 In philosophy the correct analysis of the concept of knowledge has proved to be profoundly elusive. In mathematics, the analysis of the concept of the limit of a function was a triumph, as was the analysis of the concept of an effectively calculable (computable) function. Church would view these as cases where analysans and analysandum designate the same concept but express radically different senses; and this does seem exactly right. Some, however, have thought that Church’s way of dealing with the paradox of analysis and his way of dealing with Mates’ problem are incompatible. This is discussed in  supplement C.2.