followed by eighteen Democrats). If Democrats and Republicans are equally likely, this event has probability 2^(-41) or approximately 1 in 2 trillion. Improbable, yes, but by itself not enough to implicate Caputo in cheating. What, then, additionally do we need to confirm cheating (and thereby design)? To implicate Caputo in cheating it's not enough merely to note a preponderance of Democrats over Republicans in some sequence of ballot line selections. Rather, one must also note that a preponderance as extreme as this is highly unlikely. A crucial distinction needs to be made here. Probabilists distinguish between outcomes or elementary events on the one hand and composite events on the other. To roll a six with a single die is an outcome or elementary event. On the other hand, to roll an even number with a single die is a composite event that includes (or subsumes) the outcome of rolling a six, but also includes rolling a four or two.

In the Caputo case, it's not the event E (Caputo's actual ballot line selections) whose improbability the likelihood theorist needs to compute but the composite event E* consisting of all possible ballot line selections that exhibit at least as many Democrats as Caputo selected. This composite event -- E* -- consists of 42 possible ballot line selections and has improbability 1 in 50 billion. It's this event and this improbability on which the New Jersey Supreme Court rightly focused. Moreover, it's this event that the likelihood theorist needs to identify and whose probability the likelihood theorist needs to compute to perform a likelihood analysis (Sober and colleagues concede this point when they  admit that the event of interest is one in which Democrats are "listed first on all or almost all of the ballots" -- in other words, it's not the exact sequence of Caputo's ballot line selections but all of which are as extreme as his).

But how does the likelihood theorist identify this event? Let's be clear that observation never hands us composite events like E* but only elementary events like E (i.e., Caputo's actual ballot line selection and not the ensemble of ballot line selections as extreme as Caputo's). But whence this composite event? Within the Fisherian framework the answer is clear: E* is a prespecified rejection region, in this case given by a test-statistic that counts number of Democrats selected over Republicans. That's what the court used and that's what likelihood theorists use. Likelihood theorists, however, offer no account of how they identify the composite events to which they assign probabilities. If the only events they ever considered were elementary events, there would be no problem. But that's not the case. Likelihood theorists and Bayesians routinely consider composite events. In the case of Bayesian design inferences, those composite events are given by specifications. But how do Bayesian probabilists and likelihood theorists more generally individuate the events they employ to discriminate among chance hypotheses? This questions never gets answered in Bayesian or likelihood terms. Yet it is absolutely crucial to their project.

Lecture 2 - Another Way to Detect Design?: Why Natural Selection Can't Design Anything

Let me paint the picture more starkly. Consider an elementary event E. Suppose initially we see no pattern that gives us reason to expect an intelligent agent produced it. But then, rummaging through our background knowledge, we suddenly see a pattern that signifies design in E. Under a likelihood analysis, the probability of E given the design hypothesis suddenly jumps way up. That, however, isn't enough to allow us to infer design. As is usual in a likelihood or Bayesian scheme, we need to compare a probability conditional on design to one conditional on chance. But for which event do we compute these probabilities? As it turns out, not for the elementary outcome E, but for the composite event E* consisting of all elementary outcomes that exhibit the pattern signifying design. Indeed, it does no good to argue for E being the result of design on the basis of some pattern unless the entire collection of elementary outcomes that exhibit that pattern is itself improbable on the chance hypothesis. The likelihood theorist therefore needs to compare the probability of E* conditional on the design hypothesis with the probability of E* conditional on the chance hypothesis. The bottom line is this: the likelihood approach offers no account of how it arrives at the (composite) events upon which it performs its analyses. The selection of those events is highly intentional and, in the case of Bayesian design inferences, needs to presuppose an account of specification.

So simple and straightforward do Sober and his colleagues regard their likelihood analysis that they mistakenly conclude: "Caputo was brought up on charges and the judges found against him."[8] Caputo was brought up on charges of fraud, but in fact the New Jersey Supreme Court justices did not find against him.[9] The probabilistic analysis that Sober and fellow likelihood theorists find so convincing is viewed with skepticism by the legal system, and for good reason. Within a likelihood approach, the probabilities conferred by design hypotheses are notoriously imprecise and readily lend themselves to miscarriages of justice.[10]

