456 



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



develope the objections which the pure onymatic system, as well as other views, furnish 

 against the Hamiltonian doctrine that all enunciation is equation of quantity : but even those 

 who would not admit their force will guess what they are. 



Let us now introduce the notion of multitude of objects which, considered as having a com- 

 mon designation, give the idea of class, part of the universe separated from the rest. Each class 

 — except when singular— has sub-classes which are its parts, and — except when penultimate — 

 is a sub-class of classes which are its wholes. Any collection of objects which is itself only part 

 of the universe may be called a class, as capable of receiving a common designation which is 

 also distinctive. We shall find the eight onymatic forms starting up in the following simple 

 appearance, without the reality, of system : this I say because, as shall be shewn, we have 

 only a systematic selection from a complete system. The remainder, after the selection 

 is made, will contain restrictive propositions, or their denials. And this will happen 

 in all attempts to systematize which involve quantity, and which make a full use of all 

 correlatives which are admitted at all. Observe that we do not admit the universe as 

 distinctively a whole, because it is a whole of all terms, and not itself a term. 



Some class is part of both X and Y 

 No class is part of both X and Y 

 Some class is whole of both X and Y 

 No class is whole of both X and Y 

 Some class is whole of X and part of Y 

 No class is whole of X and part of Y 

 Some class is part of X and whole of Y 

 No class is part of X and whole of Y 



X parti ent of Y 

 X external of Y 

 X coinadequate of Y 

 X complement of Y 

 X species of Y 

 X exient of Y 

 X genus of Y 

 X deficient of Y 



() 

 )•( 



)C 



(•) 

 )) 

 (•( 

 (( 

 )•) 



Here we see terms without their contraries; '■some' with one terminal extreme, 'none', but 

 without the other, 'every' ; conjunctions, as 'both part of X and part of Y', without the 

 corresponding disjunctions, as in 'either part of X or part of Y'; conjunctions of affirma- 

 tions only, without the corresponding cases of one affirmation and one negation, or of two 

 negations. If the whole system were formed, every case which does not reproduce one of tlie 

 above, would either require terms coextensive with the universe, or penultimate, or singular ; 

 or would deny propositions requiring such terms. But as this point will presently receive 

 sufficient illustration, I shall proceed no further with it at present : I shall also presently 

 have occasion to go some way into the extension. 



Both the preceding systems of enunciation have an exemplar character : in both the 

 forms we see ' there does exist an instance of...' denied by ' there does not exist any instance 

 of.,.'. I will now proceed to an exemplar system in which part or whole of one term is in 

 affirmation identified with part or whole of the other ; the unlimited selection any, and the 

 possibly limited selection some, either or both, being used in all combinations. The restric- 

 tive propositions will be denoted as follows : singular identity by (: =r) ; penultimate identity 

 by (rr;); singular and penultimate identity by (:?); singular and penultimate contrariety (?i). 

 And that singular identity in which one terra and the contrary of the other are singular and 

 identical, may be denoted by ( ) or by ( ), as convenient. 



