There’s a misconception, it isn’t about finding sentences of the form A→Bi and ¬Bi, because if you do that, it immediately disproves A. It’s actually about merely finding many instances of A→Bi where P(Bi|A) has <12 probability, and this lowers the probability of A. This is kind of like how finding out about the Banach-Tarski paradox (something you assign low probability to) may lower your degree of belief in the axiom of choice.
The particular thing that prevents trolling is that in this distribution, there’s a fixed probability of drawing A on the next round no matter how many implications and B’s you’ve found so far. So the way it evades trolling is a bit cheaty, in a certain sense, because it believes that the sequence of truth or falsity of math sentences that it sees is drawn from a certain fixed distribution, and doesn’t do anything like believing that it’s more likely to see a certain class of sentences come up soon.
(I fixed your LaTex. FYI whatever your comment looks like before you post, is what it will look like after. Use ctrl-4 or cmd-4 for LaTex, depending on whether you’re using a PC or a Mac.)
There’s a misconception, it isn’t about finding sentences of the form A→Bi and ¬Bi, because if you do that, it immediately disproves A. It’s actually about merely finding many instances of A→Bi where P(Bi|A) has <12 probability, and this lowers the probability of A. This is kind of like how finding out about the Banach-Tarski paradox (something you assign low probability to) may lower your degree of belief in the axiom of choice.
The particular thing that prevents trolling is that in this distribution, there’s a fixed probability of drawing A on the next round no matter how many implications and B’s you’ve found so far. So the way it evades trolling is a bit cheaty, in a certain sense, because it believes that the sequence of truth or falsity of math sentences that it sees is drawn from a certain fixed distribution, and doesn’t do anything like believing that it’s more likely to see a certain class of sentences come up soon.
(I fixed your LaTex. FYI whatever your comment looks like before you post, is what it will look like after. Use ctrl-4 or cmd-4 for LaTex, depending on whether you’re using a PC or a Mac.)