I want therefore next to examine the very idea of hypotheses conferring probability, an idea that is mathematically straightforward but that becomes problematic once the likelihood approach gets applied in practice. According to the likelihood approach, chance hypotheses confer probability on states of affairs, and hypotheses that confer maximum probability are preferred over others. But what exactly are these hypotheses that confer probability? In practice, the likelihood approach is too cavalier about the hypotheses it permits. Urn models as hypotheses are fine and well because they induce well-defined probability distributions. Models for the formation of functional protein assemblages might also induce well-defined probability distributions, though determining the probabilities here will be considerably more difficult (I develop some techniques for estimating these probabilities in my forthcoming book No Free Lunch). But what about hypotheses like "Natural selection and random mutation together are the principal driving force behind biological evolution" or "God designed living organisms"? Within the likelihood approach, any claim can be turned into a chance hypothesis on the basis of which likelihood theorists then assign probabilities. Claims like these, however, do not induce well-defined probability distributions. And since most claims are like this (i.e., they fail to induce well-defined probability distributions), likelihood analyses regularly become exercises in rank subjectivism.

Consider, for instance, the following analysis taken from Sober's text _Philosophy of Biology_.[11] Sober considers the following state of affairs: E -- "Living things are intricate and well-suited to the task of surviving and reproducing." He then considers three hypotheses to explain this state of affairs: H1 -- "Living things are the product of intelligent design"; H2 -- "Living things are the product of random physical processes"; H3 -- "Living things are the product of random variation and natural selection." As Sober explains, prior to Darwin only H1 and H2 were live options, and E was more probable given H1 than given H2. Prior to Darwin, therefore, the design hypothesis was better supported than the chance hypothesis. But with Darwin's theory of random variation and natural selection, the playing field was expanded and E became more probable given H3 than either H1 or H2.

Now my point is not to dispute whether in Darwin's day H3 was a better explanation of E than either H1 or H2. My point, rather, is that Sober's appeal to probability theory to make H1, H2, and H3 each confer a probability on E is misleading, lending an air or mathematical rigor to what really is just Sober's own subjective assessment of how plausible these hypotheses seem to him. Nowhere in this example do we find precise numbers attached to Sober's likelihoods. The most we see are inequalities of the form P(E|H1) >> P(E|H2), signifying that the probability of E given H1 is much greater than the probability of E given H2 (for the record, the "much greater" symbol ">>" has no precise mathematical meaning). But what more does such an analysis do than simply assert that with respect to the intricacy and adaptedness of organisms, intelligent design is a much more convincing explanation to Sober than the hypothesis of pure chance? And since Sober presumably regards P(E|H3) >> P(E|H1), the Darwinian explanation is for him an even better explanation of the intricacy and adaptedness of organisms than intelligent design. The chance hypotheses on which Sober pins his account of scientific rationality and testability are not required to issue in well-defined probability distributions. Sober's probabilities are therefore probabilities in name only.

But there are more problems with the likelihood approach. Even when probabilities are well-defined, the likelihood approach can still lead to wholly unacceptable conclusions. Consider, for instance, the following experimental setup. There are two urns, one with five white balls and five black balls, the other with seven white balls and three black balls. One of these urns will be sampled with replacement a thousand times, but we do not know which. The chance hypothesis characterizing the first urn is that white balls should on average occur the same number of times as black balls, and the chance hypothesis characterizing the second urn is that white balls should on average outnumber black balls by a ratio of seven to three. Suppose now we are told that one of the urns was sampled and that all the balls ended up being white. The probability of this event by sampling from the first urn is roughly 1 in 10^300 whereas the probability of this event by sampling from the second urn is roughly 1 in 10^155.

The second probability is therefore almost 150 orders of magnitude greater than the first. Thus on the likelihood approach, the hypothesis that the urn had seven white balls is vastly better confirmed than the hypothesis that it only had five. But getting all white balls from the urn with seven white balls is a specified event of small probability, and on Fisher's approach to hypothesis testing should be eliminated as well (drawing with replacement from this urn 1000 times, we should expect on average around 300 black balls from this urn, and certainly not a complete absence of black balls). This comports with our best probabilistic intuitions: Given these two urns and a thousand white balls in a row, the only sensible conclusion is that neither urn was randomly sampled, and any superiority of the "urn two" hypothesis over the "urn one" hypothesis is utterly insignificant. To be forced to choose between these two hypotheses is like being forced to choose between the moon being made entirely of cheese or the moon being made entirely of nylon. Any superiority of the one hypothesis over the other drowns in a sea of inconsequentiality.

