 We have already seen that this seems wrong for opinionated states that confine all probability to a false hypothesis. Being convinced that the number of planets in the solar system is 9 is better than being convinced that it is 9 billion. But the same idea holds for truths. Suppose you believe truly that the number of the planets is either 7, 8, 9 or 9 billion. This can be true in four different ways. If the number of the planets is 8 then, intuitively, your belief is a little bit closer to the truth than if it is 9 billion. (This judgment is endorsed by both the average and the min-sum-average proposals.) So even in the case of a true answer to some query, the value of believing that truth can depend not just on its truth and the strength of the belief, but on where the truth lies. If this is right Extensionality is misguided.