1880.] representation of logical propositions. 57 



For the general representation of disjunctives on this plan, 

 Euler's circles do not answer much better than Lambert's lines. 

 In fact we cannot even represent ' All A is B or C (only) ' by 

 circles, but are confined to 'All A is B or C (or both),' as thus : — 



for if the B and G circles are not caused to intersect one another, 

 the A circle will of course have to include something which lies 

 outside them, and accordingly the point aimed at in the disjunction 

 fails to be represented. 



Kant (Logik, i. § 29) may be also noticed here as one of the 

 very few logicians who have given a diagram to illustrate dis- 

 junctives. Like Lambert, — in fact like so many logicians, — he 

 makes all disjunctives mutually exclusive. All he does indeed 

 is to take a square and divide it up into four smaller squares; 

 these four dividing members therefore just make up between 

 them the whole sphere of the divided concept. So few however 

 have been the attempts to represent Disjunctives in Logic that it 

 seems hardly worth while to pursue the subject any further. 



Before quitting these historical points I may briefly notice 

 an application to which diagrammatic notation very readily lends 

 itself, but which seems to me none the less an abusive employ- 

 ment of it. I refer to the attempt to represent quantitatively 

 the relative extent of the terms. When, for instance, we have 

 drawn, either by lines or circles, a figure to represent ' All A is B ' 

 it strikes us at once that we have got another element at our 

 service ; or, as a mathematician would say, there is still a dis- 

 posable constant. We may draw the B circle or line of any size 

 or length we please ; why not then so draw it as to represent 

 the relative extension of the B class as compared with the A 

 class ? 



This idea seems to have occurred to logicians almost from the 

 first, as was indeed natural, considering that the use of diagrams 

 was of course borrowed from mathematics, and that a clear 

 boundary line was not always drawn between the two sciences. 

 Thus Lambert certainly seems to maintain that in strictness 

 we must suppose each line to bear to any other the due pro- 

 portionate length assigned by the extension of the terms. He 

 even recognizes the difficulty in the case of a single line, viz. as to 



