“Contrast this probabilistic situation to the qualitative reasoning where I just believe that snow is white, and believe that I believe that snow is white, and believe “‘snow is white’ is true,” and believe “my belief ‘“snow is white” is true’ is correct,” etc. Since all the quantities involved are 1, it’s easy to mix them up. Yet the nice distinctions of quantitative reasoning will be short-circuited if you start thinking “‘“snow is white” with 70% probability’ is true,” which is a type error. It is a true fact about you, that you believe “70% probability: ‘snow is white’”; but that does not mean the probability assignment itself can possibly be “true.” The belief scores either -0.51 bits or -1.73 bits of accuracy, depending on the actual state of reality.” (Eliezer Yudkowsky, Rationality)