What it says in the title. We like to have things proven, and it’s great when we can do that. But proof is hard (and the more you study the underlying principles of math and science, the more true that becomes). I mean, in the strictest sense, it’s probably most correct to say a true proof is impossible. But that’s not the focus tonight.

If you only accept what can be proven, you will miss out on a lot of good in life, and a lot of truth. So to speak, it’s necessary to anticipate the truth.

For example, you may know how calculus was codiscovered by Leibniz and Newton in the 1600s. What you probably don’t know is that neither of them proved calculus. It took 200 years to prove calculus did what Newton, Leibniz, and basically every mathematician said it did (it was Cauchy and Weierstrass who are responsible for the proof). For those two hundred years, calculus was unproven; the arguments explaining calculus literally divided by zero throughout. But calculus worked just fine for those 200 years. The proof was great to have, it enriched the theory for certain, but the world would in no wise have been benefited if it had waited for the proof before it relied on calculus. Indeed, if calculus had not been used, it’s hard to know whether people would have had much urgency at all when it came to finding the proof (while I doubt it would have happened this way, one can imagine a world where the failures to prove calculus led to its abandonment).[1]

It is troubling to see scientific and mathematical methods applied to things for which they are ill-adapted. It’s worse to see people abandon ideas, or hate their holders, because the proof is not there. We do not live in a world of proof and, after any honest study of epistemology, I struggle to see how you could not be full of trepidation about the whole idea of proof. I’m not even sure that a world of proof is desirable in the first place. Trying to create a world of proof, based on the limitations we face as mortals, seems dangerous and in cases ruinous. Efforts to reduce literature and law to science produce more pseudoscience than anything and cheapen the beauty and brilliance of each field.

It’s hard to explain your beliefs to an argumentative society once you give up on proving everything. But that’s the arguer’s fault, not yours. The modern view of argument is fictitious, abusing science and stretching its claims while failing to acknowledge the essential role of belief in science itself. People like Richard Dawkins are confusing because they hate religion so avidly while their beliefs of choice are often not proven at all. One of Dawkins’ darlings: evolution as a history of all life and speciation, is far from proven–it’s natural selection as a source of speciation that’s been the subject of rigorous experimentation. And for all his criticism of dogma, Nietzsche ultimately felt compelled to acknowledge that he had in fact created a new dogma (zealotry is quite visible in his devotees).[2]

Now, the value of belief in the absence of proof applies heavily to religion. Religion is an important field, but a classic example of knowledge resistant to the scientific method. But religion is not the only reason to value belief: It is incredibly difficult to prove:

• The falsity of every flavor of fascism;
• The evil in every form of racism;
• That being good is worthwhile, even when doing the right thing is not in one’s self-interest.
• Pretty much every debate like these, whether religious, ethical, ideological, or otherwise.

If you tried to prove every theory of fascism wrong, you’ll be amazed how many subtle variations fascists can come up with, each required different arguments and disproofs. It’s a Sisyphean task (it might be closer to the slaying of the hydra if the hydra could not be burned). It is much easier to convince someone to abandon fascism or racism, if they choose to believe in doing good, than it is to convince them that fascism or racism themselves are not in their rational self-interest, scientifically invalid, etc. An anti-Semite can always find a reason to hate, no matter how often you introduce him to wonderful, kind, and good Jews. The anti-Semite will only abandon their hate by choosing to believe in Jews as a people.

And this is where we end up. Belief is the domain of most knowledge, not proof. Proof is seductive because we believe that we can force people to believe us via proof and, to be certain, this does happen once in a while. But such a proof must be unassailable and, more importantly, the audience must be willing to believe, or they will find some way to reject it. We all understand, for our own beliefs, that there are odd things we haven’t fully figured out. But we trust that the problems will ultimately get sorted out, whether in this life or the next. What I ask, or what I recommend, are two things. First, let other people have their beliefs; let them wait for things to get figured out. Give them, as people, the leniency you give your ideas. Second, let yourself believe and grow. Don’t wait for proof, don’t demand it, and, whenever you discover you were wrong, freely believe something new. And, as always, stay safe and take care.

[1] In many ways, this whole article is a rehash of The Analyst: A Discourse Addressed to an Infidel Mathematician: Wherein It Is Examined Whether the Object, Principles, and Inferences of the Modern Analysis Are More Distinctly Conceived, or More Evidently Deduced, Than Religious Mysteries and Points of Faith by George Berkeley and the history around it. He correctly criticized mathematics for its lack of rigor, even as scientists and mathematicians demanded a level of rigor from religion that they had not achieved for themselves.

[2] While I’ll take Nietzsche’s stated opposition to the Nazis and anti-Semites at face value, I’ll note that it’s not surprising at all that fascists immediately appropriated his work.