By way of finishing up the morning's lecture, Keltham will also explicitly spell out the point that - outside of particular metahypotheses you're deliberately reasoning inside - it's generally considered a bad idea to assign Probability Absolutely Zero to anything.
Like the way that the Rule of Succession metahypothesis implicitly assigns Probability 0 that the ball just always goes LEFT or always goes RIGHT, because then you can never ever learn that thing, no matter how much evidence is presented you. The Rule of Succession never figures that out for real, no matter how many cases of LEFT it sees.
If you assign Probability 0 that...
Good examples of somebody-might-think-they-were-probability-0 statements are harder for an outsider to come up with when they're relatively new to Golarion.
If you assign Probability 1 that grass is green, and then you go outside and suddenly all the grass looks blue to you, well, obviously you just conclude that your eyes are deceiving you. Sure, you're vastly more likely to see the grass looking blue, if in fact the grass looks blue. Maybe it's a million times more likely. But it's not infinity times more likely.
If you say there's Probability 1 that grass is green, you're saying that's infinity times more likely than any hypothesis where it's not green. And the evidence of your senses is always finite, they could always be mistaken. So if you have an infinite prior, that's like being something that can't notice the truth, ever, no matter how hard and how many times you're hit over the head with it.
Thankfully, human beings are just more complicated things than the sorts of hypotheses that assign Probability 0 to the ball always going LEFT. Even if your conscious deliberation somehow gets wedged into weird states where you claim to be infinitely sure of things - which, like, Keltham finds it hard to visualize anybody thinking that could possibly be a reasonable thing to do in the first place, like, how would you ever be able to Lawfully justify a claim to be able to guess something strongly enough that you could make guesses like that infinity times and be wrong zero times - but they did teach Keltham not to do that, so it's probably a sort of thing that people ever do, especially when they're kids -
- even then, a human being is a more complicated thing, and there'll be metahypotheses inside you that some part of you is still processing, still able to learn the thing that you claim to assign Probability 0.
If you say to yourself that you believe absolutely that the ball can only ever have some propensity to go LEFT or RIGHT, independently on each round, and any fraction between 0 and 1 is equally probable - and then reality shows you LEFT RIGHT LEFT RIGHT repeating forever - there will still be some part of you that notices.
Because you're not actually a kind of thing that can really assign Probability 0 or Probability 1 to anything, in all of your parts.
There'll still always be some part of you that can learn from sufficiently blatant evidence, that you're hit on the head with sufficiently repeatedly, if it's a sort of thing that humans assign probability greater than 0, if it's a sort of thing that humans can learn.
This was also told to Keltham when he was a child, and emphasized to him. He's not quite sure why it's important, no sane person would start thinking like that in the first place, but it sounded like a warning so he's repeating it.