Against Arguments from Miracles

Some theists and religious apologists use accounts of miracles as evidence for the existence of God or a specific religion. However, I think that their reasoning can be shown to rely on a mistake.

In the Bayesian reasoning employed by proponents of such arguments, for data to favor one hypothesis over another, it must be the case that the former hypothesis better predicts the data than the other (in other words, the probability of the data given the hypothesis is greater than the probability given the alternative). So, a proponent of an argument from miracles will want to elicit an intuition that his hypothesis better predicts the relevant data.

For example, if there are unusual test results taken from some religious relics, the miracle advocate will claim that this is significantly more likely given the existence of God (or given his religion specifically). Initially, this claim might seem quite plausible, and so one might think that the apparent miracle is significant evidence for the theistic/religious hypothesis.

However, for any such data, there will be other data that is similarly predicted by the same hypothesis. For example, in the case linked to above, the (supposedly reputable) claim that certain tests came back negative but one came back positive (one that normally comes back negative before the others) is taken as evidence of miraculous preservation, but presumably if it was instead claimed that there were test results suggesting better preservation, that also would have been similarly taken as evidence. And, of course, the proponents of arguments from miracles usually accept many different sorts of apparent miracles as evidence. In addition to alleged Eucharistic miracles, one might also take as evidence accounts involving apparent regrowth of limbs, Sun miracles, flying monks, and a wide variety of other unusual events. There is not much reason for expecting any specific data over other data (or if there is, it might be the sort of data which we never see, such as apparent direct communication between God and a large number of witnesses).

It seems that the intuition that some specific apparent miracle is much more likely given theism is dependent on the intuition that apparent miracles in general are more expected given theism. But now suppose, for example, that each apparent miracle has a one in a million probability of happening in a year given atheism. If there are a million potential apparent miracles with such a probability (and assuming that the probabilities are independent), it is more likely than not that an apparent miracle will happen in a given year. If the increase in probability given theism is equally distributed among apparent miracles, then it cannot be the case that, for example, some specific apparent miracle is twice as likely given theism, since this would entail that apparent miracles in general are twice as likely, which could not be the case if apparent miracles were already more likely than not. (Admittedly, the friend of miracles will presumably not want to say that the increase in probability is equally distributed. But there will presumably be a large variety of apparent miracles where there is no strong reason to prefer one over the other. Also, the stronger the prediction of some specific miracle is, the stronger the evidence against the hypothesis if the event fails to happen.)

Now, the numbers I used above are simply illustrative examples, and so cannot be used to disprove a claim that some data is much more likely given (some sort of) theism than atheism. But in general, the more general the predictions of a hypothesis are, the less the potential limit of the ratio – of the probability of the data given the hypothesis to the probability given the alternative – is (assuming that the probabilities given the alternative are non-zero and that the failure of one event does not guarantee the failure of others). This is, I think, sufficient to undermine the initial intuition one might have in some specific miracle case.

Although it might seem much more likely that, for example, the data associated with the Miracle of the Sun or the Lanciano relics will be present given (Christian) theism than otherwise, this depends on the intuition that it is much more likely that apparent miracles in general will happen given (Christian) theism; but the latter claim is doubtful. If there are many, many potential events that fall under the category of apparent miracles, it will be unsurprising that such things sometimes happen given atheism; and since the ratio of the probability of some specific apparent miracle given (Christian) theism to the probability of that same data given atheism is supposed to be strongly correlated with the ratio of the probability of apparent miracles in general given (Christian) theism to apparent miracles given atheism, it is far from obvious that the relevant data is significantly more likely given (Christian) theism than atheism.