I was talking with a friend earlier about David Hume and we brought up my formulation of an argument for miracles derived from David Hume. That’s right. David Hume, the famous scottish skeptic. When I presented his argument for my philosophy of religion tutorial, they had a fit. Arts tutorials with me are always interesting and happening. πŸ˜› Regardless, I decided to formally write down my argument here for future reference.

The Problem with Induction

In order to understand Hume’s “argument” for miracles, one needs to first understand one of Hume’s very famous argument against inductive reasoning, for the objection against miracles rest upon inductive reasoning (in fact, it is Hume’s very own objection, but then again, no one is always consistent. πŸ˜› )

Here is a crude form of the argument against induction. Induction operates on the following logic: Suppose you want to prove the following statement,

(A) All humans who die stay dead after three days

So you reason by observing that this person remained dead after three days, that person remained dead after three days, so on and so forth. And after you’ve collected a “large” enough sample, then you infer that all humans remain dead after three days.

Now according to Hume, the problem with this reasoning is that there is no connection between past events and future events. There is only a series of various independent and particular events, i.e. this person remaining dead, that person remaining dead, etc, etc. Why should a collection of many particular and independent events prove or say anything about other occurrences? Say, this person who just died a day ago? What’s the connection? And Hume’s argument is that there is no connection at all! So no matter how large your sample size, you can make absolutely no inferences about the future or any other occurrences. To use an analogy, it is like trying to prove that John will lie by pointing out that Mary lie a lot of times, that Jonathan lie a lot of times, that Bill lie a lot of time, etc. What do they all have to do with John lying? They are all distinct persons from John and have nothing to do with whether John will lie.

To come back to our case, one way we can generalise the argument is by saying that the principle of induction assumes that the future resembles the past. This means that future events will resemble past events such that the future will simply repeat the past, so if you can gather a sufficiently large amount of samples from the past, you can infer what is going to happen in the future. Unfortunately, there is absolutely no reason to believe this. Sure, it maybe pragmatic to believe this, but that isn’t the same thing as saying that it is rational to do so. To come back to our analogy, you may say that we can “prove” that John will lie by pointing out that John did lie at this occasion, and that occasion in the past, etc. But this wouldn’t do. What does John’s past have to do with his present or future? It is as if all the various past Johns are all disjoint particular events which have no relation whatsoever with his present or future. Likewise is it with all these vast past recorded events will tell you absolutely nothing about the future. (There is actually an even more philosophically generalised form of this argument, the infamous “grue” argument which says that not only do events not resemble across time but across space and historical circumstance as well, but we won’t need to get into that.)

One very common mistake which people make when reading this argument (a mistaken which even my philosophy professor made, horrors of horrors!), is that they simply think that this proves that we simply cannot be certain about the future or make sure inferences from finite samples collected, but we still have very strong probability of believing that it is so. But turn back to the example of John will lie. No matter how many people you or how large your sample size of people who have lied may be, you can’t infer anything, not even the probability or possibility of John lying. Why? Because they all have absolutely nothing to do with John. Simply apply this reasoning between various distinct and independent past events, and the logic is the same. All these events have absolutely nothing to do with one another, and the massive cumulation of all these events doesn’t say or increase one whit the probability of the event occurring for the future.

I will present a slightly more mathematically rigorous formulation of this argument to make it clearer, but for those who “get it” or can’t stand maths, you can simply skip to the next section.

The Mathematics of Hume’s Argument

Now, there is a simple example of how probability works. Say, you have a jar, containing 100 beads, and I tell you that 20 of them are red. So if I ask you, what is the probability of you picking a red bead when you take one bead from the jar, you answer has to be 20% or one out of five.

Now, let’s turn to the universe. Say you want to measure the probability of a person remaining dead after three days. Now what corresponds to the “100 beads” in my example would be the total number of people who had, have and will die. What will correspond to the “red beads” is the total number of people whom we have observed to have remained dead after three days. Thus to illustrate this more graphically

(Total no. of red beads/Total no. of beads)Β = Probability of picking a red bead

(Total no. of people observed in the past remaining dead after 3 days/Total no. of dead people in the past, present and future) = Probability of people not rising from the dead after 3 days

Now, this is where Hume comes in. He would say that the numerator of our formula is finite. We can only observe a finite number of people who have died in the past, if for no other reason then only a finite number of people have ever existed in the past. But our denominator, or sample space, is infinite. It is supposed to encompass not only the past, but all and every possible human being. When you divide a finite number by an infinite number, no matter how large you finite number, your probability is zero. Well, actually, no, not quite zero, the more mathematically precise answer is that it tends towards zero or shrinks towards zero but never quite reaching it.

