The basic mechanism here has to do with what kind of a bet would seem fair to a person. (We won’t actually do the bets, we’re Mormon. But I will ask what seems fair.) A fully rational individual judges bets by the expected value formula; the value of each outcome is multiplied by its probability. If the expected value of winning is greater than the expected value of losing, then the bet seems fair–actually, more than fair. So checking whether a bet seems fair is a good way of checking what your belief score in a particular proposition is.

A belief of 1.0, or 100% means that there is no possibility of the other alternative being true. So let’s consider the following bet. A) If the Book of Mormon is a genuine ancient history, then I pay you a dollar. B) If the Book of Mormon is not a genuine ancient history, then you agree to give up your exaltation.

Let’s use dollars as our utility unit for analyzing this bet. So the payoff from outcome A is +1. The payoff for outcome B is some immense negative number–possibly negative infinity. For present purposes, let’s rather lamely stipulate that this payoff is actually -100,000,000,000,000.

If your belief in the historicity of the Book of Mormon is actually 1.0, what is the expected utility of this bet? It is 1.0 * 1 – 0 * 100,000,000,000,000 = 1. So you would definitely take the bet and happily look forward to spending your free $1 in the next life.

What if your confidence in the historicity of the Book of Mormon is instead only 0.99? Then the expected utility of the bet is 0.99 * 1 – 0.01 * 100,000,000,000,000 = -999,999,999,999.01. This small change in belief would be enough to make you turn this down as a sucker bet.

Altering the stakes appropriately, such hypothetical bets can help you determine your actual level of belief in a given proposition, such as Book of Mormon historicity. This gives us belief numbers that have a genuine philosophical and mathematical foundation.

That said, I am unsure how helpful it is to assign different terms to different degrees of belief. Maybe “knowledge” in one context has to be 0.98 and in another context it can be as low as .80. By the way, in Bayesian theory, the only way to get a belief of 1.0 is to witness an event that is literally impossible under any alternative hypothesis. As long as we have access to explanations such as insanity and hallucination, it seem unlikely to me that any mortal experience could ever produce a 1.0 belief level in the divine.

And as such, most of us draw our own line where we feel comfortable saying “I know” something. The point I was making in this post is that I have found the “knowledge” I have received as a result of personal revelatory experiences to be the most reliable in my life so I place that on the knowledge side of the line — so much so that I am more confident in it than I am of commonly believed historical facts or even my own name or parentage. It is sort of a ranking of beliefs/knowledge I guess.

(BTW — There are some things I feel comfortable saying I know and lots of others I believe as a result of those anchor things. I have never really catalogued the differences, though. )

Of course, I suppose (and this is your point I imagine) that there is such a thing as an imperfect knowledge. This is not 100% surety and I would claim is any information gained by anything short seeing, hearing and touching something. (I assume I don’t need emotions and hunches to know that there really is a keyboard under my fingers right now.) I suggest that the varying degrees of imperfect knowledge are really degrees of conviction, conviction being a strong form of faith. We simply say “I know” as (a sometimes abusive) short-hand for this.

If we really know something then it is impossible that it is wrong. Not that we feel it impossible to be wrong, but that it really is absolutely impossible for it to be wrong. Given this view, then we know very little.

There are no degrees of knowing. There are of conviction, but not of knowing. And the scriptures, philosophers and common sense tell us that we have not received a perfect knowledge in the strictest sense without actual physical experience.

You seem to have drawn a line about when you know something. My comments here challenge that line. The line between knowing and believing is not universally accepted and I don’t accept the line you proposed in that comment.

Anyway, in my life the most real and un-forgeable knowledge I have is that seared into my soul by God himself. That is why the truth I learn through that method is top on my list of things I know.