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 complexityspecification 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(XN) 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(XN) < 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(XN), 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(XN) < 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(Xn),
which is most likely to be considerably less than P(XN).
In some cases this limitation of knowledge
might be inconsequential. If we know enough to make the calculated value of
P(Xn) > 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(XN), 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 complexityspecification
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 selforganizational 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 Dembskidefined 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(Xn) 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 nonnatural 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 complexityspecification criterion. How did he do the
computation, and what is the standing of his conclusion?
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 Contributed by: Dr. Howard Van
Till