The likelihood principle, being an inherently comparative instrument, has nothing to say about the absolute value of the probability (or probability density) associated with a state of affairs, but only their relative magnitudes. Consequently, the vast improbability of either urn hypothesis in relation to the sample chosen (i.e., 1000 white balls) would on strict likelihood grounds be irrelevant to any doubts about either hypothesis. Nor would such vast improbabilities in themselves provide the Bayesian probabilist with a legitimate reason for reassigning prior probabilities to the two urn hypotheses considered here or assigning nonzero probability to some hitherto unrecognized hypothesis (for example, a hypothesis that makes white balls overwhelmingly more probable than black balls).

The final problem with the likelihood approach that I want to consider is its treatment of design hypotheses as chance hypotheses. For Sober any hypothesis can be treated as a chance hypothesis in the sense that it confers probability on a state of affairs. As we have seen, there is a problem here because Sober's probabilities typically float free of well-defined probability distributions and thus become irretrievably subjective. But even if we bracket this problem, there is a problem treating design hypotheses as chance hypotheses, using design hypotheses to confer probability (now conceived in a loose, subjective sense) on states of affairs. To be sure, designing agents can do things that follow well-defined probability distributions. For instance, even though I acted as a designing agent in writing this paper, the distribution of letter frequencies in it follow a well-defined probability distribution in which the relative frequency of the letter e is approximately 13 percent, that of t approximately 9 percent, etc. -- this is the distribution of letters for English texts.[12] Such probability distributions ride, as it were, epiphenomenally on design hypotheses.[13] Thus in this instance, the design hypothesis identifying me as author of this paper confers a certain probability distribution on the letter frequencies of it. (But note, if these letter frequencies were substantially different, a design hypothesis might well be required to account for the difference. In 1939 Ernest Vincent Wright published a novel of over 50,000 words titled Gadsby that contained no occurrence of the letter e. Clearly, the absence of the letter e was designed.[14])

Sober, however, is much more interested in assessing probabilities that bear directly on a design hypothesis than in characterizing chance events that ride epiphenomenally on it. In the case of letter frequencies, the fact that letters in this paper appear with certain relative frequencies reflects less about the design hypothesis that I am its author than about the (impersonal) spelling rules of English. Thus with respect to intelligent design in biology, Sober wants to know what sorts of biological systems should be expected from an intelligent designer having certain characteristics, and not what sorts of random epiphenomena might be associated with such a designer. What's more, Sober claims that if the design theorist cannot answer this question (i.e., cannot predict the sorts of biological systems that might be expected on a design hypothesis), then intelligent design is untestable and therefore unfruitful for science.

Yet to place this demand on design hypotheses is ill-conceived. We infer design regularly and reliably without knowing characteristics of the designer or being able to assess what the designer is likely to do. Sober himself admits as much in a footnote that deserves to be part of his main text: "To infer watchmaker from watch, you needn't know exactly what the watchmaker had in mind; indeed, you don't even have to know that the watch is a device for measuring time. Archaeologists sometimes unearth tools of unknown function, but still reasonably draw the inference that these things are, in fact, tools."[15]

Sober is wedded to a Humean inductive tradition in which all our knowledge of the world is an extrapolation from past experience.[16] Thus for design to be explanatory, it must fit our preconceptions, and if it does not, it must lack epistemic support. For Sober, to predict what a designer would do requires first looking to past experience and determining what designers in the past have actually done. A little thought, however, should convince us that any such requirement fundamentally misconstrues design. Sober's likelihood approach puts designers in the same boat as natural laws, locating their explanatory power in an extrapolation from past experience. To be sure, designers, like natural laws, can behave predictably (for instance, designers often institute policies that are dutifully obeyed). Yet unlike natural laws, which are universal and uniform, designers are also innovators. Innovation, the emergence to true novelty, eschews predictability. A likelihood analysis generates predictions about the future by conforming the present to the past and extrapolating from it. It therefore follows that design cannot be subsumed under a likelihood framework. Designers are inventors. We cannot predict what an inventor would do short of becoming that inventor.

But the problem goes deeper. Not only can Humean induction not tame the unpredictability inherent in design; it cannot account for how we recognize design in the first place. Sober, for instance, regards the design hypothesis for biology as fruitless and untestable because it fails to confer sufficient probability on biologically interesting propositions. But take a different example, say from archeology, in which a design hypothesis about certain aborigines confers a large probability on certain artifacts, say arrowheads. Such a design hypothesis would on Sober's account be testable and thus acceptable to science. But what sort of archeological background knowledge had to go into that design hypothesis for Sober's likelihood analysis to be successful? At the very least, we would have had to have past experience with arrowheads. But how did we recognize that the arrowheads in our past experience were designed? Did we see humans actually manufacture those arrowheads? If so, how did we recognize that these humans were acting deliberately as designing agents and not just randomly chipping away at random chunks of rock (carpentry and sculpting entail design; but whittling and chipping, though performed by intelligent agents, do not)? As is evident from this line of reasoning, the induction needed to recognize design can never get started.[17] Our ability to recognize design must therefore arise independently of induction and therefore independently of Sober's likelihood framework.

