Informal Statement of the Argument
If there is a single theme unifying the history of science, it is that naturalistic explanations work. The history of science contains numerous examples of naturalistic explanations replacing supernatural ones and no examples of supernatural explanations replacing naturalistic ones. Indeed, naturalistic explanations have been so successful that even most scientific theists concede that supernatural explanations are, in general, implausible, even on the assumption that theism is true. Such explanatory success is antecedently more likely on naturalism–which entails that all supernaturalistic explanations are false–than it is on theism. Thus the history of science is some evidence for naturalism and against theism.
Formal Statement of the Argument
physical entity: the kind of entity studied by physicists or chemists. Examples of physical entities include atoms, molecules, gravitational fields, electromagnetic fields, etc.
causally reducible: X is causally reducible to Y just in case X’s causal powers are entirely explainable in terms of the causal powers of Y.
ontologically reducible: X is ontologically reducible to Y just in case X is nothing but a collection of Ys organized in a certain way.
natural entity: an entity which is either a physical entity or an entity that is ontologically or causally reducible to a physical entity.
nature: the spatio-temporal universe of natural entities.
Note: there may be additional entities currently unknown to physics but which may be discovered in the future. If and when such entities are discovered, they may be called physical and natural based on their relationship to known physical or natural entities. Thus, this definition of “nature” may only capture nature as currently understood.
supernatural person: a person that is not part of nature but can affect nature. Examples of supernatural persons include God, angels, Satan, demons, ghosts, etc.
non-natural entity: any entity that is not a natural entity. There are two kinds of non-natural entities: personal and impersonal. Personal non-natural entities are supernatural persons or agents. Impersonal non-natural entities are abstract objects.
presumption of naturalism: prior to investigation, the probability that the immediate cause of any given natural event is very high.
modest methodological naturalism: scientific explanations may appeal to the supernatural only as a last resort.
naturalistic explanation: a non-supernatural explanation.
Note: a common misunderstanding is the idea that a “naturalistic explanation” means an explanation based on metaphysical naturalism. That is not how “naturalistic explanation” is used here. Rather, a naturalistic explanation simply means any explanation that does not appeal to supernatural agency.
B: The Relevant Background Information
1. The universe is intelligible.
E: The Evidence to be Explained
1. So many natural phenomena can be explained naturalistically, i.e., without appeal to supernatural agency.
2. The history of science contains numerous examples of naturalistic explanations replacing supernatural ones and no examples of supernatural explanations replacing naturalistic ones.
Rival Explanatory Hypotheses
T: theism: the hypothesis that there exists an omnipotent, omniscient, and morally perfect person (God) who created the universe.
N: metaphysical naturalism: the hypothesis that the universe is a closed system, which means that nothing that is not part of the natural world affects it.
The Argument Formulated
(1) E is known to be true.
(2) Pr(E | B & N) >! Pr(E | B & T).
(3) T is not much more probable intrinsically than N.
(4) Therefore, other evidence held equal, T is probably false.
Defense of (2)
N entails that any true explanations must be naturalistic ones. Thus, on the assumption that N is true, we have an extremely strong reason to expect that successful scientific explanations will be naturalistic ones. In contrast, if T is true, then it could have been the case that that successful scientific explanations were supernatural explanations. For example, biology could have discovered that all animals are not the relatively modified descendants of a common ancestor; neuroscience could have discovered no correlations at all between human minds and brains, etc. If the history of science were like that, then that would have supported T over N. But then the success of science in finding naturalistic explanations must be evidence for N over T. How strong is this evidence? I agree with Draper: “the more likely it is that there are true naturalistic explanations for natural phenomena (i.e., the stronger the presumption of naturalism), the more unlikely it is that there are supernatural beings.”
Objections to AHS
Objections to (2)
Objection: AHS “depends on conflating the old pagan religions and animisms with the Abrahamic religious beliefs. . . . [T]here is a clear distinction between those who believed in the old gods and spirits, and those who held to the Judeo-Christian notion of a transcendent and eternal Creator God. What ended the attribution of supernatural causes to natural processes wasn’t the advent of rationalism through the science but the spread of Christianity and it’s adherence to a transcendent Creator God who acted uniquely in history to create a universe that acted in accordance with certain laws and principles.”
Reply: This reply confuses the distinction between what we might call the “socio-historical explanation” for E with its “metaphysical explanation.” The spread of Christianity is an example of the former, while AHS is focused on the latter. Even if that socio-historical explanation for E is correct, it doesn’t follow that T, much less Christian theism, is correct. The objection notes that the universe acts “in accordance with certain laws and principles.” That fact is irrelevant to AHS, which explicitly includes the intelligibility of the universe in its background information. At best, the fact of the intelligibility of the universe might provide evidence favoring T over N. It does not in any way undermine the claim that, given that the universe acts in accordance with certain laws and principles, the fact that science has been so successful in providing natural explanations for natural phenomena is evidence favoring N over T. To deny this point is to commit the fallacy of understated evidence.
Objection: “For at least fifteen hundred years countless theologians have developed what I call transcendent agent models of divine action in the world which view God as the primary metaphysical agent of all natural events in a way that is completely consistent with the advance of scientific [naturalistic] explanation in its proper sphere. So once again, and for good measure, the advance of science in its proper sphere which it has rightfully claimed from other disciplines, provides no evidence that those other disciplines do not have their proper spheres. And thus it provides no evidence that theism is false or that naturalism is true.”
