DISJUNCTIVE JUDGMENTS AND PROPOSITIONS 285 



us. We meet with both sorts of alternatives. For instance, the 

 propositions &quot;He will either pass or fail &quot;He was either first or 

 second in the race&quot; &quot; This book is to be bound in half -calf or in 

 morocco&quot; &quot; Every swan is either black or white&quot; give us mutually 

 exclusive predicates. But this springs from the matter, not from 

 the/orm of these statements. So far as the form of the proposi 

 tion is concerned, there is nothing to indicate that the alternatives 

 are meant to be exclusive. Nor are they exclusive in every case. 

 For example, the propositions &quot; He has either used bad text-books 

 or has been badly taught&quot; &quot; Either the witness is perjured or the 

 prisoner is guilty&quot; &quot;Every candidate must be a graduate either of 

 the Queen s or of the National or of Trinity&quot; &quot;He is either very 

 timid or very modest&quot; all offer us alternatives which are not, and 

 are not meant to be, mutually exclusive. 



Hence, since the form of expression &quot;Either X or Y&quot; is 

 capable of both interpretations, we must in logic in virtue of 

 the Law of Parsimony accept the one which bears the lesser 

 amount of meaning, and this, as we shall see presently, is the 

 non-exclusive interpretation. 



In the latter, too, we are keeping more closely to ordinary usage, 

 for here the alternatives are not as a rule meant to be mutually 

 exclusive. It is only when they are incompatible that they are 

 mutually exclusive, and in such cases we may express the judgment 

 symbolically in the form &quot;Either X or V but not both&quot; . Mr. 

 Joseph, in his Introduction to Logic 1 expresses the view that even 

 where we cannot know from the subject-matter &quot; that the alter 

 natives exclude each other ... it is perhaps safer to assume 

 that they are intended as mutually exclusive, unless the contrary 

 is stated ; a legal document is careful so to write it, where * A or B 

 or both is meant, or to write A and/or B with that significa 

 tion &quot;. But such an assumption would not be safe if applied uni 

 versally to the ordinary usage of language. Moreover, the 

 universal adoption of this exclusive interpretation would increase 

 unduly the compound character of the form in question, and 

 would lead to complicated and curious results. For example, the 

 denial of &quot; Either X or Y but not both &quot; would be &quot; Either both 

 of them or neither of them &quot;. Then, again, on the exclusive inter 

 pretation of &quot; Either X or Y&quot; the two alternatives are X Y and 

 X Y ; but these also are the two alternatives in &quot; Either X or Y 

 on the same interpretation : from which it follows that &quot; Either X 



1 p. 167. 



