Recently a criticism was leveled against Dembski’s 2005 paper Specification: the pattern that signifies intelligence. As is often the case, if you read the criticism carefully, you will realize that, even though he says Dembski is wrong, it turns out that the more exacting answer would favor Dembski’s conclusion *more* strongly, not less.

In the blog *The Dread Tomato Addiction*, professional biostatistician Dan Eastwood claims that Dembski’s paper is fundamentally flawed.

Most people use the term “fundamentally flawed” to refer to flaws that are not merely minor mistakes or oversimplifications, but rather to things which are unrecoverable. In this case, it is not a mistake, and, if it is an oversimplification, it is certainly an oversimplification that Dembski made *in favor of his critics*.

Eastwood criticizes Dembski’s formula for estimating the chance occurrence of an event E adjusted for complexity and opportunity. The formula being criticized is here:

M * N * Phi(T) * P(T|H)

If I ever get the LaTeX plugin installed, the better typeset version will be:

$$ M \cdot N \cdot \phi_S(T)\cdot\mathrm{P}(T\vert\mathrm{H}) $$

In any case P(T|H) is the base probability of a target, Phi(T) is the descriptive complexity of the target, M is the number of attempters and N is the number of attempts each one makes.

The criticism of Eastwood is that multiplying Phi(T)*P(T|H) by these other factors doesn’t leave us with a probability, because they are merely positive integers, and it leaves open the possibility of a probability greater than one.

However, he seems to be not understanding how proofs are done. Dembski, here, is not giving the actual probability, instead he is giving an *upper bound* on the probability, which Dembski says explicitly in his paper, using the term “bounded above.” Strangely, Eastwood later realizes this, but continues to criticize despite the fact that his own criticism has been undercut!

In fact, not only is Dembski employing a simple upper bounding technique, it is one of the oldest upper bounding techniques in probability history – Boole’s inequality.

Boole’s inequality simply states that if you have a set of probabilities, the probability of the union of those probabilities is going to be less than their sum. This is exactly what Dembski is doing. Since each chance is Phi(T)*P(T|H), then making M*N attempts means that each of those attempts will be Phi(T)*P(T|H). Therefore, the sum of all of those probabilities will be M*N*P(T|H), which, according to Boole’s inequality, is greater than or equal to the actual probability.

As you can see, using one of the oldest statistics upper bounding methods in history is not an error, it is just statistics. If you were to calculate the probability exactly, I believe it would just be (1 – (1 – Phi(T)*P(T|H))^(M*N)). However, this is much harder to calculate and compare with. That is why Dembski chooses instead to upper bound it – it makes direct comparisons of other quantities much easier.

So, in short, by using an upper-bounding technique, Dembski is actually *limiting* the power of CSI. The case is actually stronger than what Dembski points out. Eastwood is complaining that Dembski’s paper is “fundamentally flawed” by doing this. However, for the “flaw” that Eastwood points out, the paper’s estimates are actually in Eastwood’s favor already, and if they were corrected they would flow in Dembski’s direction, not Eastwood’s.

I always find it amusing when Darwinists slam Intelligent Design for errors, but if you look at their corrections, the result is just as bad as before, and, in this case, worse. For instance, attempting to criticize Behe, Durrett and Schmidt point out that Behe was **wrong**, **wrong**, **wrong** about his probability estimates of mutations, while simultaneously pointing out that his conclusion (that such events are “very unlikely to occur on a reasonable timescale”) is 100% correct.

If one Darwinist gives an estimate, and another Darwinist later gives a more accurate estimate, that is considered a simple improvement. If an ID’er gives an estimate, and a Darwinist later gives a more accurate estimate, despite it pointing to the same conclusion, that is considered a rebuttal and a disproof.

Hey, if you can’t score goals against your opponent, I guess you can at least score own goals.