Do extraordinary claims require extraordinary evidence? (Part 1)

Summary

How many of you have heard the statement, "Extraordinary claims require extraordinary evidence?" This is a common soundbyte from skeptics to try to discredit the existence of miracles.  But more often than not, it's used incorrectly, and that sort of disappoints me, because it shows that folks are not thinking logically.  Those who hold to this claim are essentially saying that they require evidence that is as miraculous as the miracle itself for them to be convinced a miracle happened.  Do you want to convince someone of the Resurrection?  It would take something on the order of lightning in the sky that spelled out, "Jesus rose from the dead," to convince such a skeptic.

It is actually rather simple to show this argument against miracles is false: it's because the argument only holds when you first assume miracles cannot happen.  And if you assume miracles cannot happen, then of course you are going to conclude that no evidence is enough to prove a miracle.  This is the mistake Hume made, the mistake the Jesus Seminar folks made, and the mistake that Bart Ehrman makes.

But you cannot a priori assume that miracles cannot happen; if you do this, there is no reason to have the discussion.  It is a form of circular reasoning.  Therefore, you must instead make an allowance (however small) that they can happen.  If they can happen, then any sort of everyday evidence could be evidence in favor of a miracle.  The question would then become whether the evidence is sufficiently in favor of a miracle to make someone believe, not whether something as commonplace as eyewitness testimony could be evidence of a miracle.

This can be shown rather rigorously using Bayes' Theorem, which I will do next time.  (Be forewarned: it can be a bit technical, but if you like math, or even if you don't, but you don't mind getting out a pencil and paper and following along, it should be pretty straightforward.)  Below I just give a brief, intuitive introduction to Bayes Theorem.

The intuition of Bayes Theorem

First of all, I love Bayes Theorem.  I've talked about it several times on this blog, mostly because it's really good to show that indeed, miracles can happen.  It's also super-easy to use; you just have to know a few things about probability, which are all taught in high school (I think).

Bayes Theorem is what helps us answer questions about what might be true (i.e., the converse of what we know to be true). Here's what I mean.  Let's say we know that for sure, the statement "if A then B" is true.  This means that if we know that A is true, then B must be true. But this does not mean that if B is true, then A must be true. But it seems like "B" being true adds some weight to "A" being true.  Bayes Theorem is how we figure out just how much weight that is.

Here's an example in which "B" being true definitely does not imply that "A" is true.  Let's say the statement "If I am swimming a race against Ryan Lochte (A), I will lose the race (B)" is true. Then let's say I swim in some race, and later tell my friend that I lost (B).  Can my friend infer that I must have been swimming against Ryan Lochte (A)?  Of course not.  There are many other swimmers out there that I would lose to.  In this case, B does not even come close to implying A.

On the other hand, here's an example where it seems B almost implies A: If you stand out in the rain (A), you will get wet (B).  Here, A implies B.  Does that mean if someone is wet, they stood outside in the rain?  No, but what happens if you add further evidence to the scenario?  You are in a shop, and someone comes in from the outside and they are dripping wet.  You'd probably conclude that it is indeed raining outside.  Adding further evidence, what if everyone who came in either had a wet umbrella, a wet raincoat, or was just wet (on their clothes)?  Now add the fact that when you went into the shop, you noticed dark clouds in the sky.  So yeah, you don't need to actually see the rain to be pretty sure it's raining.  (Thanks to pleaseconvinceme.com for inspiring this example.)

That's a brief, intuitive example of how Bayes' theorem works.  The more evidence that's in favor of an event (A) above and beyond other explanations, the more you can be certain that, given said evidence (B), A is true.