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“As for “absolute certainty”—well, if you say that something is 99.9999% probable, it means you think you could make one million equally strong independent statements, one after the other, over the course of a solid year or so, and be wrong, on average, around once. This is incredible enough. (It’s amazing to realize we can actually get that level of confidence for “Thou shalt not win the lottery.”) So let us say nothing of probability 1.0. Once you realize you don’t need probabilities of 1.0 to get along in life, you’ll realize how absolutely ridiculous it is to think you could ever get to 1.0 with a human brain. A probability of 1.0 isn’t just certainty, it’s infinite certainty.” (Eliezer Yudkowsky, Rationality)
I suspect that we can actually explain deductive logic with the same framework. All deductive logic requires a base assumption, which is like having a prior of 100% for a given state in inductive logic. This cannot be a true inductively achieved state for our map, since 100% certainty is infinite certainty. However, we can use deductive logic as a tool to append to our inductive logic.
“In fact, it seems to me that to prevent public misunderstanding, maybe scientists should go around saying “We are not INFINITELY certain” rather than “We are not certain.” For the latter case, in ordinary discourse, suggests you know some specific reason for doubt.” (Eliezer Yudkowsky, Rationality)
Discussions of certainty are difficult and 100% certainty is infinite certainty
“But one of the primary lessons of this gigantic list is that saying “There’s no way my choice of X can be ‘wrong’” is nearly always an error in practice, whatever the theory. You can always be wrong. Even when it’s theoretically impossible to be wrong, you can still be wrong. There is never a Get Out of Jail Free card for anything you do. That’s life.” (Eliezer Yudkowsky, Rationality)
Relates to 100% certainty is infinite certainty.