Since Michael Martin begins his chapter on atheistic teleological arguments (ATAs) with a discussion of Wesley Salmon’s 1978 article, “Religion and Science: A New Look at Hume’s Dialogues,” let us review Salmon’s argument. My goal now is simply to figure out what Salmon’s argument is; I will defer an assessment of Salmon’s argument until later. Some readers, especially those who are not philosophers or who are not familiar with the different interpretations of probability–may just want to skip this summary and jump straight to the later post in this series which gives the logical form of Salmon’s argument.
It is unfortunate (and inconvenient) that Salmon never explicitly stated the logical form of his argument in his 1978 article. For that reason, then, I’ll attempt to provide a summary of his article, without commentary, before offering what I consider to be the logical form of Salmon’s argument.
Salmon’s article divides into ten sections:
1. The Design Argument
2. Causal Hypotheses and Bayes’s Theorem
3. Philo’s Estimates
4. The Uniqueness of the Universe
5. Order and Purpose
6. The Concept of Order
7. Modern Cosmology
8. Assessment of the Hypothesis
9. The Relevance of the Scientific Evidence
10. Postscript: Hume’s Intentions
Here is a brief summary of each section.
(1) The Design Argument: Salmon sets the stage for his argument by reviewing Hume’s discussion of the design argument in his Dialogues Concerning Natural Religion. Philo, presumably speaking for Hume, focuses on “experimental theism,” viz., “the thesis that the existence of God can be approached as a scientific hypothesis, and that His existence can be established with a high degree of confirmation by observational evidence.” According to Salmon, Hume recognized that design arguments must be evaluated the same way we evaluate “causal hypotheses in science” (170).
(2) Causal Hypotheses and Bayes’s Theorem: Salmon’s stated preference for analyzing causal hypotheses is to use Bayes’s theorem. Let A be any instance of coming-into-being; B be any instance of the operation of intelligence; and C be any instance that exhibits order or design. Finally, let Pr-F represent a probability value, as interpreted by the frequency interpretation of probability, viz., the limit of the relative frequency. We can then use Bayes’s theorem to analyze the proportion of entities in B which occur in the total sample space, which is defined by A & C:
The value on the left-hand side of Bayes’s Theorem, Pr-F(B | A & C), is the final or posterior probability. Salmon identifies the three values that must be known in order to determine this value:
(a) Prior probability of B: In symbols, this is Pr-F(B | A); in English, this is the probability that an instance is the operation of intelligence, conditional upon that instance being an entity which comes into being. As Salmon correctly points out, if we know this value then we can easily calculate the other prior probability: Pr-F(~B | A) = 1 – Pr-F(B | A).
(b) Likelihood of C: In symbols, this is Pr-F(C | A & B); in English, this is the probability that an entity exhibits order, conditional upon that entity being a result of intelligence, i.e., intelligent design.
(c) Likelihood of ~C: In symbols, this is Pr-F(C | A & ~B); in English, this is the probability than an entity exhibits order, conditional upon that entity not being the result of intelligent design.
While major figures in inductive logic disagree about the best way to interpret these probability values (e.g., classical, frequency, epistemic, etc.), according to Salmon many such figures have accepted the use of Bayes’s theorem to assess scientific hypotheses.
(3) Philo’s Estimates: Salmon’s belief is that Hume addressed the three types of probability values just listed in order to assess theism using Bayes’s theorem, despite Hume’s apparent ignorance of it. Salmon then proceeds to summarize how Philo assessed the requisite values to apply Bayes’s Theorem to the hypothesis of intelligent design.
(a) Prior probability of B. Salmon explained that Philo identified four types of causation:
(i) order resulting from reproductive biological causation (hereafter, “biological generation”);
(ii) order resulting from non-reproductive biological causation, e.g., bees making honeycombs, spiders making spider webs, etc. (hereafter, “instinct”);
(iii) mechanical causation, e.g., formation of snowflakes, galaxies, etc. (hereafter, “mechanical order”); and
(iv) intelligent design.
Given the sheer quantity of known entities which fall into types (i), (ii), and (iii), Philo argued, the prior probability–i.e., the limit of the relative frequency–of something coming into being as the result of intelligence is “incredibly small” while the prior probability of its denial is high (174). As Salmon points out, the quantity of entities of type (iii), includes the number of galaxies (10 billion), stars (10-100 billion per galaxy), and atoms (1050 atoms in our sun alone), is now known to be much greater than what Hume supposed.
