The "real" problem with miracles

I'm going to comment on this post, by militant atheist Keith Parsons:

http://www.patheos.com/blogs/secularoutpost/2015/05/19/the-real-problem-with-miracles/

So, the credibility of a miracle claim given certain evidence and background comes down to three factors:(1) p(e/m & k), the likelihood that we would have the evidence e given that the miracle did take place and given our relevant background knowledge.(2) p(m/k), the prior probability of the occurrence of the miracle, that is its probability given only background knowledge and independently of the particular evidence e that we are now considering.(3) p(e/k), the likelihood of having the evidence e given only background knowledge. This is equivalent to the total probability of e: p(e/m & k) × p(m/k) + p(e/~m & k) × p(~m/k), that is, the probability that we would have evidence e whether or not m took place.

I've always had misgivings about that kind of analysis. I think it artificially partitions the evidence. 

It's as if Bayesians first hand a runner a backpack full of rocks (prior probability). Considered in isolation, he can't win or even cross the finish line with all that dead weight on his back. Yet they then proceed to lighten the load (posterior probability), which enables him to huff and puff his way past the finish line.

But why load him down with rocks in the first place if they know all along that they are going to remove most of the rocks, by taking the totality of the evidence into account? Why divide it up that way? Why not work back from their conclusion?

If we have the total evidence at our disposal, isn't it very artificial to divvy it up between prior and posterior probability? It's like we're pretending, in the prior, that we don't know as much. That we're in the dark, except for generalities. We suppress our full knowledge for the sake of distributing the odds between prior and posterior probability.

Now, that makes sense if, indeed, we don't know all the facts at the time we begin our assessment. But if, in fact, we enjoy the benefit of hindsight, then shouldn't the body of total evidence supply the frame of reference all along? 

A skeptic such as Hume, who does not presuppose the existence of God, will, of course, put p(m/k) very low, not far from zero. On the other hand, a Christian, one who believes in a God who can and on occasion will perform miracles, will often have a very different prior probability for p(m/k) for a given m. In other words, if k_s is the presumed background knowledge of the skeptic, and k_c is the presumed background knowledge of the Christian, then, for many purported miracles, p(m/k_c) ≫ p(m/k_s).

i) That's misleading. Although a miracle presumes the existence of God, it doesn't presume prior belief in God. So that objection confounds the order of knowledge with the order of being.

Suppose I don't believe in God. But if I witness a miracle, or a trusted acquaintance shares with me his experience of a miracle, then that's a reason for me to ditch my skepticism. I was skeptical because I was ignorant of the evidence. I had no exposure to firsthand or reliable secondhand information. I should say to myself, "Well, I used to be an atheist, but that's because I didn't know any better. Now that I've encountered this evidence, I see that my atheism was premature."

ii) Since a miracle involves personal agency or personal intention, overriding the ordinary course of nature, the question is how to assign a probability value to God's will to perform (or not perform) a miracle. I don't see how statistics or background knowledge regarding the general uniformity of nature is germane to how we anticipate or estimate God's intention to perform a miracle. 

This is hardly surprising since evidence quite sufficient to overcome a moderate burden of proof will be woefully insufficient to overcome a very heavy burden. 

Of course, that begs the question. Any given miracle has a very low antecedent probability. Therefore, it takes really impressive evidence to overcome the presumption that any given miracle never happened. So goes the argument. 

In fairness, one might say that's true of any particular event. But reported miracles are typically represented has demanding a higher–indeed, much higher–burden of proof than ordinary events. Indeed, that's what Parsons is insinuating. 

Yet his way of framing the issue fosters a prejudicial impression, as if the rational default position is disbelief in miracles, but if a Christian apologist can muster overwhelming evidence to the contrary, a miracle can heave itself over the finish line in one last gasp.

