Overestimating The Prior Improbability Of Miracles

Stephen Braude wrote:

First, it is moot whether psi phenomena violate any important scientific theory. Only from an already suspect reductionistic perspective would they seem to pose a threat to received science. It is more plausible that psi phenomena, like organic phenomena and the phenomena of consciousness generally, simply fall outside the domain of physics. Second, even if psi phenomena did violate some major scientific law(s), there is nothing sacred about received science. Like the received science of days past, much of it may require modification or rejection, even if only to countenance everyday mental processes such as volition and memory. Third, subjective probability assignments concerning scientifically anomalous phenomena carry little weight, as the history of science amply demonstrates.

Moreover, we know very little about ostensibly paranormal phenomena (especially, I suppose, if they are genuinely paranormal) but a great deal about misperception, naiveté, fraud, etc. But in that case, our assessments of the probability of the latter should be given greater weight than our assessments of the probability of the former. After all, we often have a solid basis for judging the likelihood of misperception, etc., occurring in spontaneous cases. But we have virtually no basis for deciding the likelihood of an event occurring - in the absence of fraud, misperception, etc. - that at least appears to violate some fundamental scientific law or metaphysical assumption. We do know, of course, that phenomena discovered in the past have deeply changed the course of science, and we know that phenomena considered impossible or highly improbable on received scientific principles have been found to be possible or not so improbable after all. So we know that genuine scientifically anomalous phenomena may occur, some of which eventually get incorporated into the science of the day. But earlier on, when the phenomena are still extraordinary and poorly understood, we lack the kind of information customarily needed to assess the probability of their having occurred. To judge whether a given event is likely in a particular circumstance, we must first know something of the event's nature and limits. That is how we determine the likelihood of misperception, fraud, etc. We know what sorts of situations might motivate fraud or encourage misperception, and we can make reasonable and well-informed judgments about their likelihood in the circumstances in question. In fact, we have a substantial and clear background of data to which we can appeal when making these judgments. But it is just this sort of background information that we lack in the case of ostensibly paranormal events. So it seems reasonable to decide the likelihood of an ostensibly paranormal event having occurred on the basis of the evidence against the occurrence of misperception, fraud, etc. (The Limits Of Influence [Lanham, Maryland: University Press of America, Inc., 1997], 46-47)

He goes on to quote some comments from C.J. Ducasse:

…assertions of antecedent improbability always rest on the tacit but often in fact false assumption that the operative factors are the same in a presented case as they were in superficially similar past cases. For example, the antecedent improbability of the things an expert conjurer does onstage is extremely high if one takes as antecedent evidence what merely an ordinary person, under ordinary instead of staged conditions can do. The same is true of what geniuses, or so-called arithmetical prodigies, can do as compared with what ordinary men can do. And that a man is a genius or a calculating prodigy is shown by what he does do, not the reality of what he does by his being a genius or prodigy. This holds equally as regards a medium and his levitations or other paranormal phenomena. (47)

Braude then comments:

It would be almost transcendentally foolish to maintain that the unprecedented mnemonic abilities reported by Luria (1968/1987) are unlikely to be genuine, due to their antecedent improbability (based on the population of normal human beings). With reasoning such as this, we could forever avoid acknowledging the existence of exceptional human abilities. But then it is presumably equally indefensible to distrust nearly a quarter-century's worth of reports of decently-illuminated table levitations by D.D. Home, on the grounds that the antecedent improbability of that ability is overwhelmingly high. (47)

McLatchie vs. Blais on miracles & probability

Just some observations after listening to the debate:

1. This wasn't primarily a debate over Hume and miracles. It started off that way, with brief argumentation involving Bayesian probabilities, but it quickly went off the rails. Rather the debate was a far-ranging debate that covered a lot of other topics. For example, some time was spent on debating Jesus' triumphal entrance into Jerusalem, biblical inconsistencies, undesigned coincidences, and the dates of the Gospel. I think Jonathan won these debates; Blais didn't seem terribly familiar with the biblical material except in broad strokes. Also, the last moments of the debate were mainly spent debating design. Jonathan easily won this part of the debate, hands-down. Blais was obviously out of his element.

2. That said, I think Blais spoke the most throughout the debate, both in terms of amount of words and amount of time. In fact, Blais seemed to realize this when at one point he admitted he didn't want to "dominate" the debate. Yet Blais still kept interrupting Jonathan throughout the debate.

In fairness, Jonathan could have been more assertive. And the moderator (not Justin Brierley) could have done a better job at steering and focusing the debate. The moderator was far too hands-off.

