56 Mr Venn, On geometrical diagrams for the [Dec. 6, 



It will be seen that we thus treat the species as mutually 

 exclusive, and very appropriately so, such mutual exclusiveness 

 being their natural characteristic. When however we attempt 

 to adapt this linear scheme to the more comprehensive case of 

 alternatives which are not mutually exclusive, we soon find it fail 

 us. Two non-exclusive alternatives indeed can be thus displayed, 

 for such a scheme as the following will adequately mark the three 



A.- 



x 



cases covered by "All A is either X or Y" ; viz. that of A beini* 

 X only, Y only, and both X and Y. But make the same attempt 

 with three classes, X, Y, Z; and we see at once that it breaks 

 down. We cannot pussibly represent, by lines, the seven cases 

 covered by "All A is either X or Y or Z" : (If the reader will try 

 he will find that no arrangement will yield more than six of the 

 needed combinations unless we make one of the lines discontinuous, 

 by breaking it into portions, which involves too violent a license 

 to be permissible) and accordingly we should be forced to appeal 

 to closed figures which possess greater capabilities in this respect. 



Having just stated that Lambert has fairly represented a 

 case of exclusive alternatives in disjunction, I must call attention 

 to the fact that he expressly says that disjunctives do not admit of 

 diagrammatic representation *. And his reason for so thinking- 

 deserves notice, as indicative of that deep distinction between 

 the different accounts of the nature of propositions to which I 

 have already had to allude. Starting with the assumption that 

 B and C must be exclusive, he says that to represent ' A is either 

 B or C we may begin by drawing the lines for B and C beside one 

 another, but then comes in the uncertainty that we do not know 

 under which of the two we are to set the A line. We have 

 grounded on a mere hypothetical and can get no further. What 

 we are here doing is to regard A as a Begriff or concept, in which 

 case it becomes a unity, and we are then naturally in uncertainty 

 as to whether to refer it to B or 0. The case is much the same as 

 if we had to exhibit the individual disjunctive 'Socrates is either 

 awake or asleep.' But interpret A in its class extent, and the 

 disjunctive 'A is either B or C becomes 'the classes B and C 

 together make up A ' and is essentially the same state of things 

 as is readily represented by the subordination of species to a 

 genus. 



* "Die disjunctivei! Siitze lassan sich gar nicht zeichnen, and zwar wicderum, 

 weil s'.e nichts positives setzen." (Neues Orgaiwn. Dian. S 190.) 



