How do I stop my brain from going: "I believe P and I believe something that implies not P -> principle of explosion -> all statements are true!" and instead go "I believe P and I believe something that implies not P -> I one of my beliefs are incorrect". It doesn't happen to often, but it'd be nice to have an actual formal refutation for when it does.
Do you actually do this - "Oh, not P! I must be the pope." - or do you just notice this - "Not P, so everything's true. Where do I go from here?".
If you want to know why you shouldn't do this it's because you never really learn not P, you just learn evidence against P which you should update with Bayes' rule. If you want to understand this process more intuitively (and you've already read the sequences and are still confused), I would recommend this short tutorial or studying belief propagation in Bayesian networks, for which I don't kn...
This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant.