Two general comments. First, I am uninterested in matters of Salmon’s interpretation of Hume, so I’m going to skip over that issue in its entirety. Second, it seems to me that the idea of using a frequency interpretation of probability for assigning probability values to ultimate metaphysical posits is fundamentally misguided; I think the epistemic interpretation of probability would be much more appropriate for the context.
A. The Argument Against an Unspecified Intelligent Designer
Since Salmon himself admits that the posterior probability of the single case of the creation of the universe “cannot be settled” (176) by this argument, I am going to skip this argument.
B. The Argument Against a Disembodied Designer
A: any instance of coming-into-being
B : any instance of the operation of intelligence
C: any instance that exhibits order or design
D: the hypothesis that the hypothesized intelligent designer is a disembodied mind. Note that D entails B; hence, Pr(D) <= Pr(B).
U: the event of the creation of the universe.
Pr(x)=y: the probability of x equals y,
Pr-F: indicates a probability value as interpreted by the frequency theory, i.e., the limit of the relative frequency
Here is the argument:
(1) For the single case of the creation of the universe, the limit of the relative frequency of artifacts produced by a disembodied intelligence is zero, i.e., Pr-F(B & D | A) = 0.
(2) Pr-F(C | A & B & D & U) is undefined.
Again, I find it difficult to make sense of the point of Salmon’s discussion regarding the limiting relative frequency of disembodied designers. He explicitly claims that the prior probability, Pr-F(B & D | A), is zero, but it’s unclear what role this claim or premise plays in any of his arguments. For now, I am simply going to evaluate that premise. Here are three objections.
First, either A includes U or it does not. If it includes U, then (1) begs the question against design theorists by assuming that the creation of the universe is not the result of an intelligent designer, which is precisely the point in dispute. If, however, A does not include U, then it seems to me that A is not the broadest homogeneous reference class. Recall the definition of a broadest homogeneous reference class: in Salmon’s own words, it is “the broadest class that cannot be relevantly subdivided” (176). But it seems to me that A can be “relevantly subdivided,” namely into the following two sub-classes:
A1: any instance of coming-into-being in space and time
A2: any instance of spacetime itself (i.e., the universe itself) coming-into-being
Even if Pr-F(B & D | A1) =0, it doesn’t follow that Pr-F(B & D | A2) = 0.
Second, the claim that Pr-F(B & D | A1) = 0 assumes that all instances of coming-into-being in space and time are not the result of intelligent design. I do not find support for that assumption in Salmon’s writings.
Third, it’s far from obvious that the frequency of A2 is even relevant to A1; if it is, this needs to be shown, not assumed.
I conclude that Salmon’s premise regarding the prior probability of disembodied design is, at best, unsupported.
C. Argument for Explanatory Parity of Mechanical Causation and Intelligent Design
Since this argument is not an argument against intelligent design, I am going to skip this argument.
D. Argument Against Theistic Intelligent Design
As I noted earlier, the crux of this argument is Salmon’s probabilistic argument from apparently gratuitous evil for atheism. In my opinion, Alvin Plantinga destroyed Salmon’s argument. Since I agree with his refutation and have nothing to add to it, I will simply refer interested readers to Plantinga’s article.
E. Argument Against Theism
Again, here is the argument:
(1) The hypothesis of intelligent design is antecedently implausible because it is in direct conflict with a large body of well-established theory.
(2) The intelligent design hypothesis makes the occurrence of the facts to be explained quite improbable if it is true.
(3) There is a plausible alternative hypothesis (i.e., the mechanical hypothesis) which makes the facts to be explained highly probable.
(4) Therefore, theism is very improbable.
Again, I am not entirely sure if it is accurate to attribute this argument to Salmon; as I wrote earlier, section 8 of his article merely suggests the argument. I have two worries about this argument. First, it seems that Salmon has failed to support (1), i.e., that the hypothesis of intelligent design “is in direct conflict with a large body of well-established theory” (188). It is unclear what Salmon takes to be the “large body of well-established theory” which makes the hypothesis of intelligent design, theistic or otherwise, “antecedently implausible.” If he has in mind the concept of disembodied intelligence, then we have seen that his claim begs the question against the theist.
If, on the other hand, he has in mind the concept of entropy (see section 8 of his essay), then (1) is also unsupported. Recall that Salmon himself identified two different kinds of order: (i) physical objects obey physical laws; and (ii) the universe “exhibits an orderly configuration” (184). Entropy is, at best, only capable of providing a mechanical explanation for the second type of order. Entropy cannot be used to provide a mechanical explanation for the first type of order since entropy is rooted in the laws of thermodynamics, which are an example of the first type of order. Thus, not only does the concept of entropy fail to show that the order exhibited by the universe is improbable if theism is true, but an appeal solely to the concept of entropy ignores the order made possible by physical laws. Salmon has provided no reason to think that physical laws themselves, including the laws of thermodynamics, are the products of mechanical causation.
Second, the only support which Salmon provides for (2) is his failed attempt at a frequentist probabilistic argument from evil, mentioned earlier.
Since Salmon has failed to support (1) and (2), I conclude, then, that this argument fails.
 For a critical response, see Ferguson 2002.
 Lewis 1982 makes this point at length.
 Cartwright 1978, 180; cf. Harris 2002, 253-54, and Shalkowski 2001.
 Plantinga 1979, 31-44.
Cartwright, Nancy. “Comments on Wesley Salmon’s ‘Science and Religion …’” Philosophical Studies 33 (1978): 177-183.
Ferguson, Sally. “Bayesianism, Analogy, and Hume’s Dialogues Concerning Natural Religion.” Hume Studies 28:1 (April 2002): 113-130.
Harris, James Franklin. Anglo-American Analytic Philosophy of Religion (Boston: Kluwer Academic, 2002).
Lewis, Delmas. “On Salmon’s Attempt to Redesign the Design Argument.” International Journal for Philosophy of Religion 13:2 (1982): 77-84.
Plantinga, Alvin. “The Probabilistic Argument from Evil,” Philosophical Studies 35 (1979): 1-53.
Salmon, Wesley. “Religion and Science: A New Look at Hume’s Dialogues.” In Michael Martin and Ricci Monier, The Improbability of God (Buffalo: Prometheus, 2006), 167-93. Originally published in Philosophical Studies 33 (1978): 143-76.
—. “Experimental Atheism.” Philosophical Studies 35 (1979): 101-104.
Shalkowski, Scott. “Atheistic Teleology.” Croatian Journal of Philosophy 1:1 (2001): 5-19.