Against Hume

The entire Christian faith rests upon a single miracle.

If Jesus of Nazareth truly rose from the dead, then we need to take him very seriously. But if Jesus did not rise from the dead, then, as St. Paul says, our faith is useless. Clearly, there is a lot at stake if miracles occur.

So, should we believe in them?

In his essay, “Of Miracles”, the Scottish skeptic David Hume argued that miracles are so inherently unlikely that we can reject any miracle claim without even considering the evidence. Hume’s argument has been extremely influential in the philosophy of religion; if he is right, then Christianity is in serious trouble — not to mention other faiths. But is Hume right?

I will argue that Hume’s argument against miracles fails for three reasons. First, it is doubtful that we can know the probabilities needed for Hume’s argument to even get off the ground. Second, Hume fails to take into account background beliefs when estimating the likelihood of miracles. Finally, there are other factors to consider besides mere likelihood when evaluating competing hypotheses. I will consider two different interpretations of Hume’s argument, and argue that they both fail. I conclude by considering a potential objection to my argument by the philosopher Edward Craig, and responding to it.

Two Arguments Against Miracles

While it is not my intent to exegete Hume, I think there are at least two ways we can interpret his argument against miracles. The first is an argument for the conclusion that miracles are impossible. Accordingly, let us call this argument “the impossibility argument against miracles.”

The Impossibility Argument Against Miracles

We can state the argument succinctly as follows:

1. A miracle is a violation of the laws of nature.
2. A violation of the laws of nature is impossible.
3. Therefore, a miracle is impossible.

The first thing to note about this interpretation of the argument is that it requires a particular definition of a miracle as “a violation of the laws of nature.” Here already, we encounter a problem with this formulation of the argument, since there is a great deal of debate about both what a miracle is, and what a law of nature is.

According to some philosophers, the laws of nature should not be seen as literal “laws” that nature must “obey,” but rather as generalized descriptions of how nature usually behaves. This consideration immediately reveals a simple way to reject this form of Hume’s argument: adopt a view of the laws of nature as generalized descriptions of nature. If the laws of nature are simply generalized descriptions of how God usually governs nature, for example, then a miracle could simply be an event in which God governs nature differently than he normally does. So what’s the problem supposed to be? In short, we can simply deny the highly controversial first premise of the argument.

Even if we were to grant for the sake of argument that the laws of nature are literal laws which nature must obey, there is still another easy way to reject the impossibility argument: deny the second premise. Upon reflection, the motivation behind the second premise of the argument is really just the idea that the universe is a closed and self-contained system, insulated from any outside activity or inputs. In short, Hume thinks that a violation of the laws of nature is impossible because the universe is causally closed from any outside activity. But, if that is the motivation behind the second premise, then the detractor of the argument can simply adopt the modus tollens form of the argument: if God acts in the world, then the universe is not causally closed, and so a violation of the laws of nature is possible.

So, whether you think a violation of the laws of nature is impossible ultimately depends on whether or not you believe the physical world is a causally closed system. But that, in turn, depends on whether you think God acts in the world or not. But if you believe that God acts in the world, then, in essence, you already believe miracles are possible. So, the impossibility argument against miracles is question-begging: whether you accept the premises depends on whether you already accept the conclusion.

The Probabilistic Argument Against Miracles

So much for the impossibility version of Hume’s argument. Now we turn to what I will call “the probabilistic argument against miracles.” Notice that if we do not commit ourselves to a specific definition of a miracle as “a violation of the laws of nature,” then we can avoid the problem of how to define a miracle, and also avoid the problem of how to define a law of nature. Instead, we can just frame the argument by saying that, whatever a miracle is, it has got to be something highly unlikely. As the philosopher Edward Craig points out, the fact that miracles are highly improbable is a reasonable assumption because of the way miracles are typically used to support religious beliefs:

Given what its role is to be in underpinning religious belief, a miraculous event must surely be one which our experience tells us is highly improbable. For if it were the sort of thing that can quite easily happen, then any old charlatan with a bit of luck or good timing could seize the opportunity to qualify as having divine authority.¹

So, we can immediately see how this form of the argument is much more powerful, since it does not rely on controversial definitions of miracles or laws of nature. Here is how we might formulate the probabilistic argument against miracles.

