And buried, He rose again: it is impossible, therefore it is certain.
- Tertullian, De Carne Christi. (ca. 130)
When anyone tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should have really happened. I weigh the one miracle against the other; and according to the superiority, which I discover, I pronounce my decision, and always reject the greater miracle.
- David Hume, Of Miracles. (1748)
[Hume's] argument is radically fallacious, because if it were sound, no perfectly new fact could ever be proved, since the first and each succeeding witness would be assumed to have universal experience against him. Such a simple fact as the existence of flying fish could never be proved, if Hume’s argument is a good one; for the first man who saw and described one, would have the universal experience against him that fish do not fly, or make any approach to flying, and his evidence being rejected, the same argument would apply to the second, and to every subsequent witness, and thus no man at the present day who has not seen a flying fish ought to believe that such things exist.
- Alfred Russell Wallace, An Answer to the Arguments of Hume, Lecky and Others, Against Miracles. (1870)
In response to Lynn’s excellent and thoughtful post about “Whom do you trust?” I’d like to start a short series of posts looking at, broadly, the relationship between science, statistics, and epistemology. In other words, how do we know what we know? Under what circumstances is it reasonable to change our beliefs? Under what circumstances may it be ‘reasonable’ to be unreasonable? How should the results of an experiment affect our decisions about what to believe? These are all interesting questions from a theoretical point of view, and several different fields of study- philosophy of science, epistemology, statistics, psychology- have devoted a lot of time to addressing them. They’re also important- critically so- from a practical perspective. They’re important to me personally, as an incipient biologist, anxious to produce interesting and novel findings that advance our understanding. All scientists are driven to find something new and different, but at the same time they’re aware that in order to be reliable and convincing, their findings must not only correspond to true and observed natural patterns, but also to the ’rules of evidence’ embodied by statistical methods. And, in a weaker sense, they should generally, though not always, be compatible with existing theory. (It’s possible that new discoveries will overturn a vast body of established theory, but it’s relatively unlikely). But more broadly, these questions are of importance to every concerned citizen, because they affect the choices we make with respect to things like nutrition, medicine, politics, religion, energy usage, etc.
In subsequent posts, I’m going to deal with the sort of day-to-day issues that we deal with when regular citizens in general, and scientists in particular, decide how to weigh evidence and come to conclusions. I’m very far from an expert- I haven’t read anything in the philosophy of science or in the particular field of epistemology, and my knowledge of statistics is limited to three grad-level courses, some additional reading as a layperson, and the experience I’ve had trying to analyze data. So I’m speaking here more as an intrested layperson than anything else. But I want to start by dealing with the ‘extreme case’ of events so seemingly unlikely, that many people (like David Hume) would deem them scientifically impossible, and would argue that the evidence in favour of them is equivalent to zero. These represent the most extreme case of ‘things that are hard to believe’, and (to some people, though not all) the ultimate example of ‘extraordinary claims requiring extraordinary proof’. I refer, of course, to miracles.
There are some liberal clergymen and apologists nowadays who would like to do away with the concept of miracles entirely, and would make the Christian faith (and others) more appealing to the spirit of a secular age, by rendering its claims less striking and unusual. These are the sort of well-meaning folks who will tell you that the real miracle of the loaves and fishes was that Jesus taught people to share, or that his exorcisms of the possessed were really early demonstrations of cognitive-behavioural therapy avant le lettre, or that his healing of the man born blind was a metaphor for spiritual enlightenment. Suffice it to say, that I think very little of these attempts, though many of the people who make them are good and decent folks. As well meaning as they may be, these folks are trying to destroy the Christian village in order to save it. You can certainly have a Taoism or a Confucianism without miracles; you can probably have a Buddhism or a Judaism; you can maybe even have a sort of Hinduism or Islam without much in the way of miracles. You can’t, in my view, have a Christianity. Other religions may be founded on mystical experience, on philosophical speculation, on intuition or reason, or on a revealed code of moral behaviour. Christianity is founded on miracles. Two key miracles, to be precise: the miracle of Christmas and the miracle of Easter (as well as all the others in between, less soteriologically important to us, but no less important to those who experienced them). “If Christ be not raised”, says St. Paul, “then our faith is in vain, and we are the most unhappy of men.” In my view, if we deny the possibility of miracles, then the whole Christian castle in the air comes crashing down. So the question of whether miracles can happen isn’t a minor issue that can be tabled. It is *the* key issue underlying the whole Christian faith.
