Representation of Propositions and Reasonings. 7 



marily meant to assist the eye and the mind by the intuitive 

 nature of their evidence, any excessive complication entirely 

 frustrates their main object. 



For four terms the simplest and. neatest figure seems to me 

 to be one composed of four equal ellipses thus arranged: — 

 It is obvious that we thus get the 

 sixteen compartments that we want, 

 counting, as usual, the outside of 

 them all as one compartment. The 

 eye can distinguish any one of them 



in a moment bv following the out- 



"o-ures. 



lines of the various component fi<^ 

 Thus the one which is asterisked is 

 instantly seen to be "X that is Y and Z, but is not W," or 

 XYZW; and similarly with any of the others. The desired 

 condition that these sixteen alternatives shall be mutually ex- 

 clusive and collectively exhaustive, so as to represent all the 

 component elements yielded by the four terms taken posi- 

 tively and negatively, is of course secured. 



With five terms ellipses fail, at least in the above simple 

 form. It would be quite possible to sketch out figures of a 

 somewhat horse-shoe shape which should answer the purpose — 

 that is, five of which should fulfil the condition of yielding 

 the desired thirty-two distinctive and exhaustive compartments. 

 For all practical purposes, however, any outline which is not 

 very simple and easy to follow with the eye, fails entirely in 

 its main purpose of affording intuitive and sensible illustra- 

 tion. What is wanted is that we should be able to distinguish 

 and identify any assigned compartment in a moment, so as 

 to see how it lies in respect of being inside and outside each 

 of the principal component figures. For this purpose, when 

 five class terms are introduced, I do not think that any 

 arrangement will much surpass the following (the small 

 ellipse in the centre is here to be reckoned as a piece of the 

 outside of Z ; i. e. its four component portions are inside of 

 Y and W, but are no part of Z). 



It must be admitted that such 

 a diagram is not quite so simple 

 to draw as one might wish it to 

 be ; but then we must remember 

 what are the alternatives before 

 any one who wishes to grapple 

 effectively with five terms and 

 all the thirty-two possibilities 

 which they yield. He must 

 either write down or in some 



