Sadly, I don't find the responses to the last post on miraculous synchronous events really addressing the question at issue, that is, the question of whether (or rather, when) it is warranted to infer divine action based on the experience of synchronous events.
So let me simplify matters with a case which will help us fine-tune the ground for invoking divine action as well as enabling me to measure the recalcitrance to drawing this conclusion from my 'oh so skeptical' audience.
The Case
Tom runs an orphanage and they have just fallen behind in their mortgage payments. If they don't make this payment, they lose the orphanage and the kids will be cast out into the slums, at which point their best prospect will be landing a supporting role in "Slumdog Millionaire 2".
Tom does not know what he owes until he receives a statement in the mail from the bank. The statement is automatically generated and mailed such that nobody but Tom knows what he owes. It is only if he fails to pay this amount within a week that the account goes into arrears and personel from the bank will be notified of his debt. In addition, the letter has arrived in a black envelope with the seal of the bank, ensuring that it has not been tampered with.
Tom opens the letter and sees the amount. Immediately he bows his head and prays silently that God would meet the financial need of the orphanage. Tom resolves in his prayer not to share the need with anybody. That is, he will not let anybody know that the orphanage is in financial straits, let alone when the deadline is or what amount is owing. Tom resolves to follow this vow of silence as an act of faith. God knows the orphanage is in trouble so God will provide the needed funds.
Even with his vow of silence, Tom's prayer is answered. Within the week Tom receives money sufficient to meet the mortgage payment. Is it justified to conclude, based on that evidence, that God answered Tom's prayer? That depends.
Who's Askin'?
It seems rather obvious that Tom is justified in concluding that divine action was at work given his background beliefs that God exists and answers prayer. Others however might be interested in gathering more specific information. Let me suggest four lines of evidence which can be combined to gauge an overall "miraculous design score" or MDS, that is, a score on the degree to which divine action is a likely explanation for the answer to prayer.
1. Temporal Proximity
Our first criterion is this: What was the temporal proximity from prayer to the need being met? Let's say that the deadline is midnight Friday. I would suggest that the closer in temporal proximity the prayer's answer is either to Tom's initial discovery of the amount or to the deadline, the stronger the evidence for divine action.
So let's say that the doorbell rang as soon as Tom said "Amen" and on the other side was a man offering a check sufficient to cover the amount. That would be more persuasive, because more finely tuned to the need, than a check that arrives two days later. At the other end, a check that arrives at the "11th hour" is also finely tuned in a way that one arriving a few days earlier is not.
2. Amount Specification
Our next criterion concerns the amount specification. Let's say the amount needed is $4536.45. The MDS rises the more that an answer is specified to the amount needed. Thus a low MDS would be three checks received which add up to $5320. A higher MDS score would be two checks which add up to $4540. And the highest score would be a single payment of $4536.45.
3. Awareness of Donor
Our third criterion concerns the awareness of the donor. Here are three different levels, moving from a lower to higher MDS:
1. I have some extra funds to share with the orphanage.
2. I was praying today and thought that you could use some funds.
3. God told me to tell you he heard your prayer and he wants the orphanage to have this specific amount of money.
4. Identity of the Donor
Is the donor a "regular" or somebody unaffiliated with the orphanage? The less connection the donor has to the orphange, the less of a "history", the higher the MDS score.
Adding up the scores
So let's give Tom's prayer the highest possible MDS.
Tom prays and a minute later a knock comes at the door. A man he has never seen before is standing there. "Hello sir!" he says. "I was just walking by this building and I felt God telling me that you needed this." With that he hands Tom a check for $4536.45.
Conclusions
Needless to say it is obvious that a Christian ought to conclude that Tom's prayer was answered. But ought an atheist? I have gotten the sense thus far that most atheists, at this blog at least, would always dismiss claimed answers to prayer a priori with various quips like "Anecdote!" or "What, God provides for orphanages but not starving African kids?"
In other words, they have taken the view that MDS scores are irrelevant. No matter what, they would not concede any evidential force to these cases.
This strikes me as unwarranted. I have seen no formal defeater provided for the claim that if there is a God then he can answer prayer. And that means that we should be interested in calculating the MDS of purported cases of divine action to see how finely tuned they really are.
So to sum up, I think the strongest case presented above is strong evidence indeed that God answered Tom's prayer. And I'm just interested to hear which of our atheists might be willing to concede that a case like this would make them at least a bit less dogmatic in their skepticism.

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