vi 



Boole has shown that " the ultimate laws of logic, those alone upon 

 which it is possible to construct a science of logic, are mathematical 

 in their form and expression, although not belonging to the mathe- 

 matics of quantity." Jevons advanced a step further, and showed 

 that the processes of logic, like those of arithmetic or algebra, are 

 purely mechanical, and can be not only exemplified but performed by 

 a logical engine. A full description of this curious contrivance is 

 given in a paper read before the Royal Society, in January, 1870, 

 and printed in the " Philosophical Transactions," vol. 160, pp. 497- 

 518. Other papers and treatises on Logic proceeded from his pen : 

 " On a General System of Numerically Definite -Reasoning" (Man- 

 chester Memoirs, 1872). "Primer of Logic" (1876). "The Prin- 

 ciples of Science" (first edition, 2 vols., 1874 ; second edition, 1 vol., 

 1877). 



The last-named work is a comprehensive treatise on Formal Logic 

 and Scientific Method : it contains the matured results of Professor 

 Jevons' researches on the subject, and is distinguished by great 

 wealth and freshness of illustration. Almost every department of 

 science is made to contribute examples in support or elucidation of 

 the author's views on the theory of reasoning and the nature and 

 limits of scientific inquiry. Perhaps the most original part of the 

 work is that which treats of the " inverse logical problem." Jevons 

 held that deductive reasoning gives the true type of all reasoning, and 

 that induction in an inverse process bearing to deduction much the 

 same relation that arithmetical division bears to multiplication, or 

 evolution to involution. The direct or deductive problem is, Given 

 certain relations among terms or notions, to determine by the applica- 

 tion of the fundamental laws of thought, all the possible combinations 

 which are consistent with these relations. The indirect or inductive 

 problem is, Given the combinations, to determine all the possible 

 relations from which these can be logically inferred. In other words, 

 induction is a reasoning back from conclusions to possible premises. 

 Whatever may be thought of this as a theory of induction, there can 

 be no doubt that the inverse problem suggested by it is highly 

 important. The solution of that problem in all its generality appears 

 to be impracticable on account of the number and variety of combina- 

 tions involved ; but Jevons succeeded in obtaining a complete solution 

 for two and for three classes ; and the late Professor Clifford made a 

 valuable contribution to the subject by determining the number of 

 types of compound statement involving four classes. Clifford found 

 the knowledge of the possible groupings of subdivisions of classes 

 which he obtained by his inquiry, of service in some of his researches 

 on hyperelliptic functions; and Professor Cayley subsequently sug- 

 gested that this line of investigation should be followed out, owing to 

 the bearing of the theory of compound combinations upon the higher 



