That's true, but it's hard to see why that means that it would be a contradiction. It's true that there is a contradiction if you say that all beliefs have a specific mathematical probability of less than one (e.g. including that 1+1=2), since probability theory also assumes that the probability of a mathematical claim is 1. But probability theory isn't supposed to be an exact representation of human beliefs in the first place, but a formalized and idealized representation. In reality we are not always completely certain even of mathematical truths, and th... (read more)