DESCRIPTION OF A NOTATION FOR THE LOGIC OF RELATIVES. 331 



For instance, the lovers of two women are not t lie same as two lovers of women, 

 that is, 



l2.w and 2./w 



are unequal; but the husbands of two women are the lame as t\ > husbands of 

 women, that is, 



&2.W= 2. Aw, 



and in general, x,2.y — i.x,y . 



The conception of multiplication we have adopted is that of the application of one 

 relation to another. So, a quaternion being the relation of one vector to anoth. 

 the multiplication of quaternions is the application of one such relation to a second. 

 Even ordinary numerical multiplication involves the same idea, for 2x3 is a pair 

 of triplets, and 3 X 2 is a triplet of pairs, where "triplet of" and "pair of" are 



evidently relatives. 



If we have an equation of the fo 



xy — z 



> 



and there are just as many z's per y as there are per thin thin,- of the untvers. 



then we have also the arithmethical equation 



" 



M W = M ■ 



For instance, if our universe is perfect men, and there arc as many te.tl, to a rVncb- 

 man (perfect understood) as there are to any one of the universe, then 



w en = p n 



holds arithmetically. So if men ar« just as apt to be black « things in general, 



[m,] [b] = [m,b] , 



where the difference between [m] and [m,] must not be overlooked. It is to be 



observed that 



pi 



i . 



Boole 





was the first to show this connection bet,een logic and p.bab.hne. He 

 - dieted, however, to absolute terms. I do not remember g n W, 



.tension of probability to -^— ^^^S^ 

 Our logic*, multiplication, then, saUsfies e ,n ^ ^ C0I1 . 



has a unity, has a conception similar to that ot 

 tains numerical multiplication as a case under it. 



