A tangent off the “I can tell for myself” sequence, between post 4 & 5.
There’s a thing it feels like to know 5+5=10.
Wait—that’s exactly the opposite of what I mean. There are many things in feels like—in some sense at least one per person who’s ever known it, in another sense as many as times it’s been known! And while I can know 5+5=10 is so true that I can be certain that if you know what I mean by 5 and + and = and 10, that you’ll agree… my knowing and your knowing are still different.
Concretely, I might be knowing 5+5=10 from a verbal memorized table that never did me wrong, and you might be imagining two nickels and a dime. Or one of us has an experience of beholding 10 fingers, 5 on each hand, the other has a sense of 5 having a halfness to it, in relation to 10, related to thinking in decimals for a lifetime. But those are just four abstract descriptions, under which many yet-unique experiences of knowing 5+5=10 could be binned—and many could not. And either or both of us might go about knowing 4+8=12 very differently than we know 5+5=10.
And those knowings are likely yet different from what it would feel like to know such a thing together.
This applies to all knowings: mundane and spiritual, mathematical and episodical. My knowing is not your knowing, and neither one is our knowing. And they aren’t the thing that is known.
Something can be true without being known: I could write a computer program that would generate a true statement that nobody had ever seen or known (such as 12364871317234+1=12364871317235, but imagine it’s longer and more convoluted) and it would still be true within that formal system, but it wouldn’t be known unless or until someone went and knew it. It could be true that there’s life on a particular exoplanet 51 Pegasi b, but it’s not currently known (as far as I know—if I’m mistaken, pick a different exoplanet). There are philosophical questions about who counts as “someone” and I am mostly going to say “definitely at least humans, in some cases animals or parts-of-humans”.
In the previous paragraph I was talking about things that are true but not known by anyone. There are also true things that are known by someone but not by someone else. You can even know OF a “true fact”, without actually knowing it. Here’s one: I’m typing this paragraph while listening to Tycho’s album Dive. One of my favorite albums. You could memorize this fact and perhaps pass it onto many other people… and maybe you even have good reason to believe me, because I’m a pretty honest guy in general and have no incentive to lie or whatever, but you don’t know it. Not directly. You can’t tell for yourself, but you can take my word for it.
A kid can know that “Santa comes on Christmas eve!” The question of whether Santa is “real” in the same senses in which the kid’s parents are real is not vital to the kid’s knowing—the kid knows that there are presents from Santa, and various other evidences such as cookie crumbs or in the case of very theatrical parents, sooty bootprints or whatever… insofar as the phrase “Santa comes on Christmas eve!” refers to that event, the kid can tell for themself that that happens. Santa sure doesn’t come on a randomly selected Tuesday in late April, for the purpose of leaving broken toasters on the lawn!
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