Chapter XXVIII · THE CONVERSION OF RELATIONS
Reading edition
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[77] 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?’
“A long pause; at last a boy, indignant at what he thought the attempted trick, cried out: ‘It couldn’t have been Mr. Smith.’ These boys had never converted the relation of father and son....”