ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 



435 



r ' Hamilton's forms. Expressed in Aristotelian forms, 



Negatives. when doubly partitive. when singly partitive. when non partitive. 



Toto-total Any X is not any Y No X is Y No X is Y No X is Y. 



Toto-partial^ Any X is not some Y Either toto-partial or Some Y is not X Some Y is not X. 



parti-partial affirma- 

 tive : any affirmative 

 which contains Some 

 Y is not X. 



Parti-total^ Some X is not any Y Either parti-total or Some X is not Y Some X is not Y. 



! parti-partial affirma- 



tive: any affirmative 

 which contains Some 

 H. is not Y. 



Parti-partial Some X is not some Y Cannot be false except when X and Y are singular and 



identical. 



[Should have been 

 'anything but a toto- 

 total negative'] 



In the hurried article (VI. 635*) we are informed in the text that the Aristotelian 'some'' 

 is 'possibly none^ ; and, in a note, that the Aristotelian 'not-some' does not definitely exclude 

 'none'. I suppose that if there be a point in which all preceding logicians agree, it is 

 that not-some is none, and not-none is some. But I do not wish to give further attention to 

 this extraordinary product of haste : I pass on to its source. When Hamilton combines 

 some-at-least and some-at-most in one word, some; not-all &nd not-none are then of course 

 constituents of the meaning of one and the same proposition. The ordinary logician, if he 

 should choose to take 'some-at-most, possibly none' into his system, — as from Hamilton's 

 words I suspect some must have done — will see two new particulars emerge, equivalents of 

 the old ones, but not identical with them. For ' some-at-least-possibly all X is Y' is con- 

 vertible with, ' Some-at-most-possibly-none X is not Y ' : and ' Some-at-least-possibly -all X 

 is not Y' is convertible with ' Some-at-most-possibly-none X is Y\ If equivalence be for a 

 moment confounded with identity, a person already accustomed to not-none and not-all in one 

 proposition, might shape his language to the supposition that the logicians who use none 



positions X))Y and X((Y; true when both are true; false 

 when either is false. It is important to note that two wholes 

 may compound into a third, without the parts of the two com- 

 pounding into the parts of the third : I never said that all is 

 compound of somes ; but only that a proposition having two 

 alls is compounded of two propositions having each one some. 

 ' That disjunctively joined affirmatives should have the 

 logical import of negatives, seems at first sight absurd : but 

 other instances of it may be found; and I suspect that, under 



limitation at least, it is a true canon. For another instance, I 

 may cite my own form (•). It is a remarkable instance of the 

 want of perception of analogies which characterises early spe- 

 culation on all subjects — and which I look at with profit and 

 amusement in my own earlier papers, nothing doubting that I 

 shall in time do the same with this one — that Hamilton, who 

 (vi. 650*) sneers at my disjunctively affirmative form of the 

 negative (■)) I'ad not long before (vi. 632*) given two of his 

 own negatives the same kind of form. 



