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 = Abe or Bc = 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 = A6c, so we find that 

 ab = abC 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 