But why should we grant that tendentious way of framing the issue? It puts the Christian apologist at an unfair disadvantage. Let's consider a few examples:

1. A high school football player drops dead of cardiac arrest during practice. The odds of this happening are low. Statistically speaking, few teenage boys die of heart attacks. 

And there's more to it than actuaries. There's the underlying reason: usually, that's the age at which the vital organs are in peak condition.

But an autopsy reveals the fact that the ill-fated player had an undiagnosed congenital heart defect. Given his specific condition, it was quite likely that he would die of heart failure from overexertion.

Perhaps that illustrates the distinction between prior and posterior probability. If so:

i) The ordinary unlikelihood of a teenage boy dying of heart failure demands a special explanation if it happens. The very fact that it's normally so improbable means that we need to investigate how it happened to discover the cause. You wouldn't autopsy a 90-year-old who died of cardiac arrest. 

ii) At the same time, the distinction between prior and posterior probability theory seems artificial after the fact. The odds may be germane before the autopsy, but after the autopsy, isn't the only relevant evidence his heart condition, and not the general odds of that happening?

It's not so much that posterior probability overcomes prior probability in this case, but that the real explanation replaces prior probability. Prior probability is just a placeholder unless and until we become more informed about the particulars of this specific case. 

2) Edwin Prescott III loses control when he tries to make the hairpin turn of the Grand Corniche. His Bugatti Veyron plunges over the cliff, and he dies in a conflagration.

An investigation turns of mechanical failure. Specifically, the brakes gave out.

However, the prior probability of brake failure on a Bugatti Veyron is very low. In addition, the car was serviced just a week before the fatal "accident."

Now, there are different ways of assessing prior probability in this case. You could begin with statistics on the failure rate of its brake system. How frequently (or infrequently) does that happen?

There's the factory specs on the average lifespan of the brakes, and factory recommendation on when they should be replaced. 

You could have an engineering analysis of the conditions under which the constituents deteriorate (e.g. metal stress). 

However, a homicide detective makes a couple of observations. Prescott's wife stood to inherit the husband's fortune in case of accidental death. And she was having an affair with the dashing automechanic who serviced the car a week before. 

The assumption, therefore, is that the brakes were tampered with, even if the car was too damaged in the conflagration to make a conclusive determination.

Assuming that illustrates the distinction between prior and posterior probability:

i) It's not as if the posterior probability subtracts from the prior probability. It's not like we sum the probability of each (prior and posterior) individually, then combine them to arrive at the sum total–do we? 

The prior probability is an admission of ignorance regarding the specifics of the case in hand. But once we know about the affair and the terms of the will, then that's what we go with.

ii) At best, the high antecedent unlikelihood of that happening makes the "accident" inherently suspect. That prompts the homicide detective to consider factors other than mechanical failure.

3. At a high-stakes poker game, a player is dealt a final card to complete a royal flush at the very time the opposing player calls his bluff. The opposing player has bet everything on this hand. He's all in. 

i) Assuming a random deck, the antecedent probability of a royal flush is low. 

But you also have the opportune timing of the hand. The lucky player is dealt a winning hand at the climax of the game, when both players have everything to gain or everything to lose. 

ii) Theoretically, one response would be to say, "That's so unlikely that I can't believe what I'm seeing! My eyes are playing tricks on me!"

Likewise, there must be some technical glitch in the casino camera footage. 

Another response might be: "Well, I guess the odds of a royal flush aren't so improbable after all!" 

iii) The antecedent odds against a royal flush in tandem with the opportune timing is very suspicious. The fix is in!

The player got to the dealer. Bribed him or put the squeeze on the dealer by threatening his family.

Let's say an investigation confirms that suspicion. If so, then isn't prior probability moot at that juncture? If you can prove that the player cheated in collusion with the dealer, then the abstract odds no longer figure at all in the final explanation. 

Once we know that the dealer is a cardsharp, isn't prior probability a moot point? It's not so much that the real explanation overcomes the prior, but that it cancels out the relevance of that consideration tout court. 

