[keithwinstein]

Sure, see my link above (http://stats.stackexchange.com/a/2287/1122). If you want to put an upper bound on the worst-case probability of making a mistake, you use a p-value. If you want to express the conditional probability of a particular hypothesis given the observation (and given a prior belief), you use a posterior probability. The Bayesians also can do silly things (see the cookie example with the inept Bayesian robots). In the end there is no free lunch.