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



negative, for the same diagram is commonly employed to stand 

 for them both, which it does indifferently well : 



Some A is B, 

 Some A is not B, 



for the real relation thus exhibited by the figure is of course 

 " some (only) A is some (only) B ", and this quantified proposition 

 has no place in the ordinary scheme. 



Euler himself indicated the distinction (so I 'judge by his 

 diagram) by the position in which he put the letter A ; if this 

 stood in the 'A not-B' compartment it meant 'some A is not B\ 

 if in the AB compartment it meant ' some A is B '. But the 

 common way of meeting the difficulty where it is at all recognized, 

 is by the use of dotted lines to indicate our uncertainty as to 

 where the boundary should lie. So far as I have been able to 

 find, this plan (as applied to closed figures) was first employed by 

 Dr Thomson in his Laius of Thought, but was doubtless suggested 

 by the device of Lambert, to be presently explained. It has been 

 praised for its ingenuity and success by De Morgan, and adopted by 

 Prof. Jevons amongst others. Uebervveg has employed a some- 

 what more complicated scheme of a similar kind. 



Any modifications of this sort seem to me (as I have elsewhere 

 explained) wholly mis-aimed and ineffectual. If we want to repre- 

 sent our uncertainty about the correct employment of a diagram, 

 the only consistent way is to draw all the figures which are covered 

 by the assigned propositions and say frankly that we do not know 

 which is the appropriate one. Of course this plan would be trouble- 

 some when several propositions have to be combined, as the con- 

 sequent number of diagrams would be considerable. Thus in 

 Bocardo, two diagrams would be needed for the major premise 

 and two for the minor, making four in all. 



The traditional logic has been so entirely confined to the 

 simultaneous treatment of three terms only (this being the number 

 demanded for the syllogism) that hardly any attempts have been 

 made to represent diagrammatically the combinations of four 

 terms and upwards. The only serious attempt that I have seen 

 in this way is by Bolzano. He was evidently trying under the 

 right conception, viz. to construct diagrams which should illustrate 

 all the combinations producible by the class terms employed, but 

 he adopted an impracticable method in using modified Eulerian 

 diagrams. The consequence is that he has effected no general 

 solution, though exhibiting a number of more or less ingenious 



