Baggett's and Wall's Proposed IBE Criteria

In an earlier post, I attempted to steelman the abductive moral argument set forth by David Baggett and Jerry Walls (hereafter, "B&W") in their book God and Cosmos. In this post, I want to pick up where that post left off and turn to my second question for evaluating the schema of B&W's schema for their abductive moral argument. Recall that my second question was as follows:

Are the proposed criteria for explanation candidates meaningful, unambiguous, and justified?

With that question in mind, then, let us review what B&W have to say about the matter. In their book, they write:

Abductive criteria for narrowing the field of explanation candidates down to one can vary, but here is one attempt at it: (1) explanatory power; (2) explanatory scope; (3) plausibility; (4) degree of "ad hoc-ness"; and (5) conformity with other beliefs. The more explanatory power and scope and the more plausibility and conformity with other beliefs an explanation has, the better an explanation it is. The less ad hoc (adjusted, contrived, artificial) the explanation, the better as well. The trick is to subject all the explanation options to these tests in order to pick the one that is the best--and therefore the most likely true--explanation. (18)

The Meaning of B&W's IBE Criteria

Let us start with the meaning of the individual criteria. In doing so, I am going to largely endorse the objections made by Robert Greg Cavin and Carlos Colombetti (hereafter, "C&C") against William Lane Craig's IBE argument for the historicity of the resurrection of Jesus. Despite the obvious differences between that argument and B&W's moral argument, their list of IBE criteria has much in common. If, as I believe, Craig's IBE criteria are problematic, those same criteria in B&W's IBE argument will also be problematic.

"Explanatory Scope" and "Explanatory Power": Both Craig and B&W include in their criteria "explanatory scope" and "explanatory power," but this is problematic. And so paraphrasing what C&C write (regarding Craig's argument) and applying it to B&W yields the following.

B&W are unclear regarding how the criteria of explanatory scope and explanatory power (henceforth, scope and power) are to be interpreted and how these differ. Are they independent? If not,

then how are they related? B&W do not say. Their use of the word "more" suggests that, perhaps, B&W interpret scope and power as being roughly quantitative. But, given that this is so, then, to be clear, B&W needs to explain whether and, if so, how power thus interpreted differs from power as this is understood by other leading proponents of T such as Swinburne and the McGrews -- viz., as the Bayesian likelihoods of T and its rivals. B&W's insufficiently clear IBE approach fails to show how scope and power are interrelated — a deficiency that can be rectified by the Bayesian approach. Thus, on the Bayesian approach, the scope and power of any hypothesis Hi are most naturally interpreted as correlative aspects of the Bayesian likelihood P(E|B&Hi), i.e., the degree to which it is rational to believe evidence E on the basis of Hi in conjunction with background information B. On this interpretation, the scope of Hi is the range of facts contained in E in the term P(E|B&Hi) — the greater the range of facts, the greater the scope. Correlatively, the power of Hi is the magnitude of the term P(E|B&Hi) itself — the degree of likelihood that Hi confers on E — the greater the magnitude, the greater the power. The Bayesian approach shows why these are not independent criteria, contrary to how B&W seem to treat them. For, in general, the greater/lesser the scope, the lesser/greater the power, i.e., the greater/fewer the number of facts stated in E, the lower/higher the value of P(E|B&Hi). This is not to deny that Hi may be so strong that it can attain relatively great scope and power simultaneously. But, nonetheless, if the scope is increased, then the power must decrease, and vice versa — if only minutely. (paraphrase of C&C)

"Plausibility": The meaning of "plausibility" is also problematic. And so paraphrasing what C&C write (regarding Craig's argument) and applying it to B&W yields the following.

B&W's IBE approach requires that hypotheses be compared on the basis of what they call “plausibility.” But what is plausibility and how is it to be assessed? Quoting Alvin Plantinga, B&W concede that "part of what makes an explanation good or bad is its [antecedent] probability" (20). This is just what Bayesians call "prior probability." After all, the plausibility of a hypothesis is surely a function of what the hypothesis states and of the background information relevant to it; but this is precisely the same for prior probability. Furthermore, both are matters of degree. Indeed, apart from there being a formalism for one and not the other, they seem indistinguishable. It thus seems entirely natural to identify the plausibility of any hypothesis Hi (e.g., T) with its prior probability P(Hi|B), i.e., the degree to which it is rational to believe Hi solely on the basis of B. Identifying plausibility with prior probability provides a clear interpretation of this notion. Thus, for example, the plausibility of the hypothesis that Galileo would be charged with heresy is simply its prior probability and is thus determined in precisely the same way — using the same background information. Moreover, prior probability has the advantage of occurring within a Bayesian framework that gives it a more precise function in determining the probability of a hypothesis on the total evidence for it. What B&W mean by plausibility seems indistinguishable from prior probability. (paraphrase of C&C)

There is an important difference between the Resurrection explanation (R), "God raised Jesus from the dead," and the explanation of classical theism (T), which I take B&W to define as something like the proposition, "There exists the greatest possible being who exemplifies all the great-making properties to the greatest maximal degree and to the greatest extent to which they're mutually consistent with one another."[1] Because T is a potential "ultimate" metaphysical explanation, there are no facts in our background information, extrinsic to the definition of T, which could affect the plausibility or prior probability of T. Only the content of T itself can affect T's prior probability. But because the content is "intrinsic" to T, it makes more sense to speak of T's "intrinsic probability" rather than its "prior probability." Although I won't defend these claims here, I believe the following two statements are true:

1. Intrinsic probability is determined by modesty, coherence, and nothing else.
2. The intrinsic probability of T is much lower than the intrinsic probability of naturalism, but not hopelessly lower.

"Degree of Ad Hoc-ness": B&W appeal to "degree of ad hoc-ness." I have no objection to how they define it, but I do wonder how "degree of ad hoc-ness" differs from "plausibility." As before, it seems to me that the Bayesian approach here is superior to the IBE approach. Suppose we make a distinction between a "core" hypothesis, such as classical theism, and an auxiliary hypothesis, such as Christian theism. If we wanted to determine if Christian theism were ad hoc, we could look at two things First, we could assess the prior probability of Christian theism conditional upon our background knowledge (including, for the sake of argument, classical theism). Second, we could assess whether there is any independent evidence for the auxiliary hypothesis, by using P(I|B&Christian Theism), where I represents "independent evidence, that is, evidence independent of the evidence for classical theism" and B represents our background knowledge. In my opinion, this is much more clear than the IBE approach favored by B&W.

"Conformity with Other Beliefs": This criterion seems clear enough; I have no "in principle" objection to it. In practice, I wonder how B&W will apply this criterion to the rival explanations they consider. But we may leave that topic for another time.

Summary

B&W explicitly state they intend their argument to be understood as an IBE. Their proposed IBE criteria are problematic in large part because most of them contain varying degrees of ambiguity. I believe that all of these ambiguities could be clarified by eschewing an IBE approach and instead adopting a Bayesian approach.

Notes

[1] See David Baggett and Jerry Walls, Good God: The Theistic Foundations of Morality (New York: Oxford University Press, 2011), 52. Given that "classical theism" is B&W's preferred explanation for the facts about morality which they believe require an explanation, it strikes this writer as extremely odd that an explicit definition of "classical theism" appears nowhere to be found in their later book, God and Cosmos. At the time I wrote this blog post, I had read up to page 79 of the latter. I would have expected to find an explicit definition by this point in the book.