THE LOGICAL MACHINE. 129 



A B except in the double form of A = AB and B = AB. 

 To work the proposition A = B it is therefore necessary to 

 press the keys A (subj.), Copula, A (pred.), B (pred.), Full 

 stop, B (subj.), Copula, A (pred.), B (pred.), Full stop. 

 The same double operation will be necessary whenever 

 the proposition is not of the kind called a partial 

 identity (p. 47). Thus AB - CD, AB - AC, A = B I C 

 A I B = C I D, all require to be read from both ends 

 separately. This is a remarkable fact which some per 

 sons may consider as militating against the equational 

 form of proposition, but I do not think this is really 

 the case. 



Before leaving the subject I may remark that these 

 mechanical devices are not likely to possess great prac 

 tical utility. We do not require in common life to be 

 constantly solving complex logical questions. Even in 

 mathematical calculation the ordinary rules of arithmetic 

 are generally sufficient, and a calculating machine could 

 only be used with advantage in peculiar cases. But the 

 machine and abacus have nevertheless two important 

 uses. 



i. I trust that the time is not very far distant when 

 the predominance of the ancient Aristotelian Logic will 

 be a matter of history, and the teaching of logic will 

 be placed on a footing more worthy of its supreme 

 importance. It will then be found that the solution of 

 logical questions is an exercise of mind at least as valu 

 able and necessary as mathematical calculation. I believe 

 that these mechanical devices, or something of the same 

 kind, will then become useful for exhibiting to a class 

 of students a clear and visible analysis of logical problems 

 of any degree of complexity, the nature of each step 

 being rendered plain to the eye. For this purpose I 

 have already often used the machine or abacus in my 

 class lectures at the Owens College. 



