90 THE PRINCIPLES OF SCIENCE. 



An example of a still more complex proposition may 

 be found in De Morgan's writings' 1 , and is as follows: 

 ' He must have been rich, and if not absolutely mad was 

 weakness itself, subjected either to bad advice or to most 

 unfavourable circumstances.' 



If we assign the letters of the alphabet in succession, 

 thus, 



A = he 

 B = rich 



C = absolutely mad 

 D = weakness itself 

 E = subjected to bad advice 



F = subjected to most unfavourable circumstances, 

 the proposition will take the form 



A = AB{C|D(E|F)}, 



and if we develop the alternatives, expressing some of 

 the different cases which may happen, we obtain 

 A = ABC | ABcDEF f ABcDE/* ABcDeF. 



Inference by Disjunctive Propositions. 



Before we can make a free use of disjunctive propositions 

 in the processes of inference we must consider how dis- 

 junctive terms can be combined together or with simple 

 terms. In the first place, to combine a simple term with 

 a disjunctive one, we must combine it with every alter- 

 native of the disjunctive terra. A vegetable, for instance, 

 is either a herb, a shrub, or a tree. Hence an exogenous 

 vegetable is either an exogenous herb, or an exogenous 

 shrub, or an exogenous tree. Symbolically stated this 

 process of combination is as follows 



A(B-|- C) = AB| AC. 



Secondly, to combine two disjunctive terms with each 

 other, combine each alternative of one separately with each 



h 'On the Syllogism,' No. iii. p. 12. Camb. Phil. Trans., vol. x. 

 part i. 



