CHAP, v.] DISJUNCTIVE PROPOSITIONS. 



livate animal is either a mammal, bird, reptile, or fish." 

 Nor is there auy limit to the number of possible alterna- 

 tives. "An exogenous plant is either a ranunculus, a 

 poppy, a crucifer, a rose, or it belongs to some one of the 

 other seventy natural orders of exogens at present recog- 

 nized by botanists." A cathedral cliurch in England must 

 be either that of London, Canterbury, Winchester, Salis- 

 bury, ]\IanchesteT, or of one of about twenty-four cities 

 possessing such churches. And if we were to attempt to 

 specify the meaning of the term " star," we should reqiiire 

 to enumerate as alternatives, not only the many thousands 

 of stars recorded in catalogues, but the many millions un- 

 named. 



Whenever we thus distinguish the parts of a general 

 notion we employ a disjunctive proposition, in at least one 

 side of which are several alternatives joined by the so- 

 called disjunctive conjunction or, a contracted form of other. 

 There must be some relation between the parts thus con- 

 nected in one proposition ; we may call it the disjimdive or 

 alternative relation, and we must carefully inquire into its 

 nature. This relation is that of ignorance and doubt, 

 giving rise to choice. Whenever we classify and abstract 

 we must open the way to such uncertainty. By fixing our 

 attention on certain attributes to the exclusion of otliers, 

 we necessarily leave it doubtful what those other attributes 

 are. The term " molar tooth " bears upon the face of it 

 thiit it is a part of the wider term " tooth." But if we 

 meet with the simple term "tooth" there is nothing to in- 

 dicate whether it is an incisor, a canine, or a molar tooth. 

 I'liis doubt, however, may be resolved by further informa- 

 tion, and we have to consider what are the appropriate 

 logical processes for treating disjunctive propositions in 

 connection with other propositions disjunctive or otherwise. 



Expression of the Alternative Relation. 



In order to represent disjunctive propositions with con- 

 venience we require a sign of the alternative relation, 

 equivalent to one meaning at least of the little conjunc- 

 tion or so frequently used in common language. I pro- 

 ])03e to use for this purpose the syml)ol -i- . In my fir.st 

 logical essay I followed tiie practice of Boole and adopted 



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