(b) Likelihood of C. Salmon, like Hume, acknowledges this value may be “quite high,” but points out the posterior probability of B “may still be quite low” if Pr-F(~B | A) and Pr-F(C | A & ~B) are large enough (175). According to Salmon, “Philo brings out these considerations quite explicitly” (175).
(c) Likelihood of ~C. As Salmon correctly points out, Philo provided evidence that this value is not negligible, given his examples of reproductive biological, non-reproductive biological, and mechanical causation.
Salmon concludes that Hume provided arguments to justify all of the values “which appear on the right-hand side of Bayes’s theorem” (175). Accordingly, if we apply Bayes’s theorem to “an unspecified entity, which came into being and exhibited order,” the (frequency) probability that it “was produced by intelligent design is rather low” (175).
(4) The Uniqueness of the Universe: Based on the results of the previous section, one might be tempted to construct a Bayesian argument against theism, based upon the evidence that the universe is an object exhibiting order. Salmon correctly points out, however, the matter “cannot be settled that easily” (176): the event of the creation of the universe is a single case. Salmon is well aware that single case probabilities are notoriously problematic in probability theory, especially for the frequency interpretation of probability, which is Salmon’s interpretation. The general rule for dealing with single case probabilities, as he puts it, “is to refer to the individual case to the broadest homogeneous class available–i.e., to the broadest class that cannot be relevantly subdivided” (176).
Let’s suppose that Salmon is right about (i) and (ii). What, then, is the “broadest homogeneous reference class” for the event of the creation of the universe, according to Salmon? He doesn’t say explicitly. As I read him, he seems to consider three possible answers. Let us consider each in turn.
(a) The Disembodied Designer Option. Traditional theism defines God as, among other things, a disembodied mind. So this option identifies the broadest homogeneous reference class to be artifacts produced by a disembodied intelligence. Using that reference class, Salmon argues that “since disembodied intelligence has never operated in any fashion,” the relative frequency of artifacts resulting from disembodied intelligence is zero. Hence, Pr-F(B | A) = 0. Pr-F(C | B & A) is undefined.
(b) The Mechanical Order and Design Hypothesis without Moral Attributes Option: Let M represent mechanical order. Since M entails ~B, M is logically equivalent to M & ~B. According to Salmon, that the prior probability of mechanical order is equal to or greater than the prior probability of intelligent design sans moral attributes, i.e., Pr-F(M | A) >= Pr-F(B | A). Furthermore, the likelihood of the order exhibited by the universe is equal on both the mechanical hypothesis and the design hypothesis (sans moral attributes), i.e., Pr-F(C | M & A) = Pr-F(C | A).
(c) The Mechanical Order and Design Hypothesis with Moral Attributes Option: Let O represent the hypothesis that the intelligent designer is omnibenevolent. If we include moral attributes in the definition of the intelligent designer, Salmon argues, then the intelligent design hypothesis has a lower likelihood than the mechanical hypothesis, i.e., Pr-F(C | M & A) > Pr-F(C | O & B & A).
How does Salmon support that judgment of likelihood values? By employing a probabilistic argument about apparently gratuitous evil. Salmon points out that Philo, in the eleventh dialogue, asks if empirical facts about the world are what we would antecedently expect on theism. Philo then lists four ways in which an all-powerful creator could have reduced the amount of evil in the world if He had wanted to: (i) pain need not be inflicted upon man; (ii) God need not have governed the world by inviolable general laws; (iii) God could have endowed human beings and other species with additional abilities to make their existence less hazardous; and (iv) God could have better designed the universe so that the “springs and principles” of nature do not run into one of the 2 extremes of “feast or famine.” Salmon concludes that Pr(B & O | A & C) is very low.
If the prior probability of M and B & O are equal but M has a higher likelihood, then it follows that the mechanical hypothesis has a higher posterior probability than the moral designer hypothesis (i.e., theism), i.e., Pr-F(M | A & C) > Pr(B & O | A & C).
(5) Order and Purpose: In Hume’s Dialogues, Cleanthes’ most careful statement of the design argument “describes the universe as a ‘great machine,’ composed of a prolific array of ‘lesser machines,’ all of which are characterized by ‘the curious adapting of means to ends'” (182). In other words, Cleanthes “appeals to a teleological conception of order” in his defense of the design argument (182). Philo, however, responded to Cleanthes by pointing out that equating order and design “flagrantly begs the question” (183). Salmon contends that the theist who proclaims that the order exhibited by the universe is evidence of intelligent design must make an “a priori announcement,” an “anthropomorphic concept” which the proponent of “experimental theism” eschews (183).
