1 $ Mr. Venn on the Diagrammatic and Mechanical 



ment, and we have made our alternatives exclusive ; i. e. the 

 X is then Y or Z o/ify. 



Of course the same plan is easy to adopt with any number 

 of premises. Our first data abolish, say, such and such classes. 

 This is final ; for, as already intimated, all the resultant ele- 

 mentary denials which our propositions yield must be regarded 

 as absolute and unconditional. This first step then leaves the 

 field open to any similar accession of knowledge from the next 

 data ; and so more classes are swept away. Thus we go on till 

 all the data have had their fire ; and the muster-roll at the 

 end will show what classes may be taken as surviving. If, 

 therefore, we simply shade out the compartments in our figure 

 which have thus been successively proved to be empty, nothing 

 is easier than to go on doing this till all the information yielded 

 by the data is exhausted. In doing this it may, of course, often 

 happen that some of the data wholly or partially go over the 

 same ground as others. In that case, whichever of such data 

 is considered after the other, finds its work already done for it 

 entirely or in part ; the class which we were going to mark 

 for destruction is found to be already gone, and there is nothing 

 to do so far as it is concerned. 



As the syllogistic figures are the form of reasoning most 

 familiar to ordinary readers, I will begin with one of them, 

 though they are too simple to serve as effective examples. 

 Take, for instance, 



No Y is Z, 



All X is Y, 



.-. No X is Z. 



This would commonly be exhibited thus, 



It is easy enough to do this; for in drawing our circles we have 

 only to attend to two terms at a time, and consequently the 

 relation of X to Z is readily detected ; there is not any of 

 that troublesome interconnexion of a number of terms simul- 

 taneously with one another which gives rise to the main per- 

 plexity in complicated problems. Accordingly such a simple 

 example as this is not a very good one for illustrating the 

 method now proposed ; but, in order to mark the distinction, 



the figure to represent it is given, thus, 



In this case the one particular relation asked for, viz. that 

 of X to Z, it must be admitted, is not made more obvious on 



