“It would be a great mistake to suppose that vague knowledge must be false. On the contrary, a vague belief has a much better chance of being true than a precise one, because there are more possible facts that would verify it. If I believe that so-and-so is tall, I am more likely to be right than if I believe that his heigh is between 6 ft. 2 in. and 6 ft. 3 in. In regard to beliefs and propositions, though not in regard to single words, we can distinguish between accuracy and precision. A belief is precise when only one fact would verify it; it is accurate when it is both precise and true. Precision diminishes the likelihood of truth, but often increases the pragmatic value of a belief if it is true — for example, in the case of the water that contained the typhoid bacilli. Science is perpetually trying to substitute more precise beliefs for vague ones; this makes it harder for a scientific proposition to be true than for the vague beliefs of uneducated persons to be true, but it makes scientific truth better worth having if it can be obtained.”