ON VARIOUS POINTS OP THE ONYMATIC SYSTEM. 



471 



I finish this part of the subject by noticing that in any proposition one spicula' may be 

 read as a verb, subject to rejections on account of the production of restrictives asserted or 

 denied. The modes of reading are: — 



X), X is in ; X(, X takes in ; X (•, X is not in ; X)., X does not take in. 

 ( X, takes in X; ) X, is in X ; •) X, does not take in X ; -(X, is not in X. 



Examples are seen in 



X ) ) Y, All X is in Y ; X ( ■( Y, Some X is not in Y; 

 X ( •) Y, Any whole of X does not take in Y, 

 and so on. 



I shall now sketch out the whole of which the Hamiltonian attempt is a part. It will 

 not be worth while to reduce it to tables, because the complex syllogisms to which it leads are 

 easily reduced to compositions of simple ones, and would really appear in this way, except 

 only when they show the junctions of universals which are seen in the system of terminal preci- 

 sion. The particulars of this system are of very infrequent occurrence compared with the 

 universals. My object in giving this account is not to detail the system as for use, but to 

 make it a lesson upon the necessity of giving full action and equal prominence to all sides of 

 every correlation : and further, to show that the defects of an incomplete system are magnified 

 when the part selected from the whole system is not an aliquot part. The Aristotelian table 

 of enunciation, for instance, is a true bisection of system : it selects the lesser universals and 

 the greater particulars. But the system of sj'Uogism is not a true bisection : nineteen syllo- 

 gisms cannot be a real aliquot part of any system. I postulate — in my own mind I say I 

 have demonstrated — that the eight onymatic forms are essential to any complete system of 

 enunciation. 



We are to take in both all and some-not-all as quantifiers : that is, ' some affirmed to be 

 air, and ' some denied to be all'. At the outset then we are asked to select two out of three 

 alternatives, without allusion to the third. We know that Xs, if Xs enter into thought at all, 

 enter as some ; and this some is either affirmed as all, or neither affirmed nor denied as all, 

 or denied as all. Any some must appear in enunciation under one, and only one, of these 

 three relations to all. The Aristotelian system makes a fair bisection of this set of alterna- 

 tives. When there are three alternatives of which one is equally and symnjetrically related to 



» The ''mysterious spiculae" make a powerful language. 

 In using one symbol, ), as in X)Y, to denote botli the total 

 quantity of the subject and the particular quantity of the pre- 

 dicate, 1 followed the plan by which a fraction is represented, 

 in which one symbol distinguishes both numerator and deno- 

 minator: and I ultimately marked the symbol twice. If a 



fraction had been denoted by =, a and b would have been 







convenient symbols for a as a numerator and J as a denominator ; 

 and might be made useful even as it is. Forgetting that I 

 was not writing wholly for mathematicians, I used expressions 

 on this subject which were misunderstood. In my magazine 

 of animadversions (vi. 650*) there is a spirited criticism of my 

 notation, the colouring of which is heightened by assuming to 

 be one my two syllogistic notations, pictorial and arbitrary ; 



Vol. X. Part II. 



the first only a study, the second a language for use. In it we 

 find — "We need hardly, therefore, be surprised, that, in the 

 end, Mr De Morgan should actually laud the farrago for ex- 

 pressing diametrically opposite things ("the universality of 

 tlie subject," "the particularity of the predicate") by the 

 self -same representation." Had I held, with the logicians, the 

 exclusive right of the onymatic relations to be logical forms, 

 I should now have dropped the word spicular, already borrowed 

 from Hamilton, and have substituted farraginal, vitb the 

 motto 



Quicquid agunt homines nostri est farrago libelli. 



If, as I suspect, I am on the way to a much wider use of the 

 complex forms )), (.(, &c., the second adjective may yet find 

 an introduction. 



60 



