William James made it his life's work to argue the legitimacy of belief (or faith) without evidence to support a claim. The Will to Believe was a lecture given by James in 1896. This lecture mostly pertains to religious belief but can apply to a broader scope, too, as you will see later. The thesis of The Will to Believe is found in the brief section IV and reads as follows:

Our passional nature not only lawfully may, but must, decide an option between propositions, whenever it is a genuine option that cannot by its nature be decided on intellectual grounds; for to say under such circumstances, "Do not decide, but leave the question open," is itself a passional decision—just like deciding yes or no—and is attended with the same risk of losing truth.

Let's unpack this thesis statement. What does James mean by "passional nature"? Passional in this sense is not meant in a romantic or biblical way (i.e., the passion, or suffering, of Christ). Passional means emotional here. Where the objective of thought is Truth (with a capital T), it is generally held that humans investigate Truth in one of two ways: via logic/reason or emotion/intuition. James is arguing that the emotional way is just as valid as the logical in pursuit of Truth. Whatever "cannot [...] be decided on intellectual grounds" must be decided via the passional nature. Trust your intuition, James might have said. As you can imagine, this is a fiercely criticized doctrine in an era and discipline where reason was foundational and, in some cases, penultimate.

It is important to couch James's "belief as valid" doctrine in the nineteenth century. The 1800s brought Darwin's theory of evolution, and empiricism—or employing only measurable evidence—was the dominant way of looking at the world. Science became the new God of the nineteenth century. Philosophers like Immanuel Kant and Jean-Jacques Rousseau were reacting to the eighteenth century's Romanticism, which is probably where James's The Will To Believe would have fit more readily and been much more welcomed.

In support of his thesis, James gives examples of "self-fulfilling beliefs" in section IX. He writes:

Do you like me or not?—for example. Whether you do or not depends, in countless instances, on whether I meet you half-way, am willing to assume that you must like me, and show you trust and expectation. The previous faith on my part in your liking's existence is in such cases what makes your liking come. But if I stand aloof, and refuse to budge an inch until I have objective evidence, until you shall have done something apt [...] ten to one your liking never comes. [...] The desire for a certain kind of truth here brings about that special truth's existence; and so it is in innumerable cases of other sorts.

Here, James argues that belief is necessary for proper sociability. Let's say there's a new person at school— let's call him Charlie. How do you know if you and Charlie will like each other? If both you and Charlie do not act on the belief that the other is deserving of friendship, you will never be friends! There are many examples of James's doctrine in social behavior: How do you decide you love someone, for example? Humans make decisions based on emotional Truth all the time. James is only arguing that belief is just as valid and just as useful as reason in determining Truth. He was defending the right of religious people to believe in God, an ultimately unprovable claim by any empirical evidence.