120 PROF. W. STANLEY JEVONS ON THE 



In two essays % and in my paper " On the Mechanical 

 Performance of Logical Inference " f, I have attempted to 

 represent, with the "utmost generality and simplicity, the 

 processes of formal logic by which, from any proposition 

 or series of propositions, we arrive at the combinations of 

 terms possible under the condition of their truth. The 

 inverse problem yet remains, I believe, to be considered. 

 Given certain combinations, what are the propositions 

 stating their conditions? I proceed to explain how this 

 problem can be resolved in the case of two or three 

 terms. 



According to the laws of thought, two terms, say A and 

 B, can be present or absent in four combinations, thus — 



AB, Kb, aB, ab. 



A small italic letter indicates the absence or negation of 

 the corresponding large one. The above combinations are 

 unconditioned, except by the primary conditions of thought 

 itself; but if we remove any one of the combinations, say 

 Ab, the meaning will be that A tvhich is not B cannot 

 exist. Thus, the three combinations AB, «B, ab being 

 given, we pass back to the law all A's are B's, or, if A 

 mean metal and B conductor, to a law such as " all metals 

 are conductors." 



We arrive at the utmost number of cases which can 

 occur by omitting any one or more of the four com- 

 binations. The number of possible cases is therefore 

 2x2x2x2, or 1 6 ; and they are all shown in the follow- 

 ing table, in which the sign c indicates the non-existence 

 of the combination given at the left hand, and the mark I 

 its presence. 



* Pure Logic: London, 1864 (Stanford). The Substitution of Similars: 

 London, 1869 (Macmillan). 



f Philosophical Transactions, 1870, vol. clx. p. 497. 



