Figure 8.1 represents the EF as it has been variously described by Dembski (1998a, 1998b, 1999, 2002b). It is appropriate to modify a model system in response to criticism or as a reflection of changes in your thought, and Dembski's inconsistencies are not pointed out as criticisms per se. Rather, my intent is to relate the various explanatory filters as they have evolved.

I begin on the left side of figure 8.1, with Dembski's (1998c) questions: "(1) Does a law explain it? (2) Does chance explain it? (3) Does design explain it?" He continues: "I argue that the Explanatory Filter is a reliable criterion for detecting design. Alternatively, I argue that the Explanatory Filter successfully avoids false positives. Thus whenever the Explanatory Filter attributes design, it does so correctly" (107).

The central portion of figure 8.1 reflects the EF of Dembski (1999), where it was presented as a conventional flowchart. Here we note two important refinements: the notions of complexity and specification. The probabilistic nature of Dembski's argument is fully realized in No Free Lunch (2002b), represented on the right side of figure 8.1.

To implement the EF, we begin with the observation of an event. If no natural law-like explanation for the event is possible, Dembski asks whether there is a chance explanation. If no chance explanation is possible, then

Dembski decides that the event is the result of design. Design in the model is the default result when natural and chance explanations fail.

The notion of specified complexity provides a more-positive criterion. Dembski draws on Behe (1996) and his notion of irreducible complexity by equating specified complexity with irreducible complexity as the signature of design. Dembski (1998a, 46-47) offers an example of the EF's design detection in which a teacher receives two nearly identical student papers. He proposes two hypotheses: independent authorship and plagiarism. Dembski assigns independent authorship as the chance hypothesis and plagiarism as the design hypothesis, even though both outcomes are the result of intelligent action.

This assignment raises two significant points. First, Dembski admits that context determines how these hypotheses are to be classified as chance or design, leaving significant ambiguity in the classification. Second, his example fails to consider relevant alternate hypotheses: the students collaborated, the papers were nearly identical because of limited school resources, both students plagiarized a third party, or both were independently assisted by a third party (such as a tutor) and had no knowledge of the other's paper. These possibilities are all distinct from Dembski's plagiarism (design) hypothesis contrasted with his independent authorship (chance) hypothesis, which presumes that the students randomly generated identical papers and that the exclusive alternative is design.

Considering Dembski's plagiarism example, Fitelson et al. (1999) observe:

It is important to recognize that the Explanatory Filter is enormously ambitious. You don't just reject a given Regularity hypothesis: you reject all possible Regularity explanations (Dembski 1998:53). And the same goes for Chanceâ€”you reject the whole category: the Filter "sweeps the field clear" of all specific Chance hypotheses (Dembski 1998:14, 52-53). We doubt that there is any general inferential procedure that can do what Dembski thinks the Filter accomplishes. (3)

They further point out: "Suppose you have in mind just one specific regularity hypothesis that is a candidate for explaining [event] E: you think that if E has a regularity-style explanation, this has got to be it. If E is a rare event, the filter says to conclude that E is not due to Regularity. This can happen even if the specific hypothesis, when conjoined with initial condition statements, predicts E with perfect precision" (3). The periodic observations of comets are a powerful example of rare natural events due to necessity, which, before Edmond Halley's research, were widely considered supernatural phenomena.

Without complete knowledge of all possible hypotheses, we cannot correctly assign chance and design hypotheses within the explanatory filter. It is entirely unclear how or even whether Dembski's explanatory filter could deal with multiple hypotheses, although Elliott Sober (in press) presents a likelihood method for detecting design that could offer some help to the EF. It is trivial to propose situations in which applying the EF serially to all possible hypotheses would require infinite time.

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