16 Mr. Venn on the Diagrammatic and Mechanical 



multitudinous, and often so vague and ambiguous, that they 

 may need careful consideration before they can be reduced to 

 form. Then, secondly, we have to throw these statements into 

 a form fit for the engine to work with — in this case the reduc- 

 tion of each proposition to its elementary denials. It would 

 task the energies of a machine to deal at once, say, with all 

 the premises employed even in the few examples here offered. 

 Thirdly, there is the combination or further treatment of our 

 premises after such reduction. Finally, the results have to be 

 interpreted or read off. This last generally gives rise to much 

 opening for skill and sagacity ; for though in such examples 

 as the last (in which one class, Y, was simply abolished) there 

 is but one answer fairly before us, yet in most cases there are 

 many ways of reading off the answer. It then becomes a 

 question of judgment which of these is the simplest and best. 

 For instance, in the last example but one, there are a quantity 

 of alternative ways of reading off our conclusion ; and until 

 this is done the problem cannot be said to be solved. I cannot 

 see that any machine can hope to help us except in the third 

 of these steps ; so that it seems very doubtful whether any 

 thing of this sort really deserves the name of a logical engine. 



It may also be remarked that when we make appeal, as 

 here, to the aid of diagrams, the additional help to be obtained 

 by resort to any kind of mechanical contrivance is very slight 

 indeed. So very little trouble is required to sketch out a 

 fresh diagram for ourselves on each occasion, that it is really 

 not worth while to get a machine to do any part of the work 

 for us. Still as some persons have felt much interest in such 

 attempts, it seemed worth while seeing how the thing could 

 be effected here. There is the more reason for this, since the 

 exact kind of aid afforded by mechanical appliances in rea- 

 soning, and the very limited range of such aid, do not seem to 

 be generally appreciated. 



For myself, if I wanted any help in constructing or em- 

 ploying a diagram, I should just have one of the three-, four-, 

 or five-term figures made into a stamp ; this would save a 

 few minutes sometimes in drawing them ; and we could then 

 proceed to shade out or otherwise mark the requisite com- 

 partments. More help than this would be of very little avail. 

 However, since this is not exactly what people understand by 

 a logical machine, I have made two others, in order to give 

 practical proof of feasibility. 



For instance, a plan somewhat analogous, I apprehend, to 

 Prof. Jevons's abacus would be the following : — Have the de- 

 sired diagram (say the five-term figure with its thirty-two 

 compartments) drawn on paper and then pasted on to thin 



