90 THE PRINCIPLES OF SCIENCE. 



An example of a still more complex proposition may 

 be found in De Morgan's writings 11 , 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 I- ABcDEF |- ABcDE/t 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 term. 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. 