1. A miracle is an extremely unlikely event.
2. Therefore, it is always more likely that we are mistaken about the miracle than that the miracle actually occurred.
3. If hypothesis A is less likely than hypothesis B, then it is irrational to believe A.
4. Therefore, it is always irrational to believe in miracles.

As we have already seen, the first premise has a lot going for it, since most people would surely agree that, whatever a miracle is, it has got to be pretty unlikely given its role in providing support to religious beliefs. What about the other premises? The third premise certainly appeals to common sense, since, as Hume put it, “a wise man proportions his belief to the evidence.” The idea behind the second premise also seems reasonable, that given we already know that a miracle is extremely unlikely, it is probably the case that we are mistaken about the miracle. For instance, maybe the person who is reporting the miracle is lying, or has false motives. Or maybe we only think we saw a miracle, but our senses are deceiving us. Whatever the reason could be for us being mistaken, it has still got to be more likely that we are mistaken than that the miracle itself really happened, since those things are very odd and unlikely indeed.

So, the premises of probabilistic argument seem reasonable at first glance. But how do they fare under the cold light of morning?

Probability and Vagueness

Consider again the first premise, that a miracle is an extremely unlikely event. As we saw earlier, this seems reasonable enough. But on closer inspection, this premise does seem a bit vague. Just how unlikely is a miracle exactly? For example, can we confidently assign a precise probability to this premise in terms of a percentage? Not likely. Is a miracle only 1% likely to occur? Or maybe 5% likely? How exactly are we supposed to choose between these? Upon reflection, it seems that we can’t. There is no non-arbitrary reason for assigning the percentage a bit lower or a bit higher.

Moreover, it is not even clear that all miracles have the same likelihood. Is the parting of the red sea just as likely to occur as water turning into wine? Speaking of water, what about walking on water — should we make the probability lower for each step taken on the sea? Considerations such as these raise doubts that it is possible to assign a probability for a miracle at all.

Here is one way to see it: in order to come up with a probability for an event, you must first enumerate the possible set of outcomes in which the event in question occurs, and then divide that number by the total number of possible outcomes. To roll a number five on a six-sided die, for example, you have one possible outcome in which you get a five, and there are six possible outcomes total, so you divide one by six to get a probability of ⅙, or roughly 16%. But how in the world are we supposed to calculate either of those values in the case of miracles? Is the total number of possible outcomes simply the total number of configurations of atoms in the physical space in which the miracle occurs? If so, the denominator in our calculation is going to be unfathomably high. In fact, it will be so high that whatever we put in the numerator of this fraction is hardly going to matter; it will come out to be effectively zero.

Probability and Agency

There is a further problem with estimating the likelihood of a miracle: the notion of agency. If a miracle is being performed by a divine person (i.e. an agent who makes decisions), then it seems reasonable that they could choose not to perform the miracle. How would we even begin to factor that into our probability calculation? Imagine a silly experiment in which there are a dozen people with the flu. Half of them are told to pray for a miraculous recovery, and the other half are told not to pray. Suppose that there is no difference in recovery between the two groups. Can we conclude that prayer does not work? Not at all, since we need to take into account the fact that God can choose not to answer a prayer!

So, the experiment would in fact prove absolutely nothing. It therefore seems that the first premise of the argument is nice from far, but far from nice. It is doubtful whether we can ascertain the probability of a miracle at all, let alone in an unbiased way. And that brings us to the problem with the second premise.

If we don’t know the likelihood of something, then we can’t know that it is less likely than something else. So, if we cannot know the likelihood of a miracle, then we cannot know that it is more likely that we are mistaken about it. The probabilities of both are inscrutable. Indeed, the only way to make the comparison would involve some sort of bias, and that means that there is really no way to evaluate the argument without begging the question. If you think it is more likely that miracles occur than that your senses are failing, then you will probably reject Hume’s argument. And if you think miracles are less likely than your senses failing, then you will probably accept the argument. Whichever you choose will be inescapably subjective, and probably just come down to whether you think miracles happen or not. But that was the thing Hume was trying to persuade you of.

Probability and Background Beliefs

I think I have already said enough to cast serious doubt on the probabilistic argument against miracles. However, one more point bears mention, and that is the relationship between bias, a person’s background beliefs, and what mathematicians call “prior probability.” In short, a person does not estimate probabilities in a vacuum. When evaluating competing hypotheses, we need to consider not only the likelihood of a hypothesis by itself, but its likelihood in relation to the other things we believe. For this reason, the third premise of Hume’s argument is also questionable.