According to Salmon, Hume’s eighth dialogue contains “a rather clear anticipation of a non-teleological theory of biological evolution” (183). Just as Galileo and Newton removed Aristotelian teleological conceptions from physics, Salmon argues, Darwin “rid the biological sciences of their teleological elements.” Salmon concludes, “Order in the physical world, and in its biological realms, was shown to be independent of intelligent design” (183).
(6) The Concept of Order: In this section, Salmon delivers the clarified concept of order he promised earlier in section 3. According to Salmon, the universe exhibits two kinds of order: (i) physical objects obey physical laws; and (ii) the universe “exhibits an orderly configuration” (184).
Furthermore, Salmon writes, scientists have developed the concept of entropy, which turns out to be useful for clarifying the kind of order we find in the world. Entropy, he says, is “a measure of the unavailability of energy to do mechanical work” (185). Thus, to say that the entropy of the universe is low “is tantamount to saying that the universe contains large stores of available energy” (185). Using statistical interpretations of thermodynamics and entropy, scientists discovered that low entropy is associated with non-random, highly ordered arrangements, which are relatively improbable, while high entropy is associated with random, unordered arrangements which are relatively probable.
If we apply the concept of entropy to the role “order” plays in the design argument, Salmon says, we can determine the percentage of physical systems which “come into being in low entropy states” and which “are created with conscious design” (186). What is that percentage? According to Salmon, “An exceedingly small proportion of low entropy systems–i.e., systems which are highly organized and orderly–result from an interaction with the environment which involves any conscious purpose or design.”
(7) Modern Cosmology: Relying upon physicist Steven Weinberg, Salmon rehearses the state of modern cosmology in 1978, which includes scientific evidence (a) for Big Bang cosmology; and (b) regarding the number of galaxies (10B), stars per galaxy (10B), and atoms per star (1050). Salmon takes this to be unparalleled in human history. He asks, “Where in the annals of human history can we find like numbers of systems created in low entropy states by conscious human intervention?” (187).
(8) Assessment of the Hypothesis: Salmon summarizes his assessment of the scientific evidence; he concludes that modern scientific evidence pushes “the posterior probability of intelligent design even closer to zero” (188).
(9) The Relevance of the Scientific Evidence: Salmon concludes that his analysis of the scientific evidence “tend[s] to show that there is no intelligent creator [of the universe] (although it is admittedly irrelevant to other theological hypotheses)” (189).
(10) Postscript: Hume’s Intentions: Salmon attempts to defend his interpretation of Hume. Since I am uninterested in that topic, I will not summarize this section.
 Salmon did not label his argument an “atheistic teleological argument;” in fact, so far as I can tell, Salmon did not name his argument at all. The name was coined by Michael Martin in his Atheism: A Philosophical Justification (Philadelphia: Temple University Press, 1990).
 Wesley Salmon, “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. Further references will be provided in the body of this article.
 I owe this formulation of Salmon’s classes to Sally Ferguson, “Bayesianism, Analogy, and Hume’s Dialogues Concerning Natural Religion,” Hume Studies 28:1 (April 2002): 113-130 at 119.
 Wesley Salmon, The Foundations of Scientific Inference (Pittsburgh: University of Pittsburgh Press, 1967), 90-93.
 Salmon 1967, 91-92.
 As Salmon notes, Carl G. Hempel argued for a similar requirement, his requirement of maximal specificity. Cf. Carl G. Hempel, Aspects of Scientific Explanation (New York: Free Press, 1965), 397-403, cited in Salmon 2006, 192, n. 14.
 Although Salmon states, “It is crucial to realize that Philo is not raising the traditional theological problem of evil” (178), I interpret this to mean that Philo is not raising the logical argument from evil.
 O is my invention; I have inserted O into the expression in order to make explicit the role of the designer’s moral attributes. Salmon’s article keeps that implicit and so he writes about Pr(B | A & C). Also, I am unsure which interpretation of probability Salmon had in mind when he wrote that Pr(B | A & C) is low. In the rest of the article, he employs a frequency interpretation, but his reference to “antecedently expect” followed by a listing of four reasons seems to make more sense on an epistemic interpretation than on a frequency interpretation.
 It might be more accurate to say that Galileo and Newton removed the need for a Platonic teleology (i.e., teleology put there by a divine intelligence), not an Aristotelian teleology.