Capitalizing After Colons

What’s the right policy for capitalizing words after colons? Why?

Here’s an example I just wrote:

Both emphasize fallibility: [“We” or “we”] will inevitably make mistakes, so we need philosophical thinking (including criticism) to help us find and fix mistakes.

I read some stuff that said only capitalize proper nouns in British English and don’t capitalize if you’re putting a list after the colon. And don’t capitalize if the stuff after the colon is a sentence fragment. But for American English, people keep saying you can but don’t have to capitalize if you write a complete sentence after the colon.

DD told me a policy he used for this. I don’t clearly remember it, but I might have been to capitalize if the rest of the paragraph all follows the colon, and lowercase if just the rest of that sentence follows the colon and then the next sentence is separate.

That makes some sense to me.

If you wanted the thing that would be a complete sentence on its own to actually be a complete sentence, you would have made it a complete sentence. By putting it after a colon, you’ve already made a decision that you don’t want it to be on its own, but to be related to some other chunk of text in a way that’s closer than the relationship would be if you had a stand-alone sentence. So, having made that choice, it makes sense that you wouldn’t also have to capitalize text after a colon in the way that would give it the full “dignity” of being a complete sentence.

Thinking about it a bit, I wonder if you should maybe actively avoid capitalizing in such circumstances. Like, you wouldn’t capitalize the word after a coordinating conjunction if it’s part of something that’d be a complete sentence on its own (would you?! D-: ). So just the fact that something would be a complete sentence in one grammatical context isn’t a reason for capitalizing the first word of it in a different grammatical context.