ABSTRACT
The “Conversion of Relations” does not mean what it might be supposed to mean; it has nothing to do with what Kant called “the wholesome art of persuasion.” What concerns us here is the convertibility of a logical relation. If A has a certain relation R to B, the relation of B to A, which may be denoted by Ř, is called the converse of R. As De Morgan 1 remarked, this conversion may sometimes present difficulties. The following is De Morgan’s example: “Teacher
‘Now, boys, Shem, Ham and Japheth were Noah’s sons; who was the father of Shem, Ham and Japheth?’ No answer.
“Teacher‘Boys, you know Mr. Smith, the carpenter, opposite; has he any sons?’
“Boys‘Oh! yes, sir! there’s Bill and Ben.’
“Teacher‘And who is the father of Bill and Ben Smith?’
“Boys‘Why, Mr. Smith, to be sure’
“Teacher‘Well, then, once more, Shem, Ham and Japheth were Noah’s sons; who was the father of Shem, Ham and Japheth?’
