We all know the famous line, and most of us probably agree with it, but I want to argue here that the main difference between believers (in ESP, ghosts, clairvoyance, astrology, etc) and Skeptics is the way they interpret and understand the ‘extraordinary claims’ bit.
Now, for believers, these claims really are not extraordinary at all. After all, they will say, people in all times and at all places have seen ghosts, communicated with the dead, and predicted the future. So if somebody down the street sees a ghost tomorrow, then that’s perfectly normal. This kind of thing happens a lot with human beings. It’s just an ordinary part of human life.
For the Skeptic, though, things are completely different. So when somebody claims to be talking to your dead mother, the skeptic will say (quite rightly, in my view) that it’s extremely improbable that your mother still exists with the same personality, emotions, values and memories but with no brain or body! They will also point to the evidence from neuroscience and the like showing that brain damage can completely change one’s personality and destroy memories.
So, I want to say that the skeptics have the correct interpretation of the ‘extraordinary claims’ part of the famous line, whereas believers really don’t get it at all. The fact that people in many or all cultures have found it extremely difficult to accept that loved ones are gone forever, and have therefore been deeply interested in things like ghosts and communication with the dead, does not make it probable that any of these things are real. You need to focus in on the specific claim being made and think about how probable that specific claim is. For example, the notion that I will continue to exist as pretty much the same person after the death of my body and brain is extremely improbable, but the notion that something might survive the death of my body (e.g. some kind of pure consciousness or something) is much more probable.
I feel it’s pretty important to try to sort these things out, because believers and skeptics have such completely different starting points in all of these debates that they just end up talking past each other, and sometimes just resorting to name-calling and personal attacks.