But the point still is, no matter how many samples of the numerator you gather, you shall never be able increase one whit or even a tiniest bit, the probability of your claim, as long as your denominator is infinitely large. Therefore, the induction samples of the past is absolutely no proof as to what is going to happen in the future, nor can you make any inference from it.

Evidence Against Miracles?

So now that we understand Hume’s arguments against induction, we can turn to Hume’s arguments against miracles. Hume’s arguments against miracles oddly enough, depends on induction. He claims that because there is an overwhelming number of instances where people who die remain dead after three days, therefore it is very unlikely Jesus Christ rose from the dead. But if we apply Hume’s arguments against induction to this case, we can legitimately pose to Hume his own argument, what does past instances of people who die remain dead after three days have anything to do with Jesus Christ remaining dead after three days? No matter how large the samples collected, they don’t increase one bit the probability of that Jesus Christ would remain dead after three days.

And we can apply pretty much apply the same argument to almost every miracle of the Scriptures. And there you have it. David Hume’s argument for miracles. Well, actually not quite. It is more of an argument against the argument against miracles.


When I pointed this out in my tutorial which was discussing Hume’s argument against miracles, that Hume had effectively shot himself, it was quite amusing to see the tutor dumbfounded and some of the students have a fit. hahahaha… Arts tutorials were always fun. πŸ˜›

Still, one can argue that if we accept Hume’s argument against induction, all of science will go to the dogs because all of the hard sciences (except mathematics) is premised upon induction. Well, true. But then again, no one ever said that science had any coherent metaphysical foundation anyway. It is pragmatic, as I said, to assume induction, but rational, is another thing.

Although of course as a Christian, I always have faith in the stability, order and uniformity of nature. But this isn’t an argument of reason, only an article of faith. πŸ™‚

4 thought on “David Hume’s Argument for Miracles”
  1. Very interesting post! Got me thinking a lot after reading it. If there's really any issue I can raise with this post, it is that you seem to conflate predictability with determinism. It is true that past results from the flipping of a coin do not determine the future result of the flipping of the same coin. But that doesn't mean the result is unpredictable. Going back to your mathematical proof, it is true that "in the long run we are all dead [metaphorically]" but that doesn't mean that short run predictions are therefore doomed to fail too. πŸ˜€

  2. Although it is my habit not to reply to anonymous comments, but since you made your point politely, I will respond.I am not sure which part of my argument involves "determinism". Predictability is premised upon the induction principle, which is premised upon the uniformity of nature and the resemblance of the present and future to the past. I do not require a 100% predictability which is what determinism would (in principle) allow. The argument refutes even the probalistic predictability.As for the long run, I'm not so sure again what does that have to do with my proof. I can simply enlarge the denominator to include the "grue" examples which are variations not only across time but across space and historical circumstances as well.

  3. Most of this post is pretty good. The section ‘The Mathematics of Hume’s Argument’, however, does not correctly summarize Hume, and he would certainly have disowned it. Hume’s point is that no conclusion about a set B can be reached based on observations of a set A disjoint from it. Whether A and/or B is finite or infinite does not come into it – as Hume specifically says. And Hume would not have accepted the ‘axioms’ of probability theory that implicit;y underlie your reasoning, nor would he have accepted that we could calculate ANY probability based on the given events. You can make the argument in the paragraph on your OWN behalf if you want to, but you are not only going beyond Hume, but even contradicting him.

  4. Re my previous comment: ‘as Hume specifically says’: the quote is THN 1-3-6 ‘From the mere repetition of any past impression, EVEN TO INFINITY (emphasis mine), there never will arise any new original idea, such as that of a necessary connexion; and the number of impressions has in this case no more effect than if we confin’d ourselves to one only.’

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