How improbable are miracles? Thoughts on Hume and the resurrection of Christ


Hume’s arguments relating to miracles have, in equal parts, fascinated and infuriated me since I first read them. I majored in (and loved) philosophy at university; I work as a maths teacher (and I love teaching probability); I am a practising Christian who believes in miracles – and Hume’s argument tickles all these significant parts of my life. The question of miracles and Hume resurfaced this Easter, fittingly, on Twitter, prompting me to think about it again:

Great question! In this post I will try and answer, via Hume: how improbable is a miraculous event like the resurrection? And what implications does this have for the rationality of belief in it? (Note: I won’t be focusing on the substantive issue of ‘what evidence is there for the resurrection?’. Like Hume’s arguments, my focus will be conceptual, looking at what miracles are, what probability is, and what this implies for belief.) First: let’s look at Hume’s argument…

Hume’s argument:

‘A miracle is a violation of the laws of nature … When any one 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 really have happened.’

And the summarized into a general, reasonable sounding principle:

‘No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous than the fact which it endeavours to establish.’

Some key questions, from these formulations: Firstly, does the argument work on its own terms? Secondly, what exactly is the probability of such miracles?

  1. Does the argument work?

Hume refers to miracles’ ‘absolute impossibility’. Many have criticised him for thus committing a circular argument: if he defines miracles as impossible, then of course we should never believe in them, since they can’t occur! However, his argument is subtler. Miracles’ impossibility comes from the concept itself: they are defined, by believers themselves, as violations/suspensions/exceptions to laws of nature. Now, according to Hume, laws of nature have their firm status because of human experience: ‘it is the same experience, which assures us of the laws of nature’. Thus, when he refers to miracles’ ‘impossibility’, he means only that the occurrence of miracles stands against all human experience to the contrary. In all the history of the world, bar a handful of disputed cases, humans have been observed to die and then remain dead. Thus, throughout human history, around a hundred billion people have died and stayed dead. The chance of resurrection, therefore, must be smaller than something on the order of 1 in 100,000,000,000: pretty impossible, no?

So, to restate Hume’s argument, if someone stands up, proclaiming that their eyes have seen a dead man rise, it seems much more probable that they are lying, or deceived themselves, or misremembering, or deluded. After all, everyone has lied countless times throughout their lives; many have been deceived by, say, cult leaders/politicians/unscrupulous salesman; millions of people have suffered mental illnesses. So, we should believe anything other than that resurrection has occurred.

That’s the argument. My objections: Firstly, Hume relies on a frequentist account of probability. This is the account you probably learnt at school (and that is usually taught!): the probability of something is determined by how often it has occurred in a large number of trials. I used it implicitly in the last two paragraphs, when calculating the probabilities of resurrection vs. false testimony.

I contend that this account of probability runs into serious problems whenever agency is involved. Take this example. I could go to the supermarket and buy a list of ingredients and cook a dish that has never been cooked and eaten before in the history of the world. Here’s one off the top of my head: a madras lamb curry and vanilla sponge cake, glazed with a Sichuan peppercorn & saffron icing, filled with a truffle oil infused maple syrup buttercream, finished with scallop sashimi pieces and chorizo garnish. (If you’re not convinced this would be a literally unique dish, I can keep adding world foods onto the garnish). I could then cook it, eat it, and then tell you I’ve done so. Now, since humans eat a few meals a day throughout their lives, the frequentist probability that this dish has ever been eaten is way lower than the probability of resurrection. Every single human meal that has ever been eaten is a counterexample to the existence of this meal. Its occurrence will thus have an upper limit of probability of about 1 in 2,190,000,000,000,000 (my assumptions: of the 100 billion people who’ve ever lived, an average lifespan of 30 years, eating two meals a day for those 30 years) – far far lower than the frequentist-calculated probability of a resurrection, since many more meals are eaten than deaths occur. So, by the same logic as Hume, surely you should never ever believe that I could cook and eat this dish. Yet if you put a few thousand quid that it never (great bet, given the odds), I’ll happily take up the bet.

It’s a slightly facetious example, but I hope it is illustrative of the point: the probability of resurrection should not be determined simply by the fact that we’ve observed billions die and stay dead. Because we’ve observed even more tens of billions of meals and no one has ever cooked that cake, yet it’s eminently possible and believable. There’s something wrong with the frequentist account which just counts up non-occurrences as the basis of establishing probabilities.

I anticipate the facetiousness of my example brings out this reply: ‘your example is stupid. There is something manifestly different about miracles, which violate steadfast laws of nature. Your cake is totally obviously POSSIBLE, despite its never having occurred before. You can just go out and buy it and cook it – in fact, anyone can. However, dead men can’t just rise.’

I agree that there is something manifestly different about miracles. But notice where this counterargument takes us: it exposes you to the original criticism that Hume’s argument is circular and rules out ruling out the possibility of miracles from the outset. If you take the counterargument in this direction, then you’re saying ‘miracles can never happen. So it’s more likely to believe anything else’ – which is to beg the question: why do you say miracles can never happen? And as I’ve just established, it is insufficient simply to appeal to the relative lack of frequency of resurrections to back up this premise, since you can generate an identical argument, mutatis mutandis, using my sashimi cake. So, beware the circular argument.