3. At times, Blais came across like he was attempting the Gish gallop. The stated debate topic was on Hume and miracles, but Blais brought up the existence of God, the various flavors of theism (e.g. Blais thinks the Norse god Loki counts), the historical reliability of the Bible, biblical inconsistencies, the reliability of testimonial evidence, extraordinary claims require extraordinary evidence, the canonical status of biblical books (e.g. Timothy), scribal interpolations (e.g. the woman caught in adultery), Jesus mythicism, parallels between early Christianity and other religions (e.g. Mormonism), parallels or analogies between miracles and UFO sightings, the progress of science dispelling superstition, and so on as if he expected Jonathan to address each and every one of these. Yet each of these could make for separate debates in their own right.

4. Nevertheless, there wasn't anything particularly novel or unfamiliar with what Blais brought up, at least not to anyone who has followed Christian and atheist debates. Blais cites and is obviously heavily relying on secular atheists like Carl Sagan, Robert Price, Richard Carrier, Sean Carroll, among others. There have been reasonable responses to most if not all of these by Triablogue members and many other Christian apologists.

5. Blais expected testimonial evidence about miracles to rise to the standard of a randomized controlled trial in modern medical research. However, why should an RCT even be an appropriate test of miracle claims in the first place? Also, it's not as if it'd be empirically possible to do an RCT on someone rising from the dead. And as far as that goes, there's nothing necessarily wrong with accepting the reliability and credibility of a single case study that's been well documented. Indeed, it only takes one bona fide miracle to demonstrate the possibility of miracles.

6. Blais tried to draw parallels between UFO sightings and Christian miracle claims. However, he needs to present an argument for why UFO sightings parallel or are analogous to Christian claims about miracles in the first place. Otherwise it's like seeing parallels between (say) Jesus' death and resurrection and the Osiris myth, but on closer inspection they're not alike.

Do miracles have a higher burden of proof?

This is something I frequently discuss because it's a mainstay of atheism. Atheists typically say there's an overwhelming presumption against miracles. In addition there are Christian Bayesian theorists who say miracles have a higher burden of proof, but it's not insurmountable. Let's take a couple of comparisons.

Suppose I'm abducted and sedated. Next thing I know I wake up in the middle of nowhere. A wilderness with a river nearby. Is it safe for me to wade in the river?

Some rivers are hazardous.  Some rivers are frequented by crocodiles, anacondas, electric eels, or bull sharks.

What's the antecedent probability that the river is safe or hazardous to wade in? Unless I know where I am, I have no frame of reference. There's no presumption one way or the other to overcome.

I can't begin to calculate the probabilities in a vacuum. I need to know where I am. 

Or take another example. Suppose a driver spots a license plate in the parking lot. What are the odds that that car would be at the same time and place he was? In principle, you could consider the number of in-state license plates, and make an educated guess about out-of-state drivers. 

But suppose the driver is a bookie on the run from the mafia, and the car with that particular license plate belongs to triggermen who are shadowing him. That drastically changes the odds.

Now in Bayesian probability theory, as I understand it, you divvy up the odds into prior and posterior probabilities. The prior improbability may be high, but that can be overcome with more specific evidence. 

But my problem is that if the probability theorist already has all the information when he begins his analysis, why bifurcate the evidence into prior and posterior compartments? Why artificially bracket off some of what he knows to assign a prior probability value, which creates a presumption that must then be overcome? What's the point? It's not like he discovered new evidence in the process of his analysis. 

I don't think it's meaningful to lay odds on miracles in the abstract. It depends on the kind for world we live in as well as specific evidence for specific reports. 

Are specific claims improbable?

One atheist objection I've run across goes like this: the more specific a claim, the more antecedently improbable the claim. There's an inverse relation between specificity and probability. So, for instance, Christian theism is more antecedently improbable than mere theism. 

To which I'd respond:

i) For anything to exist, there must be a minimum threshold of complexity. So it's artificial to speak in the abstract about the prior probability of specific claims, as if something simpler is more likely to exist or occur than something more complex. Reality isn't incrementally reducible to zero. 

By that logic, it's more antecedently probable that nothing whatsoever exists. But if nonexistence is the default assumption, why does anything exist? For that matter, probability theory is quite complex. Does that make it antecedently improbable that probability theory exists? But it takes probability theory to probabilify anything. So it can't be self-referential.  

ii) Even assuming for argument's sake that the principle is true, it's misleading inasmuch as a more specific claim may have more specific evidence than a less specific claim. Christian theism may have a lot more evidence than mere theism. 

Thanks, atheism!

Quantifying miracles

i) The issue miracles is often framed in terms of mathematical odds. Like there's a presumption against having a license plate with that particular number, given tens of millions of license plates, but that presumption can be overcome by specific evidence to the contrary. By the same token, miracles are said to be very rare. Therefore, the mathematical odds against the occurrence of a miracle are high, though not insurmountable. 