The direction of Sober's logic is from design hypothesis to designed object, with the design hypothesis generating predictions or expectations about the designed object. Yet in practice we start with objects that initially we may not know to be designed. Then by identifying general features of those objects that reliably signal design, we infer to a designing intelligence responsible for those objects. Still further downstream in the logic is an investigation into the specific design characteristics of those objects (e.g., How was the object constructed? How could it have been constructed? What is its function? What effect have natural causes had on the original design? Is the original design recoverable? How much has the original design been perturbed? How much perturbation can the object allow and still remain functional?). But what are those general features of designed objects that set the design inference in motion and reliably signal design? The answer I am urging is specification and complexity.

Lecture 3 - Another Way to Detect Design?: The Chance of the Gaps

3. Design by Elimination

The defects in Sober's likelihood approach are, in my view, so grave that it cannot provide an adequate account of how design hypotheses are inferred.[18] The question remains, however, whether specified complexity can instead provide an adequate account for how design hypotheses are inferred. The worry here centers on the move from specified complexity to design. Specified complexity is a statistical and complexity-theoretic notion. Design, as generally understood, is a causal notion. How do the two connect?

In The Design Inference and then more explicitly in No Free Lunch, I connect the two as follows. First, I note that intelligence has the causal power to generate specified complexity. About this there is no controversy. Human artifacts, be they Hubble space telescopes, Cray supercomputers, D�rer woodcuts, gothic cathedrals, or even such humble objects as paperclips exhibit specified complexity. Moreover, insofar as we infer to nonhuman intelligences, specified complexity is the key here too. This holds for animal intelligences as well as for extraterrestrial intelligences. Indeed, short of observing an extraterrestrial life form directly, any signals from outer space that we take to indicate extraterrestrial life will also indicate extraterrestrial intelligent life. It is no accident that the search for extraterrestrial intelligence, by looking to radio signals, cannot merely detect life as such but must detect intelligent life. Moreover, radio signals that would warrant a SETI researcher in inferring extraterrestrial intelligence invariably exhibit specified complexity.

To show that specified complexity is a reliable empirical marker of design, it is therefore enough to show that no natural cause has the causal power to generate specified complexity (natural causes being understood here as they are in the scientific community, namely, as undirected, blind, purposeless causes characterized in terms of the joint action of chance and necessity). Showing that natural causes cannot generate specified complexity seem like a tall order, but in fact it is not an intractable problem. Natural causes, because they operate through the joint action of chance and necessity, are modeled mathematically by nondeterministic functions known as stochastic processes. Just what these are in precise mathematical terms is not important here. The important thing is that functions map one set of items to another set of items and in doing so map a given item to one and only one other item. Thus for a natural cause to "generate" specified complexity would mean for a function to map some item to another item that exhibits specified complexity. But that means the complexity and specification in the item that got mapped onto gets pushed back to the item that got mapped. In other words, natural causes just push the problem of accounting for specified complexity from the effect back to the cause, which now in turn needs to be explained. It is like explaining a pencil in terms of a pencil-making machine. Explaining the pencil-making machine is as difficult as explaining the pencil. In fact, the problem typically gets worse as one backtracks specified complexity.

Stephen Meyer makes this point beautifully for DNA.[19] Suppose some natural cause is able to account for the sequence specificity of DNA (i.e., the specified complexity in DNA). The four nucleotide bases are attached to a sugar-phosphate backbone and thus cannot influence each other via bonding affinities. In other words, there is complete freedom in the sequencing possibilities of the nucleotide bases. In fact, as Michael Polanyi observed in the 1960s, this must be the case if DNA is going to be optimally useful as an information bearing molecule.[20] Indeed, any limitation on sequencing possibilities of the nucleotide bases would hamper its information carrying capacity. But that means that any natural cause that brings about the specified complexity in DNA must admit at least as much freedom as is in the DNA sequencing possibilities (if not, DNA sequencing possibilities would be constrained by physico-chemical laws, which we know they are not). Consequently, any specified complexity in DNA tracks back via natural causes to specified complexity in the antecedent circumstances responsible for the sequencing of DNA. To claim that natural causes have "generated" specified complexity is therefore totally misleading -- natural causes have merely shuffled around preexisting specified complexity.

