Is atheism a scientific perspective?

[Angrboda]

The Specification Condition

To reject Chance, the evidence E must be “specified.” This involves four conditions -- CINDE, TRACT, DELIM, and the description D* that you use to delimit E must have a low probability on the Chance hypothesis. We consider these in turn.

CINDE

Dembski says several times that you can’t reject a Chance hypothesis just because it says that what you observe was improbable. If Jones wins a lottery, you can’t automatically conclude that there is something wrong with the hypothesis that the lottery was fair and that Jones bought just one of the 10,000 tickets sold. To reject Chance, further conditions must be satisfied. CINDE is one of them.

CINDE means conditional independence. This is the requirement that Pr(E | H & I) = Pr(E | H), where H is the Chance hypothesis, E is the observations, and I is your background knowledge. H must render E conditionally independent of I. CINDE requires that H capture everything that your background beliefs say is probabilistically relevant to the occurrence of E.

CINDE is too lenient on Chance hypotheses -- it says that their violating CINDE suffices for them to be accepted (or not rejected). Suppose you want to explain why Smith has lung cancer (E). It is part of your background knowledge (I) that he smoked cigarettes for thirty years, but you are considering the hypothesis (H) that Smith read the works of Ayn Rand and that this helped bring about his illness. To investigate this question, you do a statistical study and discover that smokers who read Rand have the same chance of lung cancer as smokers who do not. This study allows you to draw a conclusion about Smith -- that Pr(E | H&I) = Pr(E | not-H &I). Surely this equality is evidence against the claim that E is due to H. However, the filter says that you can’t reject the causal claim, because CINDE is false -- Pr(E | H&I) [is not equal to] Pr(E | H).6

TRACT and DELIM

The ideas examined so far in the Filter are probabilistic. The TRACT condition introduces concepts from a different branch of mathematics – the theory of computational complexity. TRACT means tractability – to reject the Chance hypothesis, it must be possible for you to use your background information to formulate a description D* of features of the observations E. To construct this description, you needn’t have any reason to think that it might be true. For example, you could satisfy TRACT by obtaining the description of E by “brute force” – that is, by producing descriptions of all the possible outcomes, one of which happens to cover E (150- 151). Whether you can produce a description depends on the language and computational framework used. For example, the evidence in the Caputo example can be thought of as a specific sequence of 40 Ds and 1 R. TRACT would be satisfied if you have the ability to generate all of the following descriptions: “0 Rs and 41 Ds,” “1 R and 40 Ds,” “2 Rs and 39 Ds,” ... “41 Rs and 0 Ds.”

Whether you can produce these descriptions depends on the character of the language you use (does it contain those symbols or others with the same meaning?) and on the computational procedures you use to generate descriptions (does generating those descriptions require a small number of steps, or too many for you to perform in your lifetime?). Because tractability depends on your choice of language and computational procedures, we think that TRACT has no evidential significance at all. Caputo’s 41 decisions count against the hypothesis that he used a fair coin, and in favor of the hypothesis that he cheated, for reasons that have nothing to do with TRACT. The relevant point is simply that Pr(E|Chance) << Pr(E|Design). This fact is not relative to the choice of language or computational framework.

The DELIM condition, as far as we can see, adds nothing to TRACT. A description D*, generated by one’s background information, “delimits” the evidence E just in case E entails D*. In the Caputo case, TRACT and DELIM would be satisfied if you were able to write down all possible sequences of D’s and R’s that are 41 letters long. They also would be satisfied by generating a series of weaker descriptions, like the one just mentioned. In fact, just writing down a tautology satisfies TRACT and DELIM (165). On the assumption that human beings are able to write down tautologies, we conclude that these two conditions are always satisfied and so play no substantive role in the Filter.

Do CINDE, TRACT, and DELIM “Call the Chance Hypothesis into Question”?

