THE CONVERSION OF RELATIONS
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 [vR], 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...."
FOOTNOTES:
[77] _Trans. Camb. Phil. Soc._, vol. x., 1864, part ii., note on page
334.