  Thus Williams assimilates the problem of induction to an application of the statistical syllogism (also called direct inference or the proportional syllogism). A standard syllogism concerns complexions of 100%, and has a determinate conclusion: if all S are P, and this present item is an S, then it must be P. A statistical syllogism deals with complexions of less than 100%, and its conclusion is not definite but only probable: for example, if 95% of S are P, this present S is probably P. Some logicians claim that the probability in question is exactly 0.95, but Williams does not need to rely on that additional claim. It is enough that the probability be high. Applying the statistical syllogism to Williams’ reversal of the Bernoulli result, we have: 95% of reasonably-sized samples are closely representative of their population, so the sample we have, provided there are no grounds to think otherwise, is probably one of them. On that basis, we are rationally entitled to infer that the population probably closely matches the sample, whose complexion is known to us. The inference is only probable. Induction cannot deliver certainty. In any given case, it is abstractly possible that our sample may be a misleading, unrepresentative one. But to expect an inference from the observed to the unobserved to yield certainty is to expect the impossible.