Well, of course, it is tempting to go for something like, "That the wheel, agriculture, and the Macarena were all actually invented by yetis." Or to do the sophomoric pseudo-ironic logic twist of, "That every truth can eventually be proven." Or to get up my hackles, draw up to my full height and intone, "Sir, we scientists believe in nothing that cannot be proven by the whetstone of science, verily our faith is our lack of faith," and then go off in a lab coat and a huff.
The first two aren't worth the words, and the third just isn't so. No matter how many times we read Arrowsmith, scientists are subjective humans operating in an ostensibly objective business, so there 's probably lots of things we take on faith.
So mine would be a fairly simple, straightforward case of an unjustifiable belief, namely that there is no god(s) or such a thing as a soul (whatever the religiously inclined of the right persuasion mean by that word). I'm very impressed, moved, by one approach of people on the other side of the fence. These are the believers who argue that it would be a disaster, would be the very work of Beelzebub, for it to be proven that god exists. What good would religiosity be if it came with a transparently clear contract, instead of requiring the leap of faith into an unknowable void?
So I'm taken with religious folks who argue that you not only can, but should believe without requiring proof. Mine is to not believe without requiring proof. Mind you, it would be perfectly fine with me if there were a proof that there is no god. Some might view this as a potential public health problem, given the number of people who would then run damagingly amok. But it's obvious that there's no shortage of folks running amok thanks to their belief. So that wouldn 't be a problem and, all things considered, such a proof would be a relief—many physicists, especially astrophysicists, seem weirdly willing to go on about their communing with god about the Big Bang, but in my world of biologists, the god concept gets mighty infuriating when you spend your time thinking about, say, untreatably aggressive childhood leukemia.
Finally, just to undo any semblance of logic here, I might even continue to believe there is no god, even if it was proven that there is one. A religious friend of mine once said to me that the concept of god is very useful, so that you can berate god during the bad times. But it is clear to me that I don't need to believe that there is a god in order to berate him.