David Hume, in the quotation above, denies the possibility of miracles. He does so on the basis of the principle that I’m pretty sure he first formulated explicitly (though people probably used it before him), and that Lynn quoted in her post: “Extraordinary claims require extraordinary proof”. He then goes further, though, and takes the principle so far that essentially no evidence would be sufficient to establish a miracle. This is because a miracle would violate the laws of nature, and we know that the laws of nature hold true in all cases that have been hitherto observed. We also know that people can hallucinate or lie, so in a case where we see something that seems to violate the laws of nature, it is more likely that someone (you, or the person who told you they saw a miracle) are hallucinating, lying, insane, etc. than that the laws of nature have really been violated. And therefore, this particular piece of evidence for a miracle can be discounted. The same can be applied to every subsequent claim of the miraculous, such that no amount of testimony or experience is ever sufficient to establish that miracles occur. It is always more likely that someone, consciously or subconsciously, is being decieved.
Hume’s formulation of this argument has always seemed to be wildly fallacious (although a more reasonable, weaker version of the ‘extraordinary claims require extraordinary proof’, that doesn’t rule out miracles entirely, can be presented within a Bayesian framework). Nevertheless, there are a lot of very smart and intelligent people who nod sagely in aggreement with Hume, and who think he was onto something very smart and insightful. So it’s worth looking at Hume’s argument in a little more detail to see exactly what’s wrong with it.
The first thing to notice is, of course, that it’s not falsifiable. And therefore, in Karl Popper’s sense of the word, not scientific. Now, I don’t think that’s necessarily a problem; you can certainly make a case that not all claims ought to be scientific, or that falsifiability is a poor guideline to what makes something scientific. I don’t want to get into that whole debate, partly because I haven’t read or thought deeply about the philosophy of science, but I would just point out that a lot of people, including the celebrated ‘New Atheists’ of today, talk a lot about making science, and falsifiability, the mesure of all things. Fair enough, but you can’t have it both ways. “The laws of nature brook no exceptions” is a nonfalsifiable claim, and therefore, a nonscientific one. In the last analysis, science cannot prove its own foundations (that nature is, usually, lawful and predictable) to be true according to scientific standards of proof, and therefore, science must ultimately rely on philosophy to justify its own assumptions.
The second thing, at a more philosophical level, is that Hume is making a critical assumption: that the laws of nature are unbreakable and have no exceptions, and that they can’t be overturned at the pleasure of God, the devil, the holy or unholy angels, the saints, etc. That assumption, again, isn’t a scientific one, but more deeply than that, it’s also not very well grounded philosophically or mathematically either. Suppose the universe were set up such that it wasn’t materialistic or deterministic, but only appeared to be. Maybe the universe is full of miraculous interventions by supernatural agents, but they confine their interventions to situations where they won’t be detectable by scientific means, or where they are statistically indistinguishable from pure chance. (‘Pure chance’, residual variation, experimental error, etc. are normally pretty important factors in any observation of a complex system, and include a lot of ground for God or gods to be working behind the scenes.) Maybe this is their way of preserving human freedom to believe or disbelieve. Maybe the universe does feature miraculous interventions, but at a very low level of frequency, that to a casual observer is indistinguishable from zero. That would make a big difference in estimating whether a miracle was likely or unlikely to have happened in any particular case. If a man is raised from the dead on average every 100 years, it’s unlikely we would ever witness it happening, but it also means that a purported case of resurrection can’t be ruled out a priori. Maybe miracles happen only when a particular set of circumstances, that God or his agents deems appropriate, are met.
There are all sorts of scenarios which would produce the seemingly orderly, materialistic universe that we see, but that are compatible with supernatural agents having the power to overturn the laws of nature and enact miracles. It’s very difficult to distinguish, by observation or experience, between a naturalistic universe and a pseudo-naturalistic one (one that appears materialistic, but isn’t). And Hume’s formulation only makes sense if naturalistic (the idea that the laws of nature are unbreakable) is true. If the nature of God was such that He only performed resurrections in cases where, say, the resurrection had been prophecied beforehand, or where it would increase the faith of the audience, or at a specific stage in history, then the fact that we don’t normally see people raised from the dead tells us nothing about whether it really happened to Jesus, Lazarus, the daughter of Jairus, and a few others. It’s possible, too, that the laws of nature are more complex than we think. Wallace raises this point when he talks about the example of flying fish. He points out that if Hume were right, we would never credit that biological curiosities- the platypus, the flying fish, the welwitschia plant- actually exist, because the testimony of each succesive witness would be discarded.
