Agency detection

Atheists dismiss reports of answered prayer and miracles as, at best, coincidence. Sometimes they invoke the law of large numbers. 

But do atheists have any principled way to distinguish a coincidence from a noncoincidence? If they don't, then it's arbitrary for an atheist to automatically discount reports of answered prayer or miracles as sheer coincidence. Before proceeding, I'll quote two concrete examples: 

Around the 15-17 min. mark, Licona gives an example:

It's from an atheist. Someone who is today an atheist. Someone who's an atheist today, but when this happened was a Christian:

One time my church desperately needed $7641 in order to keep going. After an all-night prayer meeting my dad [a deacon] went to get the mail, and in it was a check for exactly $7641.00–from somebody who didn't even know the church needed the money, but had heard one of the pastors speak a few years ago. My dad contacted the giver and she said that after she heard the pastor speak she felt God wanted her to put some cash in an annuity and give it to our church. The process took years and just days before she decided to close the account and send the accrued money to the church, and it happened to be the exact amount that was needed–right after an all-night prayer meeting.

https://www.youtube.com/watch?v=IW9w6c2RWmA 

J. P. Moreland:

Now the same thing takes place in specific answers to prayer. To illustrate, early in my ministry, while attending a seminar in Southern California, I heard a presentation on how to pray in a more specific way.

Knowing that in a few weeks, I would be returning to Colorado to start my ministry at the Colorado School of Mines in Golden with Ray Womack, a fellow Campus Crusade worker, I wrote a prayer request in my prayer notebook — a prayer which was known only to me. I began to pray specifically that God would provide for the two of us a white house that had a white picket fence, a grassy front yard, a close proximity to the campus (specifically, within two or three miles), and a monthly payment that was no more than $130.

I told the Lord that this request was a reasonable one on the grounds that (a) we wanted a place that provided a homey atmosphere for students, was accessible from campus and that we could afford, and (b) I was experimenting with specific prayer and wanted my faith to be strengthened.

I returned to the Golden area and looked for three days at several places to live. I found nothing in Golden and, in fact, I only found one apartment for $135/month about 12 miles from campus. I told the manager that I would take it and she informed me that a couple had looked at the place that morning and had until that afternoon to make a decision. If they didn't want it, then I could move in the next day.

I called late that afternoon and was informed that the couple took the apartment which was the last available one in the complex. I was back to square one. Now remember, not a single person knew that I had been praying for a white house.

That evening, Kaylon Carr (a Crusade friend) called me to ask if I still needed a place to stay. When I said yes, she informed me that earlier that day, she had been to Denver Seminary. While there, she saw a bulletin board on which a pastor in Golden was advertising a place to rent, hopefully to seminary students or Christian workers. Kaylon gave me his phone number, so I called and set up an appointment to meet the pastor at his place at nine the next morning. Well, as I drove up, I came to a white house with a white picket fence, a nice grassy front yard, right around two miles from campus, and he asked for $110 per month rent. Needless to say, I took it, and Ray and I had a home that year in which to minister.

http://www.trueu.org/Academics/LectureHall/A000000425.cfm

1. An atheist might say it's more likely that these are tall tales. But he might resort to the last-ditch position that even if they happened, it's just a coincidence. But if that's a coincidence, what is not a coincidence? What's their criterion to distinguish random from nonrandom events? If they can't say, then their skepticism is ad hoc. 

2. Many atheists take the position that any naturalistic explanation, however implausible, is more plausible than any supernatural explanation. But a problem with that posture is that it begs the question. If you already know for a fact that we inhabit a world where supernatural events never happen (because there are no supernatural agents), then that makes sense. But what's your evidence that we inhabit a world where supernatural events never happen? You can only use that benchmark to discount reported miracles if all the available evidence counts against reported miracles. Yet reported miracles are prima facie evidence that we don't inhabit a world where supernatural events never happen. So the posture of the atheist is viciously circular. He's artificially privileging some kinds of evidence to preemptively disregard counterevidence. But his starting-point is arbitrary. Why not start with evidence to the contrary? 

Moreover, evidence that we don't inhabit a world where supernatural events occur is, at most, negative evidence. But that's easily overcome by positive evidence to the contrary. 

Talking to a lot of atheists is like talking to a potted plant. At best they're foils. Usually it's a waste of time. They're not listening. 

But that raises the question, Is there a rigorous definition of coincidence? Are there established criteria in the philosophical/mathematical/statistical literature to distinguish a coincidence from a noncoincidence?

3. Christians attribute certain phenomena to supernatural agency. That's a type of personal agency. How do we detect personal agency? When is that inference warranted? 

