222 



face continued through thirty-three years, has recorded no instance 

 of such a transit. It is probable that now attention has been espe- 

 cially drawn to the subject, future observations, accompanied by 

 measures (of which Lescarbault's are the first instance), may throw 

 light on the nature of these phenomena. 



April 23, 1860. 



Professor De Morgan read a paper " On the Syllogism, No. IV., 

 and on the Logic of Relations." 



In the third paper were presented the elements of a system in 

 which only onymatic relations were considered ; that is, relations 

 which arise out of the mere notion of nomenclature — relations of 

 name to name, as names. The present paper considers relation in 

 general. It would hardly be possible to abstract the part of it 

 which relates to relation itself, or to the author's controversy with 

 the logicians, who declare all relations material except those which 

 are onymatic, to which alone they give the name of formal. Mr. 

 De Morgan denies that there is any purely formal proposition except 

 "there is the probability a that X is in the relation L to Y;" and 

 he maintains that the notion ' material' non suscipit magis et minus ; 

 so that the relating copula is as much materialized when for L we 

 read identical as when for L we read grandfather. 



Let X . . LY signify that X stands in the relation L to Y ; and 

 X . LY that it does not. Let LM signify the relation compounded 

 of L and M, so that X . . LMY signifies that X is an L of an M of Y. 

 In the doctrine of syllogism, it is necessary to take account of 

 combinations involving a sign of inherent quantity, as follows : — 



By X . . LM'Y is signified that X is an L of every M of Y. 



By X . . L,MY it is signified that X is an L of none but Ms of Y. 



The contrary relation of L, not -L, is signified by /. Thus X . LY is 

 identical with X . . IY. The converse of L is signified by L -1 : thus 

 X . . LY is identical with Y..L _1 X. This is denominated the 

 h-verse of X, and may be written LX by those who prefer to avoid 

 the mathematical symbol. 



The attachment of the sign of inherent quantity to the symbols of 

 relation is the removal of a difficulty which, so long as it lasted, pre- 

 vented any satisfactory treatment of the syllogism. There is nothing 

 more in X . . LM'Y than in every M of Y is an L -1 of X, or 

 MY))L~'X, X and Y being individuals; and nothing more in 

 X . . L ; MY than in L -1 X))MY, except only the attachment of the 

 idea of quantity to the combination of the relation. 



When X is related to Y and Y to Z, a relation of Xto Z follows: 

 and the relation of X to Z is compounded of the relations of X to Y 

 and Y to Z. And this is syllogism. Accordingly every syllogism 

 has its inference really formed in the first figure, with both premises 

 affirmative. For example, Y . LX and Y . . MZ are premises stated 



