This is a great question.
Seeing it on the cover of a book in Sisters' (Oregon) Paulina Springs Books made me instantly believe, "I'll be standing at the cash register soon with my VISA card in hand."
I couldn't have proven that I'd end up buying What We Believe But Cannot Prove, yet I believed it. And it turned out that I was right.
What I didn't know at the time, though, was that all of the mini-essays in the book are available for free online at Edge. So if you want to learn how some of the most brilliant minds in the world answered this question, you don't need a credit card.
I'm scientifically minded, though not a scientist (I did spend two years in a Systems Science Ph.D. program and finished all the coursework, but never got the degree). Like the people who contributed to this Edge project, I'm also very much into looking past the Known into the vast reaches of Possibly True.
This isn't the same as holding a religious belief, though, as planetary scientist Carolyn Porco makes clear in her essay.
This is a treacherous question to ask, and a trivial one to answer. Treacherous because the shoals between the written lines can be navigated by some to the conclusion that truth and religious belief develop by the same means and are therefore equivalent. To those unfamiliar with the process by which scientific hunches and hypotheses are advanced to the level of verifiable fact, and the exacting standards applied in that process, the impression may be left that the work of the scientist is no different than that of the prophet or the priest.
Of course, nothing could be further from reality.
The whole scientific method relies on the deliberate, high magnification scrutiny and criticism by other scientists of any mechanisms proposed by any individual to explain the natural world. No matter how fervently a scientist may "believe'"something to be true, and unlike religious dogma, his or her belief is not accepted as a true description or even approximation of reality until it passes every test conceivable, executable and reproducible. Nature is the final arbiter, and great minds are great only in so far as they can intuit the way nature works and are shown by subsequent examination and proof to be right.
There's a humility, openness, and willing embrace of uncertainty in these essays which is noticeably missing in religious holy books.
Priests, imams, gurus, rabbis, yogis, and such also believe a lot of stuff that they don't know to be true. However, they're usually not willing to admit that their faith isn't founded on demonstrable facts.
Leon Lederman, who won the Nobel Prize in physics, says in his essay:
To believe something while knowing that it cannot be proved (yet) is the essence of physics.
This shows that those who claim that embracing science means casting aside mystery, imagination, and creativity are talking nonsense. My interest in exploring the nature of human consciousness -- especially the possibility that it survives bodily death in some fashion -- is just as strong now in my churchless phase as when I was a true believer.
The only difference is that I no longer consider that what I want to believe really is true. It's just a hypothesis, a possibility, a wish.
Psychologist Jesse Bering speaks of this almost universal yearning to live on after we die in his essay:
In the United States alone, as much as 95% of the population reportedly believes in life after death. How can so many people be wrong? Quite easily, if you consider that we're all operating with the same standard, blemished psychological hardware.
...It seems that the default cognitive stance is reasoning that human minds are immortal; the steady accretion of scientific facts may throw off this stance a bit, but, as Unamuno found out, even science cannot answer the "big" question. Don't get me wrong. Like Unamuno, I don't believe in the afterlife. Recent findings have led me to believe that it's all a cognitive illusion churned up by a psychological system specially designed to think about unobservable minds. The soul is distinctly human all right. Without our evolved capacity to reason about minds, the soul would never have been. But in this case, the proof isn't in the empirical pudding. It can't be. It's death we're talking about, after all.
Susan Blackmore, also a psychologist, talks in a somewhat similar vein. I share Blackmore's unproven belief: that while I certainly show every sign of being a separate and distinct "Me," this likely is an illusion -- and that what Buddhists call enlightenment is seeing through this charade.
It is possible to live happily and morally without believing in free will. As Samuel Johnson said "All theory is against the freedom of the will; all experience is for it." With recent developments in neuroscience and theories of consciousness, theory is even more against it than it was in his time, more than 200 years ago. So I long ago set about systematically changing the experience. I now have no feeling of acting with free will, although the feeling took many years to ebb away.
...When the feeling is gone, decisions just happen with no sense of anyone making them, but then a new question arises—will the decisions be morally acceptable? Here I have made a great leap of faith (or the memes and genes and world have done so). It seems that when people throw out the illusion of an inner self who acts, as many mystics and Buddhist practitioners have done, they generally do behave in ways that we think of as moral or good. So perhaps giving up free will is not as dangerous as it sounds—but this too I cannot prove.
As for giving up the sense of an inner conscious self altogether—this is very much harder. I just keep on seeming to exist. But though I cannot prove it—I think it is true that I don't.