When, with Boole, alternatives (A, B) are considered as mutually exclusive, logical addition may be described as the process of taking A _and_ B or A _or_ B. It is a great and rare convenience to have two terms for denoting the same thing: commonly, people denote several things by the same term, and only the Germans have the privilege of referring to, say, _continuity_ as _Stetigkeit_ or _Kontinuierlichkeit_. But Jevons[75] quoted Milton, Shakespeare, and Darwin to prove that alternatives are not exclusive, and so attained first to recognized views by arguments which were plainly irrelevant. Of course, _and_ is often used as the sign of logical addition: thus one may speak of one's brothers _and_ sisters, without being understood to mean the null-class (as should be the case), or pray for one's "relations and friends," without being sure that one's prayer would be answered,--as it certainly would if one meant to pray for the null-class, this being the class indicated. And a word like _while_ is often used for a logical addition, when exclusiveness of the alternatives is almost implied. Thus, a reviewer in _Mind_,[76] noticing the translation of Mach's _Popular Scientific Lectures_ into American, said of the lectures that: "Most of them will be familiar ... to epistemologists and experimental psychologists: while the remainder, which deal with physical questions, are well worth reading." The reader has the impression, probably given unintentionally, that Professor Mach's epistemological and psychological lectures are not, in the reviewer's opinion, worth reading. FOOTNOTES: [75] _Pure Logic_ ..., London, 1864, pp. 76-9. Cf. Venn, _S. L._, 2nd ed., pp. 40-8. [76] N. S., vol. iv. p. 261. CHAPTER XXVIII 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. CHAPTER XXIX