THE THEORY OF SYLLOGISM, ETC. 81 



to the language, or to the order of ideas, &c. The following phrase of Sir William Hamilton's 

 system, ' All A is not some B ' is very forced, both in order and phraseology ; one who sees it 

 for the first time finds it hard to make either English or sense of it. The meaning is, ' Each 

 A is not any one among certain of the Bs :' and in its place in the system alluded to, the 

 uncouth expression helps to produce system, and the perception of uniform law of inference. 



I now take an instance from the preceding list, in which it will appear that an obscurity of 

 expression, if not absolute error, which has often occured, would have been avoided if the mind 

 had been forced to an analogy or an analogy had been forced until the mind readily saw it. I 

 say that the distinction of universal and particular may be replaced by that of conclusive and 

 inconclusive. In comparing • every X is Y ' and ' some -Ys are Fs,' the first is conclusive 

 with respect to every case which can be brought to the proposition for settlement by it. Cer- 

 tain Xs, determinable or indeterminable, are proposed ; are they Fs, or not ? The universal 

 is conclusive on this point, the particular inconclusive. Had this comparison been always 

 made, we should not have had so many* writers who have expressed themselves as if the 

 'some 1 of a particular proposition excluded every other some. 



I will now go through all the cases I have named, making universal and particular the 

 standard case which is to be compared with all the rest. 



1. The distinction of universal and particular may be replaced by that of affirmative 

 and negative. The universal affirms the right to assign one or other or both of two names 

 to every object of thought in the universe of the proposition : the particular denies it. Thus, 

 x being the contrary name of X, the proposition ' Every X is V affirms that F and so fill the 

 universe ; and ' some Xs are not Fs ' denies it. 



2. The distinction of universal and particular is that of possible and impossible, or of 

 existent or non-existent, according as the proposition speaks subjectively or objectively. Let 

 PQ signify the name compounded of P and Q, and belonging to every object which has a right 

 to both names. Then ' every X is F' sets down Xy as impossible or non-existent, and • some 

 ^Ys are not Fs 1 sets down Xy as possible or existent. 



3. On the connexion of universal and particular with necessary and not-necessary (contin- 

 gent) see the doctrine of modals, passim : on the correlative connexion with sufficient and not- 

 sufficient, see F. L. p. 73. 



4. The distinction of universal and particular is that of conjunctive and disjunctive; the 

 universal speaks conjunctively, the particular disjunctively, of the same set. The Xs being 



* No small number of the elementary writers do this. But | prium of man is to have as much as is wanted. The same 



that their leaders had no such error in their heads, is clear 

 enough. Ludovicus Vives, speaking of the maxim that 

 Differentia et proprium non accipiunt magis et minus, re- 

 marks that to be fit for a physician or a sailor are propria of 

 man, and yet one man may have more fitness for either than 

 another. But this is wrong, and the error consists in introduc. 

 ing into the proprium that which is not part of it, as proprium: 

 for one beast is more fit for a sailor than another ; and the pro- 



Vol. IX. Paet I. 



maxim, non aecipit magis et minus, was practically and con- 

 sistently applied to particular quantity, though not stated of 

 it, that I am aware of: but the writers I speak of use language 

 which, but for their subsequent proceedings, would lead any one 

 to suppose that they accepted magis et minus as indefinitely 

 applicable to particulars, and definitely to the relation of uni- 

 versal and particular. 



