ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 



455 



The relations between terms, the only ones admissible because they are terms and for no other 

 reason, are those of applicable to some the same object, and not applicable to any the same 

 object. If X and Y be two terms, x and y their contraries, then, making full use of all 

 our correlative alternatives, — namely X or x, Y or y, of joint application or not of joint 

 application, — we shall obtain what must be all the forms of enunciation admissible into 

 the system of relations between terms as term^. And from our purely ooymatic enunciations 

 we may decipher the common forms of identification, or of discrimination, in which the distinc- 

 tion of term and desisrnated object of thought is afterwards lost to language^ by the application 

 of is and is not to the terms. The results are as follows : 



Onymatic relation between terms. 



X, Y have joint application 

 X, Y have no joint application 

 X, y have joint application 

 X, y have no joint application 

 X, y have joint application 

 X, y have no joint application 

 X, Y have joint application 

 X, Y have no joint application 



Proposition. 



Some Xs are Y« 



No X is Y 



Some Xs are not Ys 



Every X is Y 



Some things neither Xs nor Ys 



Everything either X or Y 



Some Ys are not Xs 



Every Y is X 



The moment we begin to speak of part of a term, we are no longer using the term 

 in the purest onymatic sense : we have made it stand for the collective group to each 

 individual of which it applies as a designation. Before we introduce the word part, I observe 

 that, as every relation has both its converse and its contrary, it is advisable in every case 

 to examine both conversion and contradiction. One converse of ' X, Y, have joint appli- 

 cation' is ' there are objects to which both of the terms, X, Y, are applicable'. We have 

 nothing to remark about this conversion except that it furnishes the most natural mode of 

 reading the new propositions (•) and )(. 



The above table exhausts, I think demonstratively, all purely onymatic relation ; that 

 is, all in which the terms are names to be applied or not applied, not names used for 

 objects by conventional substitution. There is no notion of quantity in this system : the 

 affirmatives — the assertions of joint application out of which the particulars spring — de- 

 mand 'one or more' objects to which joint application is made. But this is only tanta- 

 mount to 'There exists that which...' and its quantity is only the notion of owe which 

 precedes numeration in Omne quod est, eo quod est, singulare est. I have not space to 



that name, or its privative ? This is the most nicely balanced 

 question in logic, just as the following, which even Notes and 

 Queries cannot answer, is the most nicely balanced question in 

 geography. If all the northern hemisphere were land, and all 

 the southern hemisphere water, which should we have to say, 

 that the northern hemisphere is an island, or the southern 

 hemisphere a lalce ? I am Buridan's ass in respect to both 

 questions. 



' This distinction is usually obliterated in all cases in 

 which the term has meaning. But let abstraction be placed 



Vol. X. Part II. 



before an unpractised mind without warning, and reason may, 

 properly enough, refuse the identification of the terms by the 

 substantive verb. A book on logic was presented to a young 

 person of my acquaintance : after some time an account of pro- 

 gress was asked for. " Oh !" was the answer, " I read as far 

 as ' Every X w Y ', but I knew that wasn't true, so I left off." 

 Assuredly ' no X is V ' : every child who learns the alphabet 

 is plagued with 630 such negations. But it may chance that 

 every [thing signified by] X is [also one of the things 

 signified by] Y. 



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