Psychologist Daniel Kahneman has written a book about how cognitive illusions blind us to reason. He notes that telling Wall Street traders that their performance is no better than a roll of the dice does not shake their confidence in their ability. He marvels at the disconnect. This might at first seem to be an inherent flaw in human design, tantamount to a manufacturer’s defect in human nature.

But perhaps, surprisingly, it is just the opposite: A sort of failsafe survival mechanism to help us overcome self-doubt. We’ve all had moments of loss of confidence and know how debilitating they can be. Biologist Robert Trivers considers this alternative interpretation in his book Deceit and Self-Deception: Fooling Yourself the Better to Fool Others.

Fooling yourself, which sounds like a road to disaster, may instead be key not only to getting past your fear of inadequacy but also to being a truly innovative leader. How so? It is, at least in some cases, a critical component—the first ingredient—in the intangible combination of qualities that give some people the power to inspire others to make the impossible possible. If you doubt that, look no further than Walter Isaacson’s biography of former Apple CEO Steve Jobs.

Isaacson writes that it was called the Jobs reality distortion field, which “came from willfully defying reality, not only to others but to himself.”

And it was empowering. “It enabled Jobs to inspire his team.” As one employee noted, “You did the impossible because you didn’t realize it was impossible.”

Isaacson tells how in a presentation Jobs once quoted from Lewis Carroll’s Through the Looking Glass, referring to when Alice says she can’t believe the impossible, and the Red Queen responds, “Why, sometimes I’ve believed as many as six impossible things before breakfast.”

Motivational psychologist Heidi Grant Halvorson in her book Nine Things Successful People Do Differently also notes how belief that removes limitations can positively affect performance. She explains that it becomes a self-fulfilling prophecy: if you believe you can get smarter, if you believe that human abilities grow with effort and experience—rather than being something that each person has in a prescribed amount or to a predetermined degree—you will be more inclined to overcome whatever obstacles are placed in your path as you work toward your goals.

As she explained in a Harvard Business Review Ideacast, if you believe some people are born good leaders and some are not, at the first sign that you are not a good leader, you will give up. But, she notes, there are now decades of research proving that this is a false construct. Abilities like creativity and leadership can be developed.

Maybe some barriers can’t be overcome, but believing they can increases the likelihood that you can make it so. That’s something to keep in mind the next time you’re handed what seems like an impossible security challenge.