I've never been impressed by that way of framing the issue. To take a comparison, consider a corridor with closed doors on both sides. Let's say there are 100 doors total. What are the odds that any particular door is locked?

I don't think the mathematical odds are relevant. That's the wrong way to broach the issue. There's no presumption that the closed doors are either locked or unlocked. That depends on other variables. 

If it's during business hours, many doors may be closed but unlocked. If it's after business hours, they are more likely to be locked. Yet even then you have workaholic employees who are still slaving away in their office. Or doors may be unlocked because the cleaning crew is servicing offices. 

Some doors lead to conference rooms. These remain unlocked day or night. There might be a door to a utility room that's normally locked.

The abstract odds have no bearing on the probability that any particular door is locked or unlocked. There's no presumption one way or the other. 

ii) Even if miracles are very rare, that's not a mathematical assumption. Rather, that's an empirical observation. In our experience, miracles are (allegedly) very rare. That's not a question of a priori mathematical odds, but a posteriori evidence.

Moreover, it's ambiguous to say miracles are rare. Rare overall? We'd expect miracles to be underreported since most Christians aren't famous. Miracles might be frequent, but most of them will never be a matter of public record. 

Something can be rare but still be common if the absolute number is large even if the relative number is small. It might be a fraction of total events, yet the percentages are considerable. Green eyes are rare, but if millions of people have green eyes, that's a lot of green eyes. 

Tails up

A cliche objection miracles, popularized by Carl Sagan, is that "extraordinary claims require extraordinary evidence". This slogan is parroted by atheists, as if it's self-evidently true. 

Ironically, the slogan is a claim in its own right. Indeed, two claims bundled into one: (i) miracles are "extraordinary"; (ii) as such, it takes "extraordinary evidence" to credit them. 

The slogan itself needs to be unpacked. The key terms need to be defined and defended. So an atheist who uses Sagan's slogan has his own burden of proof.

That said, let's approach things from another angle: Suppose a reporter tells me that he saw a table with 100 coins, and every coin was tails up. Is that extraordinary? What are the odds? Does it demand extraordinary evidence to lend credence to the report? 

That's not a question we can answer in a vacuum. Is the assumption that someone flipped every coin once, and on the first flip, each quarter came up tails?

If so, would that be extraordinary? What are the odds? 

Well, that depends. Do the 100 coins represent the entire sample? Suppose the original sample was 1000 coins, some of which flipped heads and some of which flipped tails. The coins on the table represent a select subset of that larger total. In that event, there's nothing extraordinary about 100 out of 1000 coins coming up tails on the first flip.

Suppose, though, it is the original sample. But just by looking at the coins on the table, an observer can't tell how many times each coin was flipped. Maybe someone flipped each coin until he got tails. In that event, there's nothing extraordinary about 100 coins tails up. You can't tell from just looking at the end-result what caused that particular outcome. 

Or maybe the coins were never flipped to achieve that result. Maybe someone simply laid each coin on the table, tails up. In that event, there's nothing extraordinary about 100 coins tails up.

You can't tell, from viewing the event in isolation, whether the event is "extraordinary". What might be extraordinary in the case of random coin tossing might be ordinary in the case of selected results or direct action. 

And you don't need to know in advance that an agent produced the result to take agency into consideration. Indeed, if the reported outcome is astronomically improbable, absent some additional variable to orient the outcome, that's not a reason to deny the resort unless there's no good reason to suppose an agent may have been involved. And if the outcome is not in serious doubt, then agency is the only rational explanation. 

Fantastic improbability

From Doug Axe:

There's this general confusion over what probabilities mean, and that if...something has a probability and it's not zero, then that means it's not impossible.

Some people want to say, if the probability is not zero, then that means it can happen. What it really means is that if there are enough opportunities for a very small probability to become a large probability, then it can happen.

So, if something is one in a million, but you have a million shots at it, then it becomes probable. If something is one in a trillion, you're going to need a trillion shots at it for it to become probable. A million won't be enough; it's still vastly improbable.

If you push that number far enough, you reach an improbability that is so extreme that there is no way for this physical universe to give you the number of opportunities that would raise that extraordinary small probability to something that can happen, that's like, 50-50 or better.

It turns out that in these sorts of problems where you have to arrange lots of thing and get lots of things right, the improbability of each step multiples and you can get just extraordinary improbability.

So, I use the term "fantastic improbability" to refer to this sort of boundary where it's now beyond the point where this physical universe could possible overcome the improbability. That, I call "physical impossibility," distinguishing it from mathematical impossibility...One in a google [sic] is the dividing line where I say, once it's that improbable, there is no way for any real process in this physical universe to overcome that kind of improbability. That's why I call it "physically impossible."