Design Arguments and the Existence of God: Sober's Trilemma

Design arguments for the existence of human (and human-like) watchmakers are often unproblematic; it is design arguments for the existence of God that leave us at sea. - Sober.

Design arguments for the existence of God typically cite physical features of the world that have the appearance of design (perhaps means-end behavior, information-rich complexity, relevance to life-permitting conditions, or something else) and argue that God's creative activity is the best explanation for these features. If certain cases of apparent design are best explained by actual design -- in specific, the design of an immaterial, transcendent person -- then apparent design becomes evidence for actual design. In what follows, I refer to the hypothesis which claims that some feature of the world was designed by a supernatural designer as the "design hypothesis."

Elliot Sober has argued that design arguments face the following Trilemma [1]:

1.  Either (a) the design hypothesis is uninformative, (b) ad hoc/question-begging or (c) has no more predictive power than certain naturalistic hypotheses.
2. If either (a) or (b) or (c), then apparent design does not support design over non-design.
3. (Therefore) apparent design does not support design over non-design.

Consider premise 1. Let E represent a proposition describing some apparently designed feature of the world, and let D be the design hypothesis. Finally, let N be some naturalistic alternative to D. Sober maintains that we can determine whether E evidentially favors D over N by comparing the likelihoods of D and N -- Pr(E|D) and Pr(E|N), respectively. E favors D over N, just in case the following inequality holds:

(1) Pr(E|D) > Pr(E|N) [2]

However, before we can discern the value of Pr(E|D), Sober argues that D needs to specify the powers and intentions of the designer (p. 36). If D is merely the hypothesis that God exists, we'd be left wondering whether D makes E likely or not. That God exists tells us nothing about whether he wanted to design things like this or like that. Sober's principle can be stated as follows:

• The Powers/Intentions Requirement for Design Inferences: a value for Pr(E|D) (or a contrastive judgment about the inequality in (1)) is discernable only if D specifies the powers and intentions of the relevant designer. In non-probabilistic terms, we can discern D's predictive power for E only if D says something about the powers and intentions of the designer.

Hence, if theism does not specify the powers and intentions of God, it is predictively uninformative. That gives us the first disjunct of the trilemma. 

Suppose the theist accepts the above requirement and builds into her hypotheses any auxiliary assumptions necessary to entail E -- i.e., she makes it part of her hypothesis that God wants to design things as they appear. In that case, Pr(E|D) = 1. But if the theist can make this move, Sober argues, the proponent of non-design may do so as well (p. 39). Why would this dialectical move be available to the proponent of design and not to the naturalist? The naturalistic could just as easily add to N any conditions necessary and sufficient to entail E. Consequently, Pr(E|D) = Pr(E|N) and E would not support D over N (non-probabilistically: D would have no more predictive power than N). This gives us the third disjunct of premise 1.

To summarize the challenge thus far, the design hypothesis needs to specify the designers intentions and powers, otherwise it is uninformative. However, if it includes auxiliaries that entail E, the naturalist is rationally permitted to modify N so that it does so as well. 

Of course, the trouble with adding just any auxiliary assumptions is that, unless justified, doing so will either be question-begging or ad-hoc (p 36). Can the proponent of design add the auxiliaries needed to make her hypothesis informative without making her hypothesis ad hoc or question-begging? Sober thinks not. His reasoning here turns on his view of ad hocness:

• Sober's principle of ad hocness: auxiliary assumption, A, is not ad-hoc vis-a-vis hypothesis H and evidence E only if we have independent justification (evidence other than E) for A.

So if we lack independent justification for A, inclusion of it into our hypotheses will be ad hoc. And as Sober argues, we don't have independent reason to think God would want to create things any particular way. After all, God is supposedly radically different than any designers we're familiar with. If so, why think he would intend to design things the way we find them? Why think he’d want to design things the way humans would want to. And we can't use the apparently designed features themselves as justification for thinking God would have the intention to design things as they are or else right back to the question-begging problem. Again independent reasons are needed for thinking an intentions/powers pair is plausible.

If these considerations hold, then the inequality in (1) will not hold (or, at least, we have no grasp on what it is) and, hence, apparent design will not support the design hypothesis over non-design hypotheses.

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[1] This blog summarizes Sober’s argument in, "The Design Argument" (2003) in God and Design: The Teleological Argument and Modern Science. 

[2] In this case, E may even be evidence against N, if Pr(E|N) < Pr(E|~N). However, since Sober thinks we have no grasp on prior probabilities -- more strongly, that there are no objective prior probabilities, except for frequency data (p. 28) -- it follows that we cannot say whether N goes up or down in probability. The same goes for D. Probabilities rise or fall relative to a prior distribution and after conditionalizing on new information. So likelihood evaluations of the design argument will not tell us if D is more probable than not after conditionalization. In fact, even if Pr(E|D) > Pr(E|N), E might disconfirm D, since it could be that Pr(E|~D) > Pr(E|D). The upshot of likelihood evaluations, according to Sober, is that we are rationally permitted to increase our credence in D (without saying what the final probability is), if the above inequality holds (pp. 28-29). This suggests that Sober must be working with a extra-Bayesian (or non-Bayesian) confirmation-theoretic commitments.