We now have many reasons, many more than Hume could have known, for regarding it as very likely that we will have miracle reports when no miracle has occurred. 

He disregards extensive documentation for modern miracles and the paranormal. 

Much psychological research has shown the extent to which perception is constructive. 
Like perception, memory is largely a construction. We remember things as they should have been or as how we want them to have been rather than how they were.

i) That argument is self-defeating, for it undercuts Hume's appeal to uniform experience. Hume's argument against miracles is based on testimonial evidence. If, however, testimonial evidence is unreliable, that sabotages Hume's standard of comparison. 

ii) The fact, moreover, that we tend to recollect things we personally find interesting is what makes them memorable in the first place. 

Strong desires or expectations seriously bias our judgments as well as our perceptions. 

One again, that cuts both ways. It applies perforce to atheist observers. Parsons keeps raising counterproductive objections.

Hallucinations and other sensory delusions are now known to be much more common, even among psychologically healthy people than was previously believed. Oliver Sacks’ recent book Hallucinations shows that this is so. All sorts of factors can lead psychologically normal people to hallucinate—grief, emotional duress, sensory deprivation or monotony, and exhaustion, for instance. 

He simply begs the question by discounting crisis apparitions as hallucinatory. It doesn't even occur to him that his preemptory dismissal is circular.

Hypnagogic and hypnopompic hallucinations are well-known phenomena that sometimes occur just as people are going to sleep or waking. They have been known for centuries and probably account for many reported experiences of demons, witches, or ghosts. In the 1980s many people, including author Whitley Strieber, reported that they had been abducted by aliens, taken on board spacecraft, and subjected to what were apparently medical probes. These experiences seemed very real to the people that endured them, yet they were in all probability due to hypnagogic or hypnopompic hallucinations. 

He fails to draw an elementary distinction between sleep paralysis and sleep paralysis with awareness (ASP). Sleep paralysis is universal. A natural mechanism to protect the body when we dream.

But ASP or old-hag syndrome is not universal. For that reason alone, merely appealing to sleep paralysis fails to explain old-hag syndrome. Appealing to sleep paralysis fails explain why some people experience old-hag syndrome but others don't. LIkewise, it fails to explain why some people experience it at one point in life, but not another.

David Hufford is probably the world authority on old-hag syndrome. He's an academic folklorist at Penn State. Here's some of his material:

https://www.academia.edu/4041334/_From_Sleep_Paralysis_to_Spiritual_Experience_An_Interview_with_David_Hufford_Paranthropology_vol._4_no._3_2013_

https://www.youtube.com/playlist?list=PL893F2DA8DCBDCFA5

Folklorists now know how stories can grow and spread through a community and how rapidly they can take on fantastic or miraculous content. Even in an era of electronic communications, and even when eyewitnesses are alive and vigorous, false stories can and do spread widely. Consider the famous case of Flight Nineteen: In December 1945 a flight of TBF Avenger dive bombers took off for a training mission from Ft. Lauderdale, Florida and subsequently disappeared. Within thirty years, written accounts told weird stories of how the flight had met its allegedly mysterious end in the “Bermuda Triangle.” 

I don't know why he thinks urban legends like the Bermuda Triangle prove his thesis. We get most of our information about the world second hand, from history books, science textbooks, or the "news media." 

For instance, some stories turn out to be hoaxes, but that's not something the average person could know in advance. The medium is the same for hoaxes and true stories. If that's a problem for religious knowledge, that's no less a problem for secular knowledge. Parsons keeps shooting himself in the foot. 

When recounting events we tend to recall gist rather than specifics and imagination and wishful thinking are always ready to impact the story. 

To my knowledge, that's a gross overgeneralization. He fails to distinguish between events and conversations. We tend to remember the gist of a conversation, rather than verbatim recall.  But we can have specific and stable memories of events we see. Memory is selective. It can and often does select for specifics. That's because the specifics are sometimes memorable.