Is the flagellum complex? General considerations

Recall that, according to Dembski, to say that any biotic system X (such as the bacterial flagellum) is complex is to say that the probability of its actualization (its coming to be assembled or constructed as a distinct biotic structure) must be less than the “universal probability bound,” a = 10 ^{- 150}; or, to say it more concisely, X is complex if P(X) < a. Note that this makes the “complexity” of X a property, not of X itself, but of the means by which it came to be actualized. This unorthodox employment of the word complexity is an essential element in Dembski’s case for intelligent design.

Dembski’s criterion for complexity is quite easy to state, but that does not mean that it is equally easy to apply. The principal difficulty arises when we examine precisely what has to be taken into account when P(X), the probability that X will be actualized, is computed (or estimated). Two considerations lead me to the same conclusion regarding what factors the computation P(X) must take into account.

First, Dembski calls attention to the importance of computing P(X) in the context of all available “probabilistic resources that describe the number of relevant ways an event might occur.”“The important question therefore is not What is the probability of the event in question? but rather What does its probability become after all the relevant probabilistic resources have been factored in?”In the context of applying the complexity-specification criterion, the relevant probability is the probability that X came to be actualized as the outcome of unguided natural processes, whether these are a) pure chance phenomena, b) regularities described by deterministic natural laws, or c) the joint action of chance and regularity. For the sake of convenience, let us use the notation P(X|N) to denote the probability that X will be actualized by the joint action of all relevant natural processes, N. (Remember that this “N” is what Dembski most often, but not always, means by the term, “chance hypothesis.”) The complexity requirement can now be stated more clearly as: X is complex if P(X|N) < a.

Second, when Dembski develops his mathematical system for dealing with the role of natural processes in generating complex specified information (equivalent to specified complexity) he argues that “stochastic processes (representing nondeterministic natural laws and therefore the combination of chance and necessity) ... constitute the most general mathematical formalism” for dealing with both chance and necessity at the same time. “Natural causes are properly represented by nondeterministic functions (stochastic processes).”For the moment I need not agree at all with the way in which Dembski argues his case that “natural causes are incapable of generating complex specified information.” (In fact, I will later argue that natural causes can have the effect of making the generation of specified complexity wholly unnecessary.) The important consideration for the moment is simply to note that in determining the complexity of some X, all relevant natural causes - what Dembski often calls the “chance hypothesis,” or the joint action of both chance and necessity - must be taken into account. In Dembski’s system, testing for the presence of specified complexity must be done in the context of assessing the potential contributions of all relevant natural causes to the actualization of the object in question.

By either route, we come to the same conclusion: To determine if X is complex (using Dembski’s meaning of the term rather than common usage) we need to compute the value of P(X|N), the probability that X could be actualized by the joint action of all relevant natural processes - all pure chance opportunities, all regularities described by deterministic laws, all contingent histories influenced by evolutionary algorithms, and the like. If this P(X|N) < a, then Dembski counts X as exhibiting sufficient complexity to proceed with the question regarding its specification.

But there is, of course, an obvious epistemic difficulty here. In no case do we know with certainty all relevant natural ways in which some biotic system may have historically come to be actualized. If “N” represents all relevant natural causes, both known and unknown, and if we use a lower case “n” to designate only those natural causes that are known to be relevant, then it is clear that the best we can do is calculate P(X|n), which is most likely to be considerably less than P(X|N).

In some cases this limitation of knowledge might be inconsequential. If we know enough to make the calculated value of P(X|n) > a, then the question of complexity can be settled (X is not complex) without an exhaustive knowledge of all relevant natural processes. But what if our knowledge is inadequate to do the probability calculations? What if, for instance, we were able to propose one or more plausibility arguments regarding the kinds of natural processes that are likely to contribute to P(X|N), but were not yet able to translate these arguments into numerical values for probability?

Dembski does seem to recognize this as a problem when he remarks, “Now it can happen that we may not know enough to determine all the relevant chance hypotheses [which here, as noted above, means all relevant natural processes (hvt)]. 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.”In principle, this epistemic problem should introduce a considerable degree of modesty in all assessments of probability values related to the question of the complexity of any particular biotic system. Complexity - in the unorthodox sense that Dembski wishes to use this term in his complexity-specification criterion - is an elusive quality. Our ability to determine the presence or absence of it is severely hampered by our limited state of knowledge regarding the specific way in which natural causes have contributed to the formation of biotic structures.

One thing we can say, however, is that the more we learn about the self-organizational and transformational feats that can be accomplished by biotic systems, the less likely it will be that the conditions for complexity - as Dembski employs this term in relation to specified complexity - will be satisfied by any biotic system.For example, in reference to the power of evolutionary algorithms - natural processes that effectively search for increasingly better performance at some task - Dembski acknowledges that “An evolutionary algorithm acts as a probability amplifier. ... But a probability amplifier is also a complexity diminisher.”This is true not only for evolutionary algorithms, but for any natural cause that functions to explore the “possibility space” of useful biotic systems and to submit novel variations to the test of viability.

On numerous occasions Dembski asserts, in effect, that “natural causes cannot generate specified complexity.” Given the definition of specified complexity, however, such statements are, at best, only trivially true. They are nothing more than tautological statements. The principal requirement for exhibiting specified complexity is the requirement that some structure/system cannot be (or is highly unlikely to be) actualized by natural causes. The question is, however, Are there any actual objects that demonstrate this quality? If there are no biotic systems that actually have this Dembski-defined quality of specified complexity, then there would be no need to “generate” it in the first place.

The subtitle of No Free Lunch is Why Specified Complexity Cannot Be Purchased Without Intelligence. Why not? Because “cannot be purchased without intelligence” is effectively included in the definition of specified complexity! Demonstrating that some object actually exhibits specified complexity depends upon the prior demonstration that natural causes are effectively unable (because of improbability barriers) to actualize that object. The trivial truth of ID’s fundamental proposition lies in carefully crafted definitions.

In the absence of a full knowledge of the universe’s formational capabilities, computed values for P(X|n) might give the appearance of complexity where there is no actual complexity. The appearance of complexity in the absence of actual complexity constitutes a false positive indication of the need for non-natural action. In the light of later discoveries of previously unknown natural formational or transformational processes, this apparent complexity would simply vanish like ground fog vaporized in the warmth of sunlight.

And if no biotic systems have this quality of complexity, and thus no specified complexity, then Dembski’s prohibitions regarding their natural formation are inconsequential. All of the biotic systems relevant to biotic evolution are free to form as naturally as biologists have long proposed. No free lunch available? No problem; no lunch needed.

But what about the bacterial flagellum in particular? Dembski is quite confident that he has demonstrated that it is more than sufficiently complex (difficult to assemble naturally) to satisfy the complexity portion of the complexity-specification criterion. How did he do the computation, and what is the standing of his conclusion?

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