10 Mr, Venn on the Diagrammatic and Mechanical 



to interpret any of the premises which we propose to take 

 account of. 



Another way of approaching the same question is by in- 

 quiring whether the various subdivisions in our diagram are 

 to be considered as representing classes, or merely compart- 

 ments into which classes may or may not have to be put. 

 The latter view must be accepted as being the only one with 

 which we can conveniently work. We may doubtless regard 

 them as representing classes ; but if we do so, we must keep 

 in mind the proviso " if there be such a class of things in ex- 

 istence." And when this condition is insisted on, we appear 

 to express our meaning best by saying that what our diagram- 

 matic subdivisions (or, for that matter, the corresponding 

 literal symbols) stand for are compartments which may or 

 may not happen to be occupied. 



One main reason for insisting upon this point is to be found 

 in the impossibility of ascertaining, until we have fully ana- 

 lyzed our premises, whether or not any particular combina- 

 tion is possible. In the simple propositions of the common 

 logic this difficulty hardly occurs ; so that when we say " All 

 X is Y," we take it for granted, or are apt to do so, that there 

 must be both X's and Y's to be found. But if this proposi- 

 tion, or, still more, a complicated one of the same type, oc- 

 curred as one of a group of premises, matters would be very 

 different. AVe should then find that to maintain the existence 

 of all the subjects and predicates, instead of merely denying 

 the existence of the various combinations destroyed by them, 

 would sadly hamper us in our interpretation of groups of 

 premises *. 



Take, for instance, the following group of premises, which 

 are by no means of a very complicated nature : — 



All X is either both Y and Z or not-Y, 

 All XY that is Z is also W, 

 No WX is YZ. 



It would not be easy to detect, from mere contemplation of 

 these data, that though they admit the possible existence of 

 such classes as XZ and YZ, they deny that of the class XY. 

 But since, as they stand, XY is the subject of one of them, 

 we could not consistently admit such a conclusion unless we 

 restricted the force of that second premise to what it denies, viz. 



* I am not aware that it has ever been maintained that such a group 

 of elementary denials is to be regarded as an adequate interpretation of 

 these propositions. But it seems quite clear to me (on grounds too intri- 

 cate to enter upon here) that this is the view which must be considered 

 to underlie Boole's system, and, indeed, any general symbolic system of 

 logic, if it is to be worked successfully. 



