V 



He attached to the sign +,as a logical sign, a somewhat different 

 meaning from that which it bears in the works of Boole. He dis- 

 pensed altogether with the indefinite class symbol v or %, and he 

 imposed such restrictions as served to make the symbolical operations 

 always interpretable in ordinary language. Thus, in place of the 

 logical equation x=vy, he employed its equivalent x=xy, and so on. 

 By means of these and other minor modifications he succeeded in pro- 

 ducing a system by which logical problems may be worked out accord- 

 ing to the general laws developed by Boole, but in such a way as to 

 make all intermediate as well as final results interpretable. His earliest 

 work on the subject is entitled " Pure Logic, or the Logic of Quality 

 apart from Quantity : with Remarks on Boole's System, and on the 

 Relation of Logic and Mathematics" (1864). This was followed by a 

 paper in the " Proceedings of the Literary and Philosophical Society 

 of Manchester" (vol. v, pp. 161-5, Session 1865-66), giving a brief 

 account of his logical Abacus — a contrivance for reducing the pro- 

 cesses of logical inference to a mechanical form. " The purpose of 

 this contrivance," he says, " is to show the simple truth, and the per- 

 fect generality of a new system of pure qualitative logic closely analo- 

 gous to, and suggested by, the mathematical system of logic of the 

 late Professor Boole, but strongly distinguished from the latter by 

 the rejection of all considerations of quantity. This logical abacus 

 leads naturally to the construction of a simple machine which shall 

 be capable of giving with absolute certainty all possible logical con- 

 clusions from any sets of propositions or premises read off upon the 

 keys of the instrument. The possibility of such a contrivance is 

 practically ascertained ; when completed, it will furnish a more signal 

 proof of the truth of the system of logic embodied in it. Still, the 

 more rudimentary contrivance called the Abacus will remain the most 

 convenient for explaining the nature and working of formal inference, 

 and may be usefully employed in the lecture-room for exhibiting the 

 complete analysis of arguments and logical conditions and the expo- 

 sure of fallacies." 



In a little book published in 1869, entitled " The Substitution of 

 Similars," Professor Jevons simplified and extended his theory of 

 reasoning. When logical propositions are expressed in the form of 

 equations, the old distinction of subject and predicate is abolished, 

 and the dictum de omni et nullo of Aristotle ceases to be applicable. 

 Jevons therefore proposed to modify the ancient dictum and to replace 

 it by the following : — Whatever is known of a term may be stated of 

 its equal or equivalent. Or, in other words, whatever is true of a thing 

 is true of its like. He held that all reasoning can be reduced to this 

 fundamental principle. But the novelty in his views was most strik- 

 ingly exhibited in his logical analytical engine, the construction of 

 which was completed about this time. 



