DISJUNCTIVE PROPOSITIONS. 83 



we may often treat alternatives as Compossible, or true at 

 the same time. Whately gives as an example b , 'Virtue 

 tends to procure us either the esteem of mankind, or the 

 favour of God,' and he adds, 'Here both members are 

 true, and consequently from one being affirmed we are not 

 authorized to deny the other. Of course we are left to 

 conjecture in each case, from the context, whether it is 

 meant to be implied that the members are or are not 

 exclusive/ Mansel says c , ' We may happen to -know that 

 two alternatives cannot be true together, so that the 

 affirmation of the second necessitates the denial of the first ; 

 but this, as Boethius observes, is a material, not & formal 

 consequence.' Mr. J. S. Mill has also pointed out the 

 absurdities which would arise from always interpreting 

 alternatives as exclusive. ' If we assert/ he says d , ' that 

 a man who has acted in some particular way must be 

 either a knave or a fool, we by no means assert, or intend 

 to assert, that he cannot be both.' Again, 'to make an 

 entirely unselfish use of despotic power, a man must be 

 either a saint or a philosopher Does the dis- 

 junctive premise necessarily imply, or must it be construed 

 as supposing, that the same person cannot be both a 

 saint and a philosopher ? Such a construction would be 

 ridiculous.' 



I discuss this subject fully because it is really the point 

 which separates my logical system from that of the late 

 Dr. Boole. In his 'Laws of Thought' (p. 32) he expressly 

 says, ' In strictness, the words " and," " or," interposed 

 between the terms descriptive of two or more classes of 

 objects, imply that those classes are quite distinct, so that 

 no member of one is found in another.' This I altogether 



b ' Elements of Logic,' Book II. chap. iv. sect. 4. 



c Aldrich, 'Artis Logicae Rudimenta,' p. 104. 



A ' Examination of Sir W. Hamilton's Philosophy,' pp. 452-454. 



G 2 