To take a comparison, suppose I leave a message with my portfolio manager to transfer a sum of money from one account to another. I didn't speak to him directly, and I didn't hear back from him directly. A day later, when I check my accounts, a financial transfer was made for the exact amount. Is that random? Just a coincidence? Does the law of large numbers explain that? 

That's similar to certain kinds of answered prayer. Suppose we made a specific request. Maybe there's a deadline. Something happens to meet the request. It was beyond human ken to coordinate that outcome.  

4. Christians routinely thank God for answering their prayers. There are situations in which what we take to be answered prayer could be something that was going to happen any way. If a Christian apologist is using answered prayer for its evidential value, then he should pick the strongest examples. 

5. We have the intuitive sense that rolling sixes ten times in a row is a suspicious coincidence. Although it's possible, the more likely explanation is that the dice are loaded. If, however, the dice roll sixes a thousand times in a row, then we're convinced the dice are loaded. 

Is this similar to the sorites paradox? There are situations in which we can't specify an exact threshold where something becomes too coincidental to be sheer coincidence, but we can all intuitively identify examples where that's the case. Put another way, while edge cases or borderline cases are tricky, many situations fall well outside those narrow parameters.

6. It's striking how underdeveloped the concept of coincidence is, given how important it is in so many fields that we be able to detect the difference between coincidence and noncoincidence, and how this routinely crops up in debates over miracles, prayers, &c. If I understand him, Bill Dembski takes the position that coincidence is rigorously definable. And there are mathematically stringent criteria to rule in or rule out coincidence. You identify personal agency by eliminating chance. 

By contrast, Timothy and Lydia McGrew reject that paradigm. They still think you can identify personal agency, but they operate with a different paradigm. For different sides of the argument:

William A. Dembski, "Design by Elimination vs. Design by Comparison," (Chapter 33 from The Design Revolution)

  

_____, "Detecting Design by Eliminating Chance: A Response to Robin Collins."

Timothy McGrew, "Toward a Rational Reconstruction of Design Inferences," Philosophia Christi, 7/2 (2005), 253-98.

7. Here's how Lydia McGrew summarizes their position:

The short version of the answer is no, there is not one rigorous definition of notable or striking coincidence. Indeed, to a very large extent what appears to be a coincidence will depend upon one's background information. Take card games. If you don't know the rules of a card game, you won't know what a royal flush is, so the fact that a person gets a royal flush three times in a row won't appear to be a coincidence. And indeed in a game where that arrangement of cards has no special meaning, it would be correct not to think of it as a weird or noteworthy coincidence.

This issue came up quite a lot when Tim and I were working with the Intelligent Design movement and trying to convince the ID folks to abandon William Dembski's error statistical model of design inferences and go with a comparative model instead. The point we made repeatedly is that a pattern is salient in relation to an hypothesis. An hypothesis that competes with chance, one might say. Hence, the repeated royal flush is salient and striking as a suspicious coincidence in relation to the hypothesis of cheating, because we know that the royal flush is advantageous according to the rules of the game.

Or take a lottery. If we learn that the person who won the lottery was an auto mechanic, this isn't something we deem to be a striking coincidence. The winner had to have some profession. But if we learn that the winner was the first cousin of the lottery official, that's a suspicious coincidence.

We should also note that there is an ambiguity here: The word "coincidence" can mean precisely the opposite of "striking or suspicious." It can mean what one would call just a coincidence--something that is not striking, that is trivial or unimportant. We might even say that it can mean two things that are precisely the opposite of one another. But I think the two meanings can be brought closer together if we imagine a case where something initially appears strange or suspicious but we eventually decide that causally it really did happen by chance: The lottery official's cousin won the lottery fairly, so it was "just a coincidence."

8. So who's right? On the one hand, if someone rolls sixes a thousand times in a row, we're warranted in concluding that the dice are loaded without considering alternative explanations. 

On the other hand, background information does figure in our assessment. We have expectations about how fair dice should behave based on our experience of the kind of world we inhabit. Dice are very limited objects. And they're designed to perform randomly. 

In addition, a gambler has a financial motivation to cheat if he can get away with it. (Admittedly, rolling sixes a thousand times in a row is not an overly subtle way to beat the casino.) So there is an implicit frame of reference for assessing that outcome. 

9. But whichever paradigm you prefer (Dembski or the McGrews), it provides a principled basis for agency detection. Contrast that with the village atheist who simply shrugs off any example–however specific, antecedently unlikely, and well-attested–of answered prayer, as a sheer luck.