Good question. I didn’t have an answer right away. I think it’s useful because it gives structure to the act of updating beliefs. When I encounter evidence for some H I immediately know to estimate P(E|H) and P(E|~H) and I know that this ratio alone determines the direction and degree of the update. Even if the numbers are vague and ad hoc this structure precludes a lot of clever arguing I could be doing, leads to productive lines of inquiry, and is immensely helpful for modeling my disagreement with others. Before reading LW I could have told you, if asked, that P(H), P(E|H), and P(E|~H) were worth considering; but becoming acutely aware that these are THE three quantities I need, no more and no less, has made a huge difference in my thinking for the better (not to sound dogmatic; I’ll use different paradigms when I think they’re more appropriate e.g. when doing math).
How is that information by itself useful?
Good question. I didn’t have an answer right away. I think it’s useful because it gives structure to the act of updating beliefs. When I encounter evidence for some H I immediately know to estimate P(E|H) and P(E|~H) and I know that this ratio alone determines the direction and degree of the update. Even if the numbers are vague and ad hoc this structure precludes a lot of clever arguing I could be doing, leads to productive lines of inquiry, and is immensely helpful for modeling my disagreement with others. Before reading LW I could have told you, if asked, that P(H), P(E|H), and P(E|~H) were worth considering; but becoming acutely aware that these are THE three quantities I need, no more and no less, has made a huge difference in my thinking for the better (not to sound dogmatic; I’ll use different paradigms when I think they’re more appropriate e.g. when doing math).