82 THE PRINCIPLES OF SCIENCE. 



It is undoubtedly possible by the laws of optics, that the 

 same surface may at one and the same moment give off 

 light of its own and reflect the light from other bodies. 

 We speak familiarly of deaf or dumb persons, knowing 

 that the majority of those who are deaf from birth are 

 also dumb. 



There can be no doubt that in a great many cases, 

 perhaps the greater number of cases, alternatives are 

 exclusive as a matter of fact. Any one number is incom- 

 patible with any other ; one point of time or place is 

 exclusive of all others. Roger Bacon died either in 1284 

 or 1292 ; it is certain that he could not die in both years. 

 Henry Fielding was born either in Dublin or Somerset- 

 shire ; he could not be born in both places. There is so 

 much more precision and clearness in the use of exclusive 

 alternatives that we ought doubtless to select them 

 when possible. Old works on logic accordingly contained 

 a rule directing that the Membra dividentia, the parts of 

 a division or the constituent species of a genus should be 

 exclusive of each other. 



It is no doubt owing to the great prevalence and 

 convenience of exclusive divisions that the majority of 

 logicians 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 . 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 

 Sir W. Hamilton, as well as Dr. Boole, took the exclusive 

 side. But there are authorities to the opposite effect. 

 Whately, Mansel, and J. S. Mill, have all pointed out that 



a Hansel's 'Aldrich,' p. 103, and 'Prolegomena Logica,' p. 221. 



