INDUCTION. 159 



varieties may not be equivalent to others ; and trial 

 shows, in fact, that AB = ABC is exactly the same in 

 meaning as Ac = Kbc or Be = Bca. Thus the law in 

 question has but eight varieties of distinct logical mean- 

 ing. I now ascertain by actual deductive reasoning which 

 of the 256 series of combinations result from each of 

 these distinct laws, and mark them off as soon as found. 

 I now proceed to some other form of law, for instance 

 A = ABC, meaning that whatever has the qualities of A has 

 those also of B and C. I find that it admits of twenty- 

 four variations, all of which are found to be logically 

 distinct ; the combinations being worked out, I am able 

 to mark off twenty-four more of the list of 256 series. I 

 proceed in this way to work out the results of every form of 

 law which I can find or invent. If in the course of this 

 work I obtain any series of combinations which had been 

 previously marked off, I learn at once that the law is 

 logically equivalent to some law previously treated. It 

 may be safely inferred that every variety of the ap- 

 parently new law will coincide in meaning with some 

 variety of the former expression of the same law. I 

 have sufficiently verified this assumption in some cases 

 and have never found it lead to error. Thus just as 

 AB = ABC is equivalent to Ac = A&c, so we find that 

 ab = ab(j is equivalent to ac==acB. 



Among the laws treated were the two A = AB and 

 A = B which involve only two terms, because it may of 

 course happen that among three things two only are 

 in special logical relation, and the third independent ; and 

 the series of combinations representing such cases of 

 relation are sure to occur in the complete enumeration. 

 All single propositions which I could invent having been 

 treated, pairs of propositions were next investigated. 

 Thus we have the relations, 'All A's are B's and all 

 B's are C's/ of which the old logical syllogism is the 