However, there’s another thrust to this objection which deserves closer look. That’s the idea of agency – the possibility of action. Sure, my sashimi cake has never existed before, but at the same time it’s totally uncontroversial to say that it could exist. Any of us (who live near a biggish supermarket) could go out and make it. In fact, there are countless things that have never happened before in human history that we could go out and cook, and no one struggles to believe in them (see: Heston Blumenthal). And all of this is because we know that these unique events are within human power to effect. General conclusion 1: where an event is within the bounds of human agency and power to effect, frequentist probabilities stop making sense.

Here’s where miracles seem to be in a different category. The whole point of miracles is that humans can’t ordinarily do them; they must have super-natural causes. Hence the objection: miracles are different to the act of making my sashimi cake, and my counter-example by parody thus fails. Yet this objection undercuts itself. If an omnipotent creator God exists, then causing a dead man to rise again is entirely within his power to effect. He’s omnipotent, after all. Let’s go further: if an omnipotent creator God exists, any sort of miracle is even easier for him to perform than it is for me to make a sashimi cake. So, if this is the case, we can extend general conclusion 1 to general conclusion 2: where an event is within the bounds of any (human or divine or otherwise) agency or power to effect, frequentist probabilities stop making sense. And if they stop making sense, then Hume’s argument falls apart by analogy: if God exists, then a miracle like a resurrection can’t be written off simply because it’s never happened before. Lots of things have never happened before yet they are readily believable, because we know that they could be performed. As soon as something could be performed by someone, probabilities become much more confusing, and believing ‘improbable’ events becomes much less problematic.

Another angle on the same point, and my theorizing as to why Hume’s argument makes so much intuitive sense and infuriates in equal measure: it is indeed absolutely impossible that the dead rise – of their own accord. Dealing with death is an area far outside human power to control. Thus, when it is considered by an atheist or an agnostic whose presuppositions don’t include the existence of an omnipotent God, the idea that resurrection is maximally improbable immediately strikes one as indisputable. There’s no agency to muddle things up. Yet to many Christians, the argument is sometimes dismissed as philosophical trickery. ‘Of course we can believe in miracles – nothing is impossible for God! It’s simply a circular argument! Hume’s an atheist so of course it seems impossible to him.’ My view, I suppose, is in between: I agree that Hume’s problem is that he excludes the idea of God’s agency, yes; but he doesn’t do so in a circular way; however, the way this exclusion messes things up is when it comes to the interplay of probability and belief. A simplistic frequentist basis for probability is manifestly unsuitable when it comes to deciding what to believe in cases where agency is involved.

I hope this has done enough to cast sufficient doubt on Hume’s argument, and his principles. However, I still haven’t answered the first question, and Jonathan’s issue: given the problems with a frequentist account of probability, what is the probability of resurrection?

  1. What is the probability of resurrection?

This part will be slightly more substantive, but still with a main conceptual focus. My last section criticised naïve frequentist approaches to probability. There is a better one: the Bayesian approach to probability. The Bayesian approach doesn’t just look at probabilities of events in terms of their frequencies; it takes into account relevant data, or evidence, into account. Here’s an example. On a frequentist approach one might calculate the probability of my sashimi cake occurring by looking at all the meals ever cooked by humans, and seeing if any of them come close to my recipe. Yet from a Bayesian approach, one takes into account facts like: ‘Hin-Tai has written a blog post containing a recipe for a sashimi cake that he will cook’, as well as the probability of that evidence existing in the first place. The final probability then takes into account relevant evidence, and the probability of that evidence occurring. When I crunch some numbers using Bayes’ formula, the probability of my cake existing, given that I’ve talked about it and used it to prove a point, suddenly becomes much larger than the ridiculous 1 in 2,190,000,000,000,000 I calculated earlier. The Bayesian approach is much more nuanced and responsive to how we think about probability, given evidence, in real life.

Many have applied Bayes both for and against the resurrection, including eminent Christian philosophers and passionate atheists (just see here for examples). Yet I just want to sketch out some details that cast some doubt on Jonathan’s belief in the improbability of resurrection.

The first: if God existed, and he needed to demonstrate or confirm something about him – say, that Jesus Christ is his eternal Son who has died to take away the sins of mankind – then an eminently obvious way for him to confirm this would be through something only He could do: that is, a miracle. This is an important point, as I’ve heard many object ‘I could never believe in God on the basis of miracles; they are just so unlikely’. Yet how else could God demonstrate his own existence? There is the whiff of circularity about it again: miracles are only unlikely if you have already ruled out the existence of God; if you haven’t, then they make perfect sense as a divine strategy.

To develop this point, frequentist accounts of probability work well for quantifying human behaviour when there are unlikely to be any strong reasons for that behaviour to change suddenly. For example, if you picked a bunch of random and clashing ingredients that have never been used in a recipe before, it is a sure bet that no one will ever use them. However, as soon as you introduce reasons for agents to get involved – such as giving another friend a bet that he can’t cook a meal using these precise ingredients – the first probability flies out the window. Similarly: the probability that God will miraculously raise someone from the dead indeed looks very small, given the history of human deaths. Yet if God has a very strong and coherent reason to resurrect (which the Bible outlines very clearly), that starting probability flies out of the window.

Where does this leave us? I suggest: since an omnipotent God may be involved, since He has very strong reason to resurrect his crucified Son (‘God… raised him from the dead and gave him glory, so that your faith and hope are in God’ (1 Peter 1:21)), since people died claiming to be eyewitnesses, since worship of this God is still vibrant 2000 years on… it’s nowhere near as improbable as Hume argues.


2 thoughts on “How improbable are miracles? Thoughts on Hume and the resurrection of Christ

  1. Pingback: Reflections on Scorsese’s ‘Silence’ – Hin-Tai Ting

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