'2 Mr. Venn on the Diagrammatic and Mechanical 



X is Y " is represented in the form tx\ Y ) ; " No X is Y " 



is represented (x) (y) . When two propositions are to 



be combined into a syllogism, three circles are of course thus 

 introduced, the mutual relations of the first and tlr>d being 

 determined by their separate relations to the second. 



In spite of certain important and obvious recommendations 

 about this plan, it seems to me to labour under two serious 

 defects, which indeed prevent its effective employment except 

 in certain special cases. 



In the first place, then, it must be noticed that these dia- 

 grams do not naturally harmonize with the propositions of 

 ordinary life or ordinary logic. To discuss this point fully 

 would be somewhat out of place here ; and as I have entered 

 rather minutely into the question in a journal devoted to spe- 

 culative inquiry*, I will confine myself to a very short state- 

 ment. The point is this. The great bulk of the propositions 

 which we commonly meet with are founded, and rightly 

 founded, on an imperfect knowledge of the actual mutual 

 relations of the implied classes to one another. When I say 

 that all X is Y, I simply do not know, in many cases, 

 whether the class X comprises the whole of Y or only a part 

 of it. And even when I do know how the facts are, I may 

 not intend to be explicit, but may purposely wish to use an 

 expression which leaves this point uncertain. Now one very 

 marked characteristic about these circular diagrams is that they 

 forbid the natural expression of such uncertainty, and are 

 therefore only directly applicable to a very small number of 

 such propositions as Ave commonly meet with. Accordingly, 

 if we resolve to make use of them, we must do one of three 

 things. Either we must confine ourselves to propositions 

 which are actually explicit in this respect, or in which the 

 data are at hand to make them explicit — such as " X and Y 

 are coextensive," " Some only of the X's are to be found 

 amongst the Y's," and so forth ; or we must feign such a 

 knowledge where we have it not, which would of course be 

 still more objectionable ; or we must offer an alternative choice 

 of diagrams, admitting frankly that, though one of these must 

 be appropriate to the case in question, we cannot tell which it 

 is. This third is the only legitimate course, and in the case 

 of very simple propositions it does not lead to much intricacy; 

 but when we have to combine groups of propositions; the 



* 'Mind,' No. xix., July 1880. 



