ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 



467 



conclusion has 24 ways in which it can be announced with a secondary of its own quantity ; 

 and 8 ways with a secondary of the other quantity, I write down all the ways of announcing 

 the conclusions ) ) and ( ). 



Conclusion ) ) 



(( )) () )•)(( )•( (()•()•( )•) (.) () 



(•) )) )•) )( (( (( (•))•((( )( (•))•) 



()))() )•((()•( () )•()•( )•( (•) () 



(•()) )•) )) (( (( (■()•((( )) (•) )•) 



(( )) )) )•)(((•( (()•((•( )■) (•))) 



(•)))(•) )((()( (•) )•()( )( (•)(•) 



))())) (•()((•( ))(•((•( (•()•))) 

 )•( ()(•) ())()( )•((•()( ())•)(•) 



Conclusion ( ) 



((())) 

 (•) () (•) 

 ()())) 

 (•( () (•) 



((()() 



)•) )( (■( 

 )()()( 

 )■( )( (•( 

 )))()( 

 )■) )( )•( 



(( (•( (•( 



(•) (•( )( 



() (■( (•( 



(•( (•( )( 



(( (•( )•( 



)•) )•) )) 



)( )•) (■) 



)•( )•) )) 



)) )•) (■) 



)•) )•) () 



(•)())•) )()((( (•)(•((( )( )•) )•) 



))))() (•((()•( )) )•( )•( (•( (•) () 

 )•()))•) ()(((( )•()•((( () (•) ).) 



The common syllogism has a conjunctive relation of premises: as in )) () )) which 

 asserts terms — generally proved by assigning one — which are both genus of the minor and 

 species of the major; or as in )•( () (•), i.e. there are terms which are both external of the 

 minor and complement of the major. But there are disjunctive relations of premises : as 

 )■{ (■) ()' s"y term is either external of the minor or partient of the major. When the 

 secondary is thus disjunctive, the canon of validity is simply inverted as to universal and par- 

 ticular, and the canon of inference as to affirmative and negative. Thus (•( (•) )•) gives infer- 

 ence, because both premises are particular; and the conclusion is negative, (•) : if every 

 term be deficient, either of the major or the minor, these last are complements. Similar obser- 

 vations may be made on the secondary )(. The eight methods offer a crowd of analogies 

 which I shall not describe. Taking () for a standard secondary, the universal syllogisms 

 comprise all the cases in which the primary and secondary balances are of the same character, 

 and the tertiary balance uneven : when this last becomes even, we have the strengthened syllo- 

 gisms. In the particular syllogisms, there is even tertiary balance. The fourth case, uneven 

 tertiary balance accompanied by difference of character in the other two, does not give any 

 unrestricted forms. 



I now make a selection from the 512 identifications, in illustration of the danger of assert- 

 ing completeness without a very cautious examination. No one will deny, whatever he may 

 think of the system, that it is a system, and that no portion of it could be selected as com- 

 plete in itself with reference to all correlatives employed. Should any one object, his objec- 

 tion must affirm that the system is not yet complete, and that some higher power of 2 than 

 512 is the true number of cases. I take only one out of 32, as follows ^— -. 