I develop this argument in detail in chapter 3 of No Free Lunch. In the next lecture I shall consider the type of natural cause most widely regarded as capable of generating specified complexity, namely, the Darwinian mechanism. In that lecture I shall show that the Darwinian mechanism of random variation and natural selection is in principle incapable of generating specified complexity. In my final lecture, "The Chance of the Gaps," I close off one last loophole to the possibility of naturalistically generating specified complexity. A common move these days in cosmology and metaphysics (the two are becoming increasingly hard to separate) is to inflate one's ontology, augmenting the amount of time and stuff available in the physical universe and thereby rendering chance plausible when otherwise it would seem completely implausible. In my final lecture I show why inflating one's ontology does not get around the problem of specified complexity.

For the remainder of this paper I therefore want to focus on logical and foundational concerns connected with specified complexity.  This is where Sober focuses his criticism. According to Sober, the chief problem with specified complexity is that it detects design purely by elimination, telling us nothing positive about how an intelligent designer might have produced an object we observe. Take, for instance, a biological system, one that exhibits specified complexity, but for which we have no clue how an intelligent designer might have produced it. To employ specified complexity as a marker of design here seems to tell us nothing except that the object is designed. Indeed, when we examine the logic of detecting design via specified complexity, at first blush it looks purely eliminative. The "complexity" in "specified complexity" is a measure of improbability. Now probabilities are always assigned in relation to chance hypotheses. Thus, to establish specified complexity requires defeating a set of chance hypotheses. Specified complexity therefore seems at best to tell us what is not the case, not what is the case.

In response to this criticism, note first that even though specified complexity is established via an eliminative argument, it is not fair to say that it is established via a purely eliminative argument. If the argument were purely eliminative, one might be justified in saying that the move from specified complexity to a designing intelligence is an argument from ignorance (not X therefore Y). But unlike Fisher's approach to hypothesis testing, in which individual chance hypotheses get eliminated without reference to the entire set of relevant chance hypotheses that might explain a phenomenon, specified complexity presupposes that the entire set of relevant chance hypotheses has first been identified.[21] This takes considerable background knowledge. What's more, it takes considerable background knowledge to come up with the right pattern (i.e., specification) for eliminating all those chance hypotheses and thus for inferring design.

Design inferences that infer design by identifying specified complexity are therefore not purely eliminative. They do not merely exclude, but they exclude from an exhaustive set in which design is all that remains once the inference has done its work (which is not to say that the set is logically exhaustive; rather, it is exhaustive with respect to the inquiry in question -- that is all we can ever do in science). Design inferences, by identifying specified complexity, exclude everything that might in turn exclude design. The claim that design inferences are purely eliminative is therefore false, and the claim that they provide no (positive) causal story is true but hardly relevant -- causal stories must always be assessed on a case-by-case basis independently of general statistical considerations.

I want next to take up a narrowly logical objection. Sober and colleagues argue that specified complexity is unable to handle conjunctive, disjunctive, and mixed explananda.[22] Let us deal with these in order. Conjunctions are supposed to present a problem for specified complexity because a conjunction can exhibit specified complexity even though none of its conjuncts do individually. Thus, if specified complexity is taken as an indicator of design, this means that even though the conjunction gets attributed to design, each of the conjuncts get attributed to chance. Although this may seem counterintuitive, it is not clear why it should be regarded as a problem. Consider a Scrabble board with Scrabble pieces. Chance can explain the occurrence of any individual letter at any individual location on the board. Nevertheless, meaningful conjunctions of those letters arranged sequentially on the board are not attributable to chance. It is important to understand that chance is always a provisional designation that can be overturned once closer examination reveals specified complexity. Thus attributing chance to the isolated positioning of a single Scrabble piece does not contradict attributing design to the joint positioning of multiple Scrabble pieces into a meaningful arrangement.

Disjunctions are a bit trickier. Disjunctions are supposed to pose a problem in the case where some of the disjuncts exhibit specified complexity but the disjunction itself is no longer complex and therefore no longer exhibits specified complexity. Thus we would have a case where a disjunct signifies design, but the disjunction does not. How can this run into trouble? Certainly there is no problem in the case where one of the disjuncts is highly probable. Consider the disjunction, Either the arrow lands in the target or outside. If the target is sufficiently small, the arrow landing in the target would constitute a case of specified complexity. But the disjunction itself is a tautology and the event associated with it can readily be attributed to chance.

