112 THE PRINCIPLES OF SCIENCE. [CHAP. 



proposition and read and play the keys again in the trans- 

 posed order of the terms. So long as this rule is observed 

 the true result must always be obtained. There can be no 

 mistake. But it will be found that in the case of partial 

 identities, and some other similar forms of propositions, 

 the transposed reading has no effect upon the combinations 

 of the Logical Alphabet. One reading is in such cases all 

 that is practically needful. After some experience has 

 been gained in the use of the machine, the worker naturally 

 saves himself the trouble of the second reading when 

 possible. 



It is no doubt a remarkable fact that a simple identity 

 cannot be impressed upon the machine except in the form 

 of two partial identities, and this may be thought by some 

 logicians to militate against the equational mode of repre- 

 senting propositions. 



Before leaving the subject I may remark that these 

 mechanical devices are not likely to possess much 

 practical 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 can only 

 be used with advantage in peculiar cases. But the machine 

 and abacus have nevertheless two important uses. 



In the first place I hope that the time is not very far 

 distant when the predominance of the ancient Aristotelian 

 Logic will be a matter of history only, and when 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 valuable 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 eyes of the students. I 

 often used the machine or abacus for this purpose in 

 my class lectures while I was Professor of Logic at 

 Owens College. 



Secondly, the more immediate importance of the machine 

 seems to consist in the unquestionable proof which it 

 affords that correct views of the fundamental principles of 



