N'ew System of Logical N'otatioii. 



The notation explained in the present paper is appro- 

 priate to a set of propositions stated by De Morgan in the 

 paper ah'eady quoted, but without detailed demonstration. 

 The present writer, trying to improve on De Morgan, is but 

 a dwarf on a giant's shoulders, or rather a dwarf with his 

 feet on the shoulders of two giants, De Morgan and Boole ; 

 but it may be maintained with much plausibility that giants 

 were made in order to carry dwarfs ; and I think it will 

 be found that, for the present purposes at least, my notation 

 is clearer, less arbitrary, and more appropriate than De 

 Morgans. The theorems are as follows ; — they arrange 

 themselves in pairs of converses. 



Every ancestor is an ancestor Every descendant is a des- 



of all descendants (of his 

 descendants),and adescen- 

 dant of none but their an- 

 cestors ; a non-ancestor of 

 none but their non-descen- 

 dants, and a non-descen- 

 dant of all their non- 

 ancestors. 



cendant of all ancestors 

 (of his ancestors), and an 

 ancestor of none but their 

 descendants ; a non-des- 

 cendant of none but their 

 non-ancestors, and a non- 

 ancestor of all their non- 

 descendants. 



Every non-ancestor is a non- 

 ancestor of all ancestors, 

 and an ancestor of none 

 but non-ancestors. 



Every non-desce4idant isa non- 

 descendant of all descen- 

 dants, and a descendant of 

 none but non-descendants. 

 Writing ancestors E, and descendants conversely E"'^ ; non- 

 ancestor e, and non-descendant conversely c~'^ ; these 

 theorems are thus written in our notation : — 



lE- 



— E X I 



lE. 



-1 



iE-\ 

 : i~'e 



