The importance of investigating the diviner's answer lies in the fact that we often think we have given a meaning to a statement P if only we assert “I feel (or I believe) that P is the case.” (We shall talk at a later occasion of Prof.Hardy saying that Goldbach's theorem is a proposition because he can believe that it is true.) We have already said that by merely explaining the meaning of the words “three feet” in the usual way, we have not yet explained the sense of the phrase “feeling that water is three feet, etc.” Now we should not have felt these difficulties had the diviner said that he had learnt to estimate the depth of the
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water, say, by digging for water whenever he had a particular feeling and in this way correlating such feelings with measurements of depth. Now we must examine the relation of the process of learning to estimate with the act of estimating. The importance of this examination lies in this, that it applies to the relation between learning the meaning of a word and making use of the word. Or, more generally, that it shows the different possible relations between a rule given and its application.