DISJUNCTIVE PROPOSITIONS. 75 



Solids or liquids or gases are electrics or conductors 



of electricity 



is an example of the doubly disjunctive form. The mean- 

 ing of such a proposition is that whatever falls under any 

 one or more alternatives on one side must fall under one 

 or more alternatives on the other side. From what has 

 been said before, it is apparent that the proposition 



A -I- B=C.|-D 



will correspond to 



ab = cd, 



each member of the latter being the negative of a member 

 of the former proposition. 



As an instance of a complex disjunctive proposition 1 

 may give Senior's definition of wealth, which, briefly 

 stated, amounts to the proposition "Wealth is what is 

 transferable, limited in supply, and either productive of 

 pleasure or preventive of pain." 1 

 Let A = wealth 



B = transferable 

 C = limited in supply 

 D = productive of pleasure 

 E = preventive of pain. 

 The definition takes the form 



A = BC(D -I- E) ; 



but if we develop the alternatives by a method to be 

 afterwards more fully considered, it becomes 

 A = BCDE -I- BCDe -|- BCE. 



An example of a still more complex proposition is 

 found in De Morgan's writings, 2 as follows : " He must 

 have been rich, and if not absolutely mad was weakness 

 itself, subjected either to bad advice or to most unfavour- 

 able circumstances." 



If we assign the leUei-s of the alphabet in succession, 

 thus, 



A = he 



B = rich 



C = absolutely mad 



D = weakness itself 



E = subjected to bad advice 



1 Boole's Laws of Thought, p. 106. Jevons' Pure L 

 a On the Sylloyism, No. iii. p. 12. Camb. Phil, 

 part i 