How else might specified complexity run into trouble with disjunctions? Another possibility is that all the disjuncts are improbable. For instance, consider a lottery in which there is a one-to-one correspondence between players and winning possibilities. Suppose further that each player predicts he or she will win the lottery. Now form the disjunction of all these predictions. This disjunction is a tautology, logically equivalent to the claim that some one of the players will win the lottery (which is guaranteed since players are in one-to-one correspondence with winning possibilities). Clearly, as a tautology, this disjunction does not exhibit specified complexity and therefore does not signify design. But what about the crucial disjunct in this disjunction, namely, the prediction by the winning lottery player? As it turns out, this disjunct can never exhibit specified complexity either. This is because the number of disjuncts count as probabilistic resources, which I define as the number of opportunities for an event to occur and be specified (more on this in my final lecture). With disjunctions, this number is the same as the number of lottery players and ensures that the prediction by the winning lottery player never attains the degree of complexity/improbability needed to exhibit specified complexity. A lottery with N players has at least N probabilistic resources, and once these are factored in, the correct prediction by the winning lottery player is no longer improbable. In general, once all the relevant probabilistic resources connected with a disjunction are factored in, apparent difficulties associated with attributing a disjunct to design and the disjunction to chance disappear.

Finally, the case of mixed explananda is easily dispatched. Suppose we are given a conjunction of two conjuncts in which one exhibits specified complexity and the other does not. In that case one will be attributed to design and the other to chance. And what about the conjunction? The conjunction will be at least as improbable/complex as the first conjunct (the one that exhibits specified complexity). What's more, the pattern qua specification that delimits the first conjunct will necessarily delimit the conjunction as well (conjunctions always restrict the space of possibilities more than their conjuncts). Consequently, the conjunction will itself exhibit specified complexity and be attributed to design. Note that this is completely unobjectionable. Specified complexity, in signaling design, merely says that an intelligent agent was involved. It does not require that intelligent agency account for every aspect of a thing in question.

In closing I want to take the charge that specified complexity is not a reliable instrument for detecting design and turn it back on critics who think that likelihoods provide a better way of inferring design. I showed earlier that the likelihood approach presupposes some account of specification in how it individuates the events to which it applies. More is true: The likelihood approach can infer design only by presupposing specified complexity.

To see this, take an event that is the product of design but for which we have not yet seen the relevant pattern that makes its design evident to us (take a Search for Extraterrestrial Intelligence example in which a long sequence of prime numbers, say, reaches us from outer space, but suppose we have not yet seen that it is a sequence of prime numbers). Without that pattern we will not be able to distinguish between the probability that this event takes the form it does given that it is the result of chance, and the probability that it takes the form it does given that it is the result of design. Consequently, we will not be able to infer design for this event. Only once we see the pattern will we, on a likelihood analysis, be able to see that the latter probability is greater than the former. But what are the right sorts of patterns that allow us to see that? Not all patterns signal design. What's more, the pattern needs to delimit an event of sufficient improbability (i.e., complexity) for otherwise the event can readily be referred to chance. We are back, then, to needing some account of complexity and specification. Thus a likelihood analysis that pits competing design and chance hypotheses against each other must itself presuppose the legitimacy of specified complexity as a reliable indicator of intelligence.

Nor is the likelihood approach salvageable. Lydia and Timothy McGrew, philosophers at Western Michigan University, think that likelihoods are ideally suited for detecting design in the natural sciences but that my Fisherian approach to specified complexity breaks down. Taking issue with both Sober and me, they argue that the presence of irreducible complexity in biological systems constitutes a state of affairs upon which the design hypothesis confers greater probability than the Darwinian hypothesis.[23] Irreducible complexity is biochemist Michael Behe's notion. According to Behe, a system is irreducibly complex if it is "composed of several well-matched, interacting parts that contribute to the basic function, wherein the removal of any one of the parts causes the system to effectively cease functioning."[24]

The McGrews are looking for some property of biological systems upon which the design hypothesis confers greater probability than its naturalistic competitors. This sounds reasonable until one considers such properties more carefully. For the McGrews specified complexity is disallowed because it is a statistical property that depends on Fisher's approach to hypothesis testing, and they regard this approach as not rationally justified (which in The Design Inference I argue it is once one introduces the notion of a probabilistic resource). What they apparently fail to realize, however, is that any property of biological systems upon which a design hypothesis confers greater probability than a naturalistic competitor must itself presuppose specified complexity.

