v ] DISJUNCTIVE PROPOSITIONS. 71 



expression, points out whether terms are exclusive or not. 1 

 In bills, policies, and other kinds of legal documents, it 

 is sometimes necessary to express very distinctly that 



alternatives are not exclusive. The form is then 



or 



used, and, as Mr. J. J. Murphy has remarked, this form 

 coincides exactly in meaning with the symbol -|- . 



In the first edition of this work (vol. i., p. 81), I took 

 the disjunctive proposition " Matter is solid, or liquid, or 

 gaseous," and treated it as an instance of exclusive altern- 

 atives, remarking that the same portion of matter cannot be 

 at once solid and liquid, properly speaking, and that still less 

 can we suppose it to be solid and gaseous, or solid, liquid, 

 and gaseous all at the same time. But the experiments of 

 Professor Andrews show that, under certain conditions of 

 temperature and pressure, there is no abrupt change from 

 the liquid to the gaseous state. The same substance may be 

 in such a state as to be indifferently described as liquid and 

 gaseous. In many cases, too, the transition from solid to 

 liquid is gradual, so that the properties of solidity are at least 

 partially joined with those of liquidity. The proposition 

 then, instead of being an instance of exclusive alternatives, 

 seems to afford an excellent instance to the opposite effect. 

 When such doubts can arise, it is evidently impossible to 

 treat alternatives as absolutely exclusive by the logical 

 nature of the relation. It becomes purely a question of 

 the matter of the proposition. 



The question, as we shall afterwards see more fully, is 

 one of the greatest theoretical importance, because it 

 concerns the true distinction between the sciences of 

 Logic and Mathematics. It is the foundation of number 

 that every unit shall be distinct from every other unit; 

 but Boole imported the conditions of number into the 

 science of Logic, and produced a system which, though 

 wonderful in its results, was not a system of logic at all. 



Laws of the Disjunctive Eelation. 



In considering the combination or synthesis of terms 

 (p. 30), we found that certain laws, those of Simplicity 

 1 Pure Logic, pp. 76, 77. 



