458 



Mr DE morgan, ON THE SYLLOGISM, No. V. AND 



extended cumular system is not in any sense arbitrary. Take what plan we please, carry the 

 correlations fairly out, and we arrive at the eight onymatic forms, together with restric- 

 tives and their denials. I shall take two more cases, observing that restrictives have appeared 

 in every system except the original, in which nothing appears except terms as distinctive 

 names, under the relation to objects of applicable or not applicable. 



First, I take the exemplar form in which some or other extent, or any extent — some class 

 or any class — is identified, conjunctively or disjunctively, with both whole or part of X 

 and whole or part of Y. This is that portion of extension which I previously announced 

 that I should give. I write down only the apparent affirmatives, leaving the reader to con- 

 struct the negatives : for brevity, I also write * some X ' for ' some one part of X ', and 

 'any X' for 'any one part of X\ And first of conjunctive comparisons. 



Any class is both any X and any Y 

 Some class is both any X and any Y 

 Any class is both any X and some Y 

 Some class is both any X and some Y 

 Any class is both some X and some Y 

 Some class is both some X and some Y 

 Any class is both some X and any Y 

 Some class is both some X and any Y 



Universe of one individual. No terms 



X and Y singular and identical 



Universe of one individual. No terms 



X species of Y. ) ) 



X and Y universal. No terms 



X partient of Y. ( ) 



Universe of one individual. No terms 



X genus of Y. ( ( 



Among these assertions and their denials we have the Aristotelian forms complete : and 

 our assertions give the affirmatives, our denials the negatives. The disjunctive forms may 

 now follow : eitfier meaning either or both, the true' contrary of neither. For ' both'' and ' and' 

 substitute 'either' and 'or': none* but restrictives will be found. In going through all the 

 varieties of application of part and whole, we come upon the complement, yet unseen, among 

 the correlative affirmations of exclusion : as in ' Any class is either not any whole of X or not 

 any whole of Y'. But the view opens as we proceed. Fart and whole are but synonymes 

 of species and genus: at our present point we may ask what would result if we were to 

 examine all the cases of ' Any [or some] class is both — of X and — of Y' when either 

 blank may be filled up with any of the eight names of relation .'' I certainly should not have 

 asked this question if the answer had required me to exhibit to the reader such a shaking 

 of the pepperbox as would seem necessary. The truth is that I have all but answered the 

 question in previous writings, as shall presently appear. 



I positively assert that the first of the preceding views' contains demonstration that the 

 relations between terms, derived from their relations to objects, must be the eight forms, and 

 no others. The postulates are that by a term we mean a distinguishing mark, the sign of 

 some object or objects, not the sign of others ; and that to any collection of objects which is 

 not the whole universe, we have a right to assign a term. I contend, as in my last paper, 



' "Shall I bring both ? — No need, either will do." Here 

 the either is either or both. 



' If individual were used instead of class, the restriction 

 would be removed from some propositions. Thus "any class 

 is either aome X or some V " enunciates a universe of two in- 



dividuals, one X and one Y: but "any individual is either 

 some X or some Y " means X (•) Y, without restriction. 



' The first idea of this mode of derivation is in my Formal 

 Logic (p. 105) : but I did not then see either the import or the 

 importance of what was there given. 



