If you ask a boy "What is twice two?" and the boy says "four," you take that as prima facie evidence that the boy knows what twice two is. But if you go on to ask what is twice three, twice four, twice five, and so on, and the boy always answers "four," you come to the conclusion that he knows nothing about it. Exactly similar remarks apply to scientific instruments. I know a certain weather-cock which has the pessimistic habit of always pointing to the north-east. If you were to see it first on a cold March day, you would think it an excellent weather-cock; but with the first warm day of spring your confidence would be shaken. The boy and the weather-cock have the same defect: they do not vary their response when the stimulus is varied. A good instrument, or a person with much knowledge, will give different responses to stimuli which differ in relevant ways. This is the first point in defining accuracy of response. We will now assume another boy, who also, when you first question him, asserts that twice two is four. But with this boy, instead of asking him different questions, you make a practice of asking him the same question every day at breakfast. You find that he says five, or six, or seven, or any other number at random, and you conclude that he also does not know what twice two is, though by good luck he answered right the first time. This boy is like a weather-cock which, instead of being stuck fast, is always going round and round, changing without any change of wind. This boy and weather-cock have the opposite defect to that of the previous pair: they give different responses to stimuli which do not differ in any relevant way. In connection with vagueness in memory, we already had occasion to consider the definition of accuracy. Omitting some of the niceties of our previous discussion, we may say that an instrument is ACCURATE when it avoids the defects of the two boys and weather-cocks, that is to say, when-- (a) It gives different responses to stimuli which differ in relevant ways; (b) It gives the same response to stimuli which do not differ in relevant ways. What are relevant ways depends upon the nature and purpose of the instrument. In the case of a weather-cock, the direction of the wind is relevant, but not its strength; in the case of the boy, the meaning of the words of your question is relevant, but not the loudness of your voice, or whether you are his father or his schoolmaster If, however, you were a boy of his own age, that would be relevant, and the appropriate response would be different. It is clear that knowledge is displayed by accuracy of response to certain kinds of stimuli, e.g. examinations. Can we say, conversely, that it consists wholly of such accuracy of response? I do not think we can; but we can go a certain distance in this direction. For this purpose we must define more carefully the kind of accuracy and the kind of response that may be expected where there is knowledge.