Reply: On the assumption that theism is true, what reason is there to believe that transcendent agent (TA) models of divine action in the world are true? Is there any reason that is independent of the success of non-supernatural explanations?
Pr(A | T) = Pr(A | T) x Pr(E | A & T) + Pr(~A | T) x Pr(E | T & ~A)
In the context of explanatory arguments, Draper calls that theorem the “weighted average principle” (WAP). As Draper points out, this formula is an average because Pr(A | T) + Pr(~A | T) = 1. It is not a simple straight average, however, since those two values may not equal 1/2; that is why it is a weighted average. The higher Pr(A | T), the closer Pr(E | T) will be to Pr(E | A & T); similarly, the higher Pr(~A | T), the closer Pr(E | T) will be to Pr(E | T & ~A).WAP shows that, in order to be successful, an objection to an evidential argument must do more than simply identify an auxiliary hypothesis which can explain the data. The objection must also provide an antecedent reason for thinking that A is true, i.e., a reason for thinking that A is more probable given the core hypothesis–in this case, theism–than given the negation of the core hypothesis. Without such a reason, the objection reduces to the fact that E is merely logically compatible with the core hypothesis (in this case, T), which is no objection at all to an evidential argument.
For this reason, then, this objection is, at best, incomplete. It successfully identifies a relevant auxiliary hypothesis (A), but does not (yet) provide an antecedent reason for expecting that hypothesis to be true, on the assumption that theism is true.
Objection: Theologians had Biblical reasons for adopting A.
Reply: “Biblical reasons for adopting a TA model” are evidentially relevant if and only if the pattern of probability relations specified by the Weighted Average Principle (WAP) are satisfied. Unless there is an antecedent reason to think that such Biblical reasons are more probable than not, on the assumption that theism is true, there is no reason to think A refutes premise (2) of AHS.
Objection: Theologians also had countless philosophical and theological reasons as well. For instance, TA models flow naturally from a commitment to divine simplicity and atemporality, two mainstays of classical theism. So theologians prior to the rise of science had many reasons to endorse A.
Reply: The claim, “TA models flow naturally from a commitment to divine simplicity and atemporality,” is just that: a claim, an assertion, in need of support.
Objection: Naturalism is unable to explain some 20th-century scientific discoveries, ranging from what happens to when one shoots a photon into space to certain 20th-century scientific discoveries, such as cosmological fine-tuning.
Reply: First, metaphysical naturalism neither logically entails nor makes probable the claim that metaphysical naturalism itself is the explanation for everything studied by the sciences. Rather, metaphysical naturalism entails that all true scientific explanations are non-supernatural explanations. According to (2), the fact that so many true scientific explanations are non-supernatural explanations is antecedently much more probable on the assumption that metaphysical naturalism is true than on the assumption that theism is true.
Similarly, the fact that non-supernatural explanations have replaced supernatural explanations, while no supernatural explanations have replaced non-supernatural explanations, is antecedently much more probable on the assumption that metaphysical naturalism is true than on the assumption that theism is true.
Second, I don’t rule out that the possibility that scientific discoveries, such as cosmological fine-tuning, could provide evidence for theism and against naturalism. Indeed, I’ve blogged on The Secular Outpost about Draper’s argument from moral agency for theism and against naturalism. I’ve gone so far as to call that argument the best argument for theism. None of this, however, undermines the conclusion of AHS, which is that the history of science is prima facie evidence against theism. The words “prima facie” are important because they highlight that the argument assesses the evidential impact of one item of evidence only. To put the point another way, AHS doesn’t claim to examine the total available relevant evidence. It’s possible that both the argument from moral agency and AHS are correct. Indeed, it’s possible that both are correct, but the former outweighs the latter!
 See Keith M. Parsons, Science, Confirmation, and the Theistic Hypothesis (Ph.D. Dissertation, Kingston, Ontario, Canada: Queen’s University, 1986), 46; Paul Draper, “Evolution and the Problem of Evil” in Philosophy of Religion: An Anthology (3rd ed., ed. Louis Pojman, Wadsworth, 1997), 223-24; and idem, “God, Science, and Naturalism” Oxford Handbook of Philosophy of Religion (ed. William Wainwright, Oxford: Oxford University Press, 2004), 38-39; and Barbara Forrest, “Methodological Naturalism and Philosophical Naturalism: Clarifying the Connection” Philo 3 (2000): 7-29.
 Draper 2004.
 Draper 2004.
 Jack Hudson, “Arguments for God: The Historically Unique Nature of God.” Wide as the Waters (August 10,2010), http://jackhudson.wordpress.com/2010/08/10/the-historically-unique-nature-of-creation/(spotted June 16, 2012).
 Paul Draper, “Partisanship and Inquiry in the Philosophy of Religion,” unpublished paper. Cf. Draper 2004, 43-44.
 Randal Rauser, “A Critical Look at Jeff Lowder’s Evidential Argument from the History of Science.” Randal Rauser (July 13, 2012), http://randalrauser.com/2012/07/a-critical-look-at-jeff-lowders-evidential-argument-from-the-history-of-science/(spotted July 13, 2012).
 Paul Draper, “Pain and Pleasure: An Evidential Problem for Theists” Noús 23 (1989): 331-50 at 340.
 Draper 1989.
 Draper 1989.
Tyson, Neil deGrasse. “The Perimeter of Ignorance.” Natural History Magazine (November 2005).