Ultimately what enables irreducible complexity to signal design is that it is a special case of specified complexity. Behe admits as much in his public lectures whenever he points to my work in The Design Inference as providing the theoretical underpinnings for his own work on irreducible complexity. The connection between irreducible complexity and specified complexity is easily seen. The irreducibly complex systems Behe considers require numerous components specifically adapted to each other and each necessary for function. On any formal complexity-theoretic analysis, they are complex. Moreover, in virtue of their function, these systems embody independently given patterns that can be identified without recourse to actual living systems. Hence these systems are also specified. Irreducible complexity is thus a special case of specified complexity.

But the problem goes even deeper. Name any property of biological systems that favors a design hypothesis over its naturalistic competitors, and you will find that what makes this property a reliable indicator of design is that it is a special case of specified complexity -- if not, such systems could readily be referred to chance. William Paley's adaptation of means to ends,[25] Harold Morowitz's minimal complexity,[26] Marcel Schutzenberger's functional complexity,[27] and Michael Behe's irreducible complexity all, insofar as they reliably signal design, have specified complexity at their base. Thus, even if a likelihood analysis could coherently assign probabilities conditional upon a design hypothesis (a claim I disputed earlier), the success of such an analysis in detecting design would depend on a deeper probabilistic analysis that finds specified complexity at its base. Consequently, if there is a way to detect design, specified complexity is it.

Let me conclude with a reality check. Often when likelihood theorists try to justify their methods, they reluctantly concede that Fisherian methods dominate the scientific world. For instance, Howson and Urbach, in their Bayesian account of scientific reasoning, concede the underwhelming popularity of Bayesian methods among working scientists.[28] Likewise, Richard Royall, who is the statistical authority most frequently cited by Sober, writes: "Statistical hypothesis tests, as they are most commonly used in analyzing and reporting the results of scientific studies, do not proceed ... with a choice between two [or more] specified hypotheses being made ... [but follow] a more common procedure...."[29] Royall then outlines that common procedure as specifying a chance hypothesis, using a test-statistic to identify a rejection region, checking whether the probability of that rejection region under the chance hypothesis falls below a given significance level, determining whether a sample falls within that rejection region, and if so rejecting the chance hypothesis.[30] In other words, the sciences look to Ronald Fisher and not to Thomas Bayes for their statistical methodology. The smart money is therefore on specified complexity -- and not a likelihood analysis -- as the key to detecting design and turning intelligent design into a full-fledged scientific research program.


1. Branden Fitelson, Christopher Stephens, and Elliott Sober, "How Not to Detect Design -- Critical Notice: William A. Dembski, The Design Inference," Philosophy of Science 66 (1999): 472-488.

2. Ibid., 487.

3. Ibid.

4. Elliott Sober, "Testability," Proceedings and Addresses of the American Philosophical Association 73(2) (1999): 47-76.

5. In Sober's account, probabilities are conferred on observations. Because states of affairs constitute a broader category than observations, in the interest of generality I prefer to characterize the likelihood approach in terms of probabilities conferred on states of affairs.

6. Elliott Sober, Philosophy of Biology (Boulder, Colo.: Westview, 1993), 30-36.

7. Fitelson et al.,  "How Not to Detect Design," 475.

8. Fitelson et al.,  "How Not to Detect Design," 474.

9. According to the New York Times (23 July 1985, B1): "The court suggested -- but did not order -- changes in the way Mr. Caputo conducts the drawings to stem 'further loss of public confidence in the integrity of the electoral process.' ... Justice Robert L. Clifford, while concurring with the 6-to-0 ruling, said the guidelines should have been ordered instead of suggested." The court did not conclude that cheating was involved, but merely suggested safeguards so that future drawings would be truly random.

10. See Laurence Tribe's analysis of the Dreyfus affair in "Trial by Mathematics: Precision and Ritual in the Legal Process," Harvard Law Review 84 (1971): 1329-1393.

11. Sober, Philosophy of Biology, 33.

12. See Simon Singh, The Code Book: The Evolution of Secrecy from Mary Queen of Scots to Quantum Cryptography (New York: Doubleday, 1999), 19.

