ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 



459 



for the right and duty of logic to treat of other relations between terms, derived from the 

 relations of objects to one another : but my present concern is with onymatic relations only. 

 I proceed to a more systematic connexion of the eight forms than I have yet given. 



Each universal is in two ways of a universal character, one of an active meaning, the 

 other of a passive. Thus, 



X))Y 

 X((Y 

 X).(Y 

 X()Y 



X wholly included in and wholly incompletive of Y 

 X wholly including and wholly uncompleted by Y 

 X wholly excluding and wholly excluded from Y 

 X wholly completive of and wholly completed by Y 



Each particular has also two characters : and by each character is inferentially attached 

 to a universal. Thus X () Y affirms that X is partially or wholly included in Y, and that X 

 partially or wholly includes Y: and X((Y affirms that X is partially or wholly excluded 

 from Y, and is partially or wholly completive of Y. 



Again, four of the relations may be called greater, and four less. A greater relation is 

 one which cannot be changed into its contrary without subtraction : a lesser relation is one 

 which cannot be changed into its contrary without addition. The greater relations are ((, (•), 

 (•(. ()> being all of which the minor term is particular: the lesser relations are )), )•(, ).),)(, 

 being all of which the minor term is universal. The Aristotelian collection includes the 

 lesser universals and the greater particulars. 



Each universal has a contranomiiial, with which it may coexist ; and two extreme^ contra- 

 ries or extreme contradictories. Thus X))Y has the contranominal X((Y= x))y and 

 the extreme contraries X)(Y and X(-)Y. 



Hence we see the connexion of each universal with two inferred particulars. Each 

 partial proposition asserts the existence of an indefinite share of the extreme extent by 

 which the universal is toto orbe divisum from one of its extreme contraries. Thus ' wholly 

 included in' which is also 'wholly incompletive of, or )), necessarily contains 'partially 

 included in' and 'partially incompletive of, () and )(, which are indefinite contraries (com- 

 monly called contradictories) of )•( and (•), of each of which )) is an extreme contradiction. 

 The connexion of the contranominals, through their extreme contraries and the particulars, 

 is illustrated in the adjacent table (W., wholly ; P., partially). The lines may also be read 

 backwards, the spicular symbols being still read forwards. 



' I hold by the amalgamation of the words contradictory 

 and contrary, in spite of the disapprobation of some who have 

 approved various points of my system. And this I do first, 

 because the common language makes synonymes of the two : 

 he who contradicts maintains the contrary. And this even 

 from the mouths of persons versed in technical logic. Dr 

 Clarke said of Collier the idealist "he can neither prove his 

 point himself, nor can the contrary be proved against him." 



Secondly, the etymology does not support the distinction. 

 Thirdly, the true opposition is that of any contradiction and 

 the extreme or total contradiction. "All are"; contradiction, 

 some (perhaps all) are not; extreme contradiction, none are. 

 Fourthly, the existing terms hide the distinction, and give a 

 notion which makes a logician say, " so far from being the con- 

 tradictory, it is not even the contrary." 