I think a better formulation of the idea that extraordinary claims require extraordinary evidence, comes about if we use a Bayesian statistical framework. Bayes’ Rule (devised by a Presbyterian minister, who was required by his job to believe in miracles) related the likelihood of a claim being true, to several different factors. It takes into account three things:
1) How likely is our prior expectation of the claim being true?
2) How likely is the observed data, if the claim was true?
3) How likely is the observed data, if the claim was not true?
The problem with Hume’s formulation is that it arbitrarily sets the prior expectation of miracles, 1), at zero. It’s not possible to simply look at nature, say “I never have seen miracles, therefore the prior probability is zero”. I’ve never seen a platypus either, but I’m certain they exist. It’s possible that particular metaphysical arrangements exist, so that miracles happen only under certain sets of conditions, which are rarely found today (or just which I personally have not come across, nor had David Hume). Setting the prior expectation of miracles to zero is not a scientific claim, it’s a philosophical one. If miracles happen, they’re outside the purview of science, which studies the laws of nature, not exceptions to the laws.
The Christian apologist Tertullian, in the second century AD, makes an interesting argument in favour of the Christian miracles being true (one that C.S. Lewis echoed in the twentieth century). He does so on the basis of item 3) above. He says that the Christian story is so absurd and illogical that it couldn’t possibly be made up, because when people lie they do so more cleverly and with more attention to plausibility. No one, trying to invent a religion from scratch, would make up a claim like “God is both Three and One, but we can’t really explain how.” Nor would they embrace other paradoxes, like “Jesus was both Man and God” or “Prophecy exists in spite of our having free will.” Nor would they have made up stories that lack so many critical elements of what makes for a good story- e.g. novelistic details about Jesus’ infancy. The fact that the Gospels are such poor works of religious propaganda- starting abruptly, missing key details, making paradoxical claims that are almost impossible to understand, containing gnomic utterances that we could ponder forever without grasping their meaning, making radical and seemingly pointless demands that we turn the other cheek and refuse to divorce adulterous spouses- offers evidence that they weren’t religious propaganda at all, they were history. Th fact that Christianity makes claims that are so paradoxical and outrageous to the mind of man, is an indication that Christianity wasn’t thought up by the mind of man at all. The fact that it seems so wildly unsuited to the time of Jesus, or to ours, is an indication that the Founder of the faith was a being that lived outside of time. Tertullian- and C.S. Lewis- argue that the Gospels can’t be myths, because they are so wildly implausible that no self-respecting mythmaker would make them up. “It is impossible”, says Tertullian, “and therefore it is certain.”
Christianity, and any other religion that makes explicitly supernatural claims, must be clearly distinguished from those pseudoscientific claims like homeopathy, etc. Homeopathy purports to state that the laws of nature are other than what we perceive them to be- that the known laws of physics and biochemistry are just *wrong*. The Raising of Lazarus makes no such claim. It claims that the laws of nature are just what science tells us they are, but that on this one occasion, arround the year 30 CE, they were temporarily suspended on one occasion, by the direct intervention of God, to raise Lazarus from the dead. It is impossible for a biochemist to believe in homeopathy and remain a biochemist: for him to do so would require him to throw out the basic theoretical and practical knowledge of his field. It is quite possible to believe in the raising of Lazarus, because to do so doesn’t challenge our expectation about what sort of patterns we expect to observe in the laboratory or in day to day life. This is why G. K. Chesterton, in his “Father Brown” stories, says “I can believe in the impossible, but not the improbable”. A frankly miraculous, supernatural claim, that explicitly says it stands outside the laws of nature and cannot be addressed by scientific means, is simply orthogonal to science, not opposed to it. A claim that seeks to reinterpret and twist the known laws of nature is quite different; these are the claims which could aptly be called anti-scientific, rather than supernatural events which I would refer to as ‘extra scientific’. Whether the supernatural exists is ultimately not a question science can address: it rests firmly in the purview of philosophy, and more deeply, in the decisions of every heart, working out its own salvation in fear and trembling.