v.j DISJUNCTIVE PROPOSiTiOII^S. 6y 



parts of a division or the constituent species of a genus, 

 should he exclusive of each other. 



It is no doubt owing to the great prevalence and con- 

 venience of exclusive divisions that the majority of logi- 

 cians have held it necessary to make every alternative "in 

 a disjunctive proposition exclusive of every other one. 

 Aquinas considered that when this was not the case the 

 proposition was actually false, and Kant adopted the 

 same opinion.^ A multitude of statements to the same 

 effect might readily be quoted, and if the question were 

 to be determined by the weight of historical evidence, 

 it would certainly go against my view. Among recent 

 logicians Hamilton, as well as Boole, took the exclusive 

 side. But there are authorities to the opposite effect. 

 AVhately, Mansel, and J. S. ]\lill have all pointed out that 

 we may often treat alternatives as Cotrqmssib/e, or true at 

 the same time. Whately gives us an example,'^ " Virtue 

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

 favour of God,'' and he adds — '• Here both members ai'e 

 true, and consequently from one being aitirmed we are not 

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

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

 meant to be implied tha,t the members are or are not 

 exclusive." Mansel says,^ " IFe mai/ happen to knoiu 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 a 

 formal consequence." Mill has also pointed out the 

 absurdities which would arise from always interpreting 

 alternatives as exclusive. " If we assert," he says,* " 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 nmst be 



either a saint or a philosopher Does tlie dis- 



junclive premise necessarily imply, or must it be construed 

 as supposing, that the same person cannot be both a 



' Mansel's Aldrich, p. ro3, and Prolegomena Lbgica, p. 221. 

 ' KUiiu'/nts of Logic, Bodk 11. chaji. iv. .sect. 4. 

 ' Alilricli, Artis Logic(E Hudiiiie.uta, p. 104. 

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



