 Let's now turn from the topic of science to the topic of religion and deal with the case studies that I mentioned before miracles and revelation. Here's a picture of David Hume, who was a Scottish philosopher, and here's a quote from one of his books. He says, There is not to be found in all history any miracle attested by a sufficient number of men of such unquestioned good sense, education, and learning as to secure us against all delusion in themselves of such undoubted integrity as to place them beyond all suspicion of any design to deceive others of such credit and reputation in the eyes of mankind as to have a great deal to lose in case of their being detected in any falsehood and at the same time a testing facts performed in such a public manner and in so celebrated a part of the world and as to render the detection unavoidable. All which circumstances are requisite to give us a full assurance in the testimony of men. Hume used this argument to say that, well, if you observe a miracle directly, then you might be justified in believing that it happened. But if you hear about a miracle through testimony, either second hand or third hand or fourth or fifth or sixth hand, then you should never believe that it actually occurred and you can see here in the quotation that I've underlined a few of the source and receiver and conduit virtues that Hume refers to in his argument. He says that there should be multiple sources. So he talks about the number of men and then he also talks about the virtues that they should have which include good sense, education, learning, as well as credit and reputation so that they have something to lose if we find out that they were lying or mistaken. So Hume thinks that we, who tend to be in the position of person N in this graph, should always disbelieve reports about miracles. This can be contrasted with the view of miracles that is articulated by Thomas Reed. Reed argued that people should observe both the principle of veracity and the principle of credulity. He says that we are social creatures by nature and that means that we have a natural propensity to speak the truth. That means that he thinks that people have a sort of inborn source virtue, that they're naturally disposed to say what they think, they're naturally disposed to report what they know and not what they merely guess or what they think is false and interlocking with this, Reed argued for the principle of credulity. He said because people observe the principle of veracity, we likewise have a natural propensity to believe what others tell us and that this is correct because after all if others are observing the principle of veracity, then it only makes sense as a receiver as someone in the position of person B in the network shown here to believe what they say. So whereas Hume said we should be skeptical receivers and skeptical about conduits and sources, Reed argued that because we're essentially interdependent social creatures, we should take seriously the words of other people even when they report things like miracles. This suggests that the kind of creatures that you think human beings are and the kinds of dispositions that you think they naturally have, the kinds of source and receiver virtues that are appropriate for humans will indicate to you what sort of credence you should put in reports about miracles. We can think about this using what's known as Bayes' law. This is an equation that tells you how much credence you should put in a proposition given a certain amount of evidence. This is a fairly mathematical bit of the story, so I'll take some time to walk through it. The large P in parentheses following it just means a probability. So we have on the left side of the equation a single probability, namely the probability of a hypothesis given some evidence, whereas on the right side of the equation we have three probabilities, the initial probability of the hypothesis to begin with, the probability of the evidence given the hypothesis, also known as the likelihood, and the probability of the evidence occurring in the first place. Bayes' law tells you that whenever you get some evidence relevant to a particular hypothesis, you can update your credence in that hypothesis by taking the product, multiplying the your initial confidence in that hypothesis by the likelihood and then dividing by the probability of the evidence in the first place. This gives us what is now called a posterior probability. So if you already had very low credence in the hypothesis to begin with, if the probability of H was say 0.01, 1%, then even if there was really strong evidence for it, you might only increase your credence in it from 0.01 or 1% to say 5%. So even really strong evidence for an incredibly unlikely hypothesis shouldn't necessarily be convincing. So let's think about this in the context of miracles. If H, the hypothesis, is that a miracle occurred, then we can let E, the evidence be either someone says that a miracle occurred, or someone says that someone says that a miracle occurred, or someone says that someone says that someone says that a miracle occurred, and so on. This represents the number of conduits that the testimony has passed through from the original source to us. And as you can see from this, the probability that a miracle occurs should generally be considered quite low. So your prior probability in any particular miraculous event should be extremely low. Unless you believe that miracles are occurring all the time, all over the place, your probability should probably be something like 0.0000001 for any particular miracle. And if someone says that a miracle occurs, well, how likely does that make it that a miracle occurs? We can think of lots of reasons why someone would say this, even if it weren't true. And we can think of even more reasons why someone would say that someone else says it, even if it weren't true. And this indicates that as Hume argued, the amount of evidence we need to get, the number of sources and the epistemic virtues associated with those sources must be extremely high for us to believe that miracles have occurred.