13. This epiphenomenal riding of chance on design is well-known. For instance, actuaries, marketing analysts, and criminologists all investigate probability distributions arising from the actions of intelligent agents (e.g., murder rates). I make the same point in The Design Inference (46-47). Fitelson et al.'s failure to recognize this point, however, is no criticism of my project: "Dembski treats the hypothesis of independent origination as a Chance hypothesis and the plagiarism hypothesis as an instance of Design. Yet, both describe the matching papers as issuing from intelligent agency, as Dembski points out (47). Dembski says that context influences how a hypothesis gets classified (46). How context induces the classification that Dembski suggests remains a mystery." ("How Not to Detect Design," 476) There is no mystery here. Context tells us when the activity of an intelligent agent has a well-defined probability distribution attached to it.

14. Ernest Vincent Wright, Gadsby (Los Angeles: Wetzel, 1939).

15. Sober, "Testability," 73, n. 20.

16. Hume himself rejected induction as sufficient for knowledge and regarded past experience as the source of a non-reflective habituation of belief.

17. Thomas Reid argued as much over 200 years ago: "No man ever saw wisdom, and if he does not [infer wisdom] from the marks of it, he can form no conclusions respecting anything of his fellow creatures.... But says Hume, unless you know it by experience, you know nothing of it. If this is the case, I never could know it at all. Hence it appears that whoever maintains that there is no force in the [general rule that from marks of intelligence and wisdom in effects a wise and intelligent cause may be inferred], denies the existence of any intelligent being but himself." See Thomas Reid, Lectures on Natural Theology, eds. E. Duncan and W. R. Eakin (1780; reprinted Washington, D.C.: University Press of America, 1981), 56.

18. Fitelson et al. ("How Not to Detect Design," 475) write, "We do not claim that likelihood is the whole story [in evaluating Chance and Design], but surely it is relevant." In fact, a likelihood analysis is all they offer. What's more, such an analysis comes into play only after all the interesting statistical work has already been done.

19. Stephen C. Meyer, "DNA by Design: An Inference to the Best Explanation for the Origin of Biological Information," Rhetoric & Public Affairs 1(4) (1998): 519-556.

20. Michael Polanyi, "Life Transcending Physics and Chemistry," Chemical and Engineering News (21 August 1967): 54-66; Michael Polanyi, "Life's Irreducible Structure," Science 113 (1968): 1308-1312.

21. Fitelson et al. ("How Not to Detect Design," 479) regard this as an impossible task: "We doubt that there is any general inferential procedure that can do what Dembski thinks the [criterion of specified complexity] accomplishes." They regard it as "enormously ambitious" to sweep the field clear of chance in order to infer design. Nonetheless, we do this all the time. This is not to say that we eliminate every logically possible chance hypothesis. Rather, we eliminate the ones relevant to a given inquiry. The chance hypotheses relevant to a combination lock, for instance, do not include a chance hypothesis that concentrates all the probability on the actual combination. Now it can happen that we may not know enough to determine all the relevant chance hypotheses. Alternatively, we might think we know the relevant chance hypotheses, but later discover that we missed a crucial one. In the one case a design inference could not even get going; in the other, it would be mistaken. But these are the risks of empirical inquiry, which of its nature is fallible. Worse by far is to impose as an a priori requirement that all gaps in our knowledge must ultimately be filled by non-intelligent causes.

22. Ibid., 486.

23. Lydia McGrew, "Likely Machines: A Response to Elliott Sober's 'Testability'," typescript, presented at conference titled Design and Its Critics (Mequon, Wisconsin: Concordia University, 22-24 June  2000).

24. Michael Behe, Darwin's Black Box (New York: Free Press, 1996), 39.

25. See the watchmaker argument in William Paley, Natural Theology: Or Evidences of the Existence and Attributes of the Deity Collected from the Appearances of Nature, reprinted (1802; reprinted Boston: Gould and Lincoln, 1852), ch. 1.

26. Harold J. Morowitz, Beginnings of Cellular Life: Metabolism Recapitulates Biogenesis (New Haven, Conn.: Yale University Press, 1992), 59-68.

27. Interview with Marcel Sch�tzenberger, "The Miracles of Darwinism," Origins and Design 17(2) (1996): 11.

28. Colin Howson and Peter Urbach, Scientific Reasoning: The Bayesian Approach, 2nd ed. (La Salle, Ill.: Open Court, 1993), 192.

29. Richard Royall, Statistical Evidence: A Likelihood Paradigm (London: Chapman & Hall, 1997), 61-62.

30. Ibid., 62