 Stalnaker’s Hypothesis might seem obvious at first, even tautological. Isn’t \(p(B\mid A)\) just the probability of the proposition \(B\mid A\), which is just shorthand for “\(B\) is true if \(A\) is”? This is a common misconception for newcomers to probability theory, one that Lewis shows leads to disastrous results. If we think of \(B\mid A\) as a complex proposition built out of the sentences \(A\) and \(B\) with a connective \(\mid \), probability theory goes to pot (see the  technical supplement  for a proof):