Martin Smith in the Oxford University Press Blog:
We often want to know how likely something is. I might want to know how likely it is that it will rain tomorrow morning; according to the Met Office website, at time of writing, this is 90% likely. If I’m playing poker, I might want to know how likely it is that my opponent has been dealt a “high card” hand. With no other information available, we can calculate the probability of this to be about 50%. There seems to be close link between likelihood and belief; if something is likely, you would be justified in believing it, and if something is unlikely, you would not be justified in believing it. That might seem obvious, and the second part might seem especially obvious – surely you can’t be justified in believing something that’s unlikely to be true? I will suggest here that, sometimes, you can.
Some philosophers and psychologists have argued that it can sometimes be a good thing for people to hold irrational beliefs. That may be right, but it’s not the point I want to make. I think that believing the unlikely can not only be a good thing, but can be fully rational. The reason has to do with testimony, and when we owe it to other people to believe what they say. So much of what we believe about the world is based on the testimony of others. And, while we don’t always accept what others tell us, disbelieving a person’s testimony is not something to be taken lightly. If someone tells me, say, that there’s a coffee shop nearby and, for no reason at all, I refuse to believe it, then this is not just about me – another person is involved, and I’m doing that person a wrong. If I refuse to believe what someone tells me, then I need to have a good reason for doing this.
What does this have to do with believing the unlikely?