An easy way to see this is as follows. Suppose that event A has a probability of 10% of occurring, and event B has a probability of 11%, a mere 1% higher probability than A. Should we blindly accept B as the hypothesis? Of course not! For there are a multitude of other factors to take into account, such as the simplicity of the hypotheses, their degree of ad-hocness, their explanatory power, and their internal coherence, to name a few. And many of these are qualitative, rather than quantitative, features of a hypothesis. So, the third premise is too naive; as a general principle, the mere occurrence of more evidence for a hypothesis does not necessarily make it more reasonable. We need to look at hypotheses in relation to worldviews as a whole.

Let’s summarize the discussion so far. Both the impossibility and the probabilistic versions of Hume’s argument ultimately beg the question. The impossibility argument ultimately turns on whether you believe God can act in the world, and the probabilistic argument, while plausible initially, withers away as we attempt to discern concrete probabilities for the relevant premises, and we find that this is impossible to do without bias. A lesson to be learned from both of these arguments is that background beliefs inescapably come into play when evaluating arguments involving possibilities and probabilities. What a person believes determines what they find possible or likely; one does not evaluate a miracle claim in a vacuum.

An Objection

I have been arguing that Hume’s argument against miracles ultimately begs the question. However, the philosopher Edward Craig argues that to say that Hume’s argument begs the question crucially mistakes what Hume was attempting to accomplish:

He was asking what reasons there may be for forming religious beliefs in the first place. That the world may look very different, and different arguments appear reasonable, when one has already formed them, he would not for one moment dispute. Nor need he dispute it: it has no bearing on the central issue, which is whether a miracle can be proved, ‘so as to be the foundation of a system of religion’.²

In Craig’s view, to say that miracles might be more likely given one’s prior religious beliefs is misguided, since miracles are the foundation of all religious beliefs in the first place. So, one cannot say that religious beliefs make miracles appear more likely, since miracles are the entire foundation of all of one’s religious beliefs to begin with.

Craig’s point is well taken. In response, however, I question whether the primary reason for holding all of one’s religious beliefs is miracles. The entire project of natural theology, for example, attempts to provide evidence for a good subset of religious beliefs (i.e. belief in a personal God who is all good and all powerful, etc.) — and most of those arguments do not appeal to miracles. So, contrary to Craig, it seems like a scenario like the following is possible.

Mary believes in a personal God partly because of philosophical arguments she takes to be cogent. This belief in God then inclines Mary to suppose that miracles are more likely, given God’s existence, than not. And so Mary finds Hume’s argument unpersuasive, since she does not think that miracles are less likely than her senses failing, given the existence of a personal God who created her cognitive faculties to function reliably. Furthermore, Mary thinks that it is likely that a personal God, being the source of moral goodness, might want to reveal his existence to the creatures he has made through acts of intervention in the world (i.e. miracles). In this case it is not correct to say that the sole foundation for all of Mary’s religious beliefs is belief in miracles; rather, she holds some of her religious beliefs for independent reasons, and then consequently finds miracles to be more likely, given those beliefs.

So, it is clearly plausible that one might have a system of religious beliefs about a personal God which are believed independently of miracle evidence, and that one then comes to believe in more specific doctrines on the basis of miracles — miracles which are more likely given the person’s initial set of religious beliefs.

Conclusion

In conclusion, then, Hume’s argument against miracles fails. The possibility version of the argument fails because it begs the question against the possibility of God acting in the world in the first place. Likewise, the likelihoods in the probabilistic version of the argument cannot be quantified without bias, and so that argument ultimately begs the question as well. The key takeaway from the failure of Hume’s argument is the need to factor in our background beliefs when estimating the likelihood of miracles, which, contrary to Edward Craig, is perfectly legitimate since not all religious beliefs are based on miracles in the first place.

So, should we believe in miracles? I will let the reader judge for himself. But if the religious person should doubt whether miracles happen, it won’t be because of the arguments of Hume and Craig.

Notes

¹ Edward Craig, Philosophy: A Very Short Introduction (Oxford: Oxford University Press, 2002), 29.

² Craig, Philosophy, 32.