Can we prove the efficacy of prayer?
Is it possible to demonstrate that praying affects the outcome of the matter prayed for, makes it more likely to occur? A number of studies have been made that seek to answer this question, or at least to provide evidence one way or another.
But prior to making or considering any such studies, what should we expect from them a priori?
In the previous blogpost, on praying for temporal goods, I argued that, if holiness does not correlate with an increase in any particular temporal goods such as health, wealth, intelligence, or the like, then we should not expect prayer to, in general, merit any increase in such goods, but only to help ensure that our use of those goods, or our way of dealing with a lack of those goods, helps us to attain heaven.
Here I give another argument that our a priori expectation should be that such studies of prayer will long-term be inconclusive or find no evidence for the efficacy of prayer, because God respects not only natural causes and laws that act necessarily, but also natural causes that act for the most part and the corresponding statistical laws.
To show that prayer is efficacious means showing that, under given conditions X, when Y is prayed for (in manner M), after controlling for the influence of the prayer on the prayer P, who makes the prayer, and any involved subjects S, who hear the prayer, Y is more likely to occur than when Y is not prayed for (in manner M). (Strictly speaking, even this won't strictly show that prayer is efficacious by reason of a non-human or supernatural power, as the prayer could be efficacious in virtue of a mental or spiritual influence of the subjects P and S on the person or thing prayed for.)
For example, if, in given weather conditions, when a farmer prays for rain it is more likely to rain within the next two weeks than when he does not pray, this shows the efficacy of his prayer, at least unless his prayer itself is partly caused by a modification of the conditions insufficiently controlled for, e.g., if he prays when he feels "in his bones" that it is high time for rain.
Or again, if patients overall have a 35% chance of recovery from a given illness in a given condition overall or when their recovery is not prayed for, and a 37% chance when their recovery is prayed for, after controlling for any direct influence of the prayer upon the patient by way of his knowing that someone his praying for him, of the doctor's who treat him knowing that someone his praying for him, etc., this would demonstrate the efficacy of prayer for healing.
A strict demonstration of the efficacy of prayer in this sense seems impossible without a miracle of providence or something approaching thereto. By that I mean the happening/working of an event possible in itself, yet with a chance less than 1 over the the number of events occurring in the entire observable history of the universe. For example, tossing a dice 1000 times in a manner such as to actually give it each time an equal probability of each number from one to six, yet in fact always getting three. Since nature is a principle not only of what is necessary, but also of what is for the most part, such an occurrence is as much praeter or contra naturam as any event such as the instantaneous regrowth of a limb.
A true demonstration of the efficacy of prayer would involve an event (or conglomerate of events considered as one) with just such a low probability. For, given that one has indeed controlled for all natural confounding factors, the efficacy of prayer would be demonstrated in that, e.g., the persons prayed for recover more frequently than the odds given all natural causes, and that in a long-term consistent manner. For 37 out of 100 persons to recover given that each has a 35% chance, has a significant chance of happening, for 370 out of 1000 a significant, but significantly smaller chance, for 3,700 out of 10,000 an even lower chance, and so on. So, for this sort of thing to happen consistently is humanly speaking certain not to happen by natural causes, and is thus a miracle of providence.
Now, given a context in which miracles of the obvious sort are rare, whether that is because God generally upholds the laws of nature he created, or because God is "a God who hides himself", it seems most reasonable to assume that miracles of providence will be similarly rare.
Consequently, to claim to a scientist, "when you consider the results when people are prayed for, you can conclude with certainty that a non-human or supernatural being is involved in answering prayers," is making as much a claim to God's working a miracle in the case as to claim "when you consider the result you're about to see — this person's arm, which was amputated, growing back within one hour — you can conclude with certainty that a non-human or supernatural being did it."
If this argument is right, our a priori expectation should be that all studies of the efficacy of prayer will, taken together, conclude with either "no evidence for the efficacy" or "inconclusive"; the evidence in the latter case tends either to show that prayer makes the event more likely, or that it makes it less likely, but is in a range that doesn't allow for any conclusion with certainty.
This conclusion may be discomfiting to some, as seeming to deny any value to prayer, but it's significance for prayer is ultimately the same as what was argued for the in the previous blogpost, that we should expect no temporal recompense for either holiness or piety, but only the grace — actual grace and the workings of providence — to use the temporal goods we have so as to attain union with God.