 Like the Bayes-Laplace argument, the solution relies heavily on the idea that straightforward a priori calculations can be done in a “direct inference” from population to sample. As we have seen, given a certain population frequency, the probability of getting different frequencies in a sample can be calculated straightforwardly based on the rules of the probability calculus. The Bayes-Laplace argument relied on inverting the probability distribution using Bayes’ rule to get from the sampling distribution to the posterior distribution. Williams instead proposes that the inverse inference may be based on a certain logical syllogism: the proportional (or statistical) syllogism.