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! 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. 



K 



