CHAPTER IX. 



DISJUNCTIVE AND ALTERNATIVE JUDGMENTS AND 

 PROPOSITIONS. 



141. VARIOUS FORMS OF DISJUNCTIVES AND ALTERNATIVES. 

 -The titles &quot; disjunctive &quot; and &quot; alternative &quot; are indiscriminately 

 applied to those forms of judgment and proposition which offer 

 us alternative subjects or alternative predicates, or a choice of simple 

 judgments. They may be represented symbolically by &quot; Either 

 AorB is C&quot; &quot;Azs either B or C&quot; &quot; Either A is B or C is D,&quot; or, 

 more briefly, by &quot;Either X or Y,&quot; where X and Y stand for 

 simple propositions. It would be better to call this form of pro 

 position alternative, and to reserve the name disjunctive for the form 

 &quot; Not both X and Y&quot; which disjoins or separates two propositions 

 by asserting that both are not simultaneously true. We shall follow 

 this usage. But it must be borne in mind that logicians generally 

 draw no distinction between the two titles (84) ; and, moreover, 

 the type of judgment just referred to as disjunctive is not really 

 different from the alternative : for every uch disjunctive involves 

 an alternative, and vice versa. &quot;Not both X and Y&quot; is equivalent 

 to &quot; Either ~X or Y&quot; : and &quot; Either X or F&quot; is equivalent to &quot; Not 

 both X and Y&quot;. &quot; No man can serve God and Mammon&quot; may also 

 be expressed, &quot;Every man must either not serve God or not serve 

 Mammon &quot; ; &quot; Every swan is either black or white &quot; may be ex 

 pressed &quot; No swan is both not-black and not-white, or which is the 

 same &quot; There is no swan that is neither black nor white&quot; . 



If we distinguish between the disjunctive and alternative forms 

 we shall have (83) : (i) the conjunctive J or copulative proposition. 

 &quot;Both X and Y&quot; denied by the disjunctive proposition &quot;Not 

 both X and Y&quot; ; and (2) the alternative proposition &quot; Either X 

 or Y&quot; denied by the remotive proposition &quot; Neither X nor Y&quot;. 



1 Some logicians use the term &quot; conjunctive &quot; to designate the &quot; If&quot; proposition, 

 inasmuch as this form also conjoins two simple propositions byjasserting a depend 

 ence of one upon the other. C/. JOSEPH, op. cit. t p. 163. 



280 