Dembski argues that CINDE, TRACT and DELIM, if true, “call the chance hypothesis H into question.” We quote his argument in its entirety:

"The interrelation between CINDE and TRACT is important. Because I is conditionally independent of E given H, any knowledge S has about I ought to give S no knowledge about E so long as --- and this is the crucial assumption --- E occurred according to the chance hypothesis H. Hence, any pattern formulated on the basis of I ought not give S any knowledge about E either. Yet the fact that it does in case D delimits E means that I is after all giving S knowledge about E. The assumption that E occurred according to the chance hypothesis H, though not quite refuted, is therefore called into question." (147)

Dembski then adds:

"To actually refute this assumption, and thereby eliminate chance, S will have to do one more thing, namely, show that the probability P(D* | H), that is, the probability of the event described by the pattern D, is small enough." (147)

We'll address this claim about the impact of low probability later.

To reconstruct Dembski's argument, we need to clarify how he understands the conjunction TRACT & DELIM. Dembski says that when TRACT and DELIM are satisfied, your background beliefs I provide you with “knowledge” or “information” about E (143, 147). In fact, TRACT and DELIM have nothing to do with informational relevance understood as an evidential concept. When I provides information about E, it is natural to think that Pr(E | I) [is not equal to] Pr(E); I provides information because taking it into account changes the probability you assign to E. It is easy to see how TRACT & DELIM can both be satisfied by brute force without this evidential condition's being satisfied. Suppose you have no idea how Caputo might have obtained his sequence of D's and R's; still, you are able to generate the sequence of descriptions we mentioned before. The fact that you can generate a description which delimits (or even matches) E does not ensure that your background knowledge provides evidence as to whether E will occur. As noted, generating a tautology satisfies both TRACT and DELIM, but tautologies don't provide information about E.

Even though the conjunction TRACT & DELIM should not be understood evidentially (i.e., as asserting that Pr[E | I] [is not equal to] Pr[E]), we think this is how Dembski understands TRACT & DELIM in the argument quoted. This suggests the following reconstruction of Dembski's argument:

   CINDE, TRACT, and DELIM are true of the chance hypothesis H and the agent S.

   If CINDE is true and S is warranted in accepting H (i.e., that E is due to chance), then S should assign Pr(E | I) = Pr(E).

   If TRACT and DELIM are true, then S should not assign Pr(E | I) = Pr(E).

   Therefore, S is not warranted in accepting H.

Thus reconstructed, Dembski's argument is valid. We grant premiss (1) for the sake of argument. We've already explained why (3) is false. So is premiss (2); it seems to rely on something like the following principle:

(*) If S should assign Pr(E|H&I) = p and S is warranted in accepting H, then S should assign Pr(E|I) = p.

If (*) were true, (2) would be true. However, (*) is false. For (*) entails

If S should assign Pr(H|H) = 1.0 and S is warranted in accepting H, then S should assign Pr(H) = 1.0.

Justifiably accepting H does not justify assigning H a probability of unity. Bayesians warn against assigning probabilities of 1 and 0 to any proposition that you might want to consider revising later. Dembski emphasizes that the Chance hypothesis is always subject to revision.

It is worth noting that a weaker version of (2) is true:

(2*) If CINDE is true and S should assign Pr(H)=1, then S should assign Pr(E | I) = Pr(E).

One then can reasonably conclude that

(4*) S should not assign Pr(H) = 1.

However, a fancy argument isn’t needed to show that (4*) is true. Moreover, the fact that (4*) is true does nothing to undermine S's confidence that the Chance hypothesis H is the true explanation of E, provided that S has not stumbled into the brash conclusion that H is entirely certain. We conclude that Dembski's argument fails to “call H into question.”

It may be objected that our criticism of Dembski's argument depends on our taking the conjunction TRACT & DELIM to have probabilistic consequences. We reply that this is a charitable reading of his argument. If the conjunction does not have probabilistic consequences, then the argument is a nonstarter. How can purely non-probabilistic conditions come into conflict with a purely probabilistic condition like CINDE? Moreover, since TRACT and DELIM, sensu strictu, are always true (if the agent's side information allows him/her to generate a tautology), how could these trivially satisfied conditions, when coupled with CINDE, possibly show that H is questionable?

How Not to Detect Design