EXTENSION OF THE ORDINARY LOGIC. 97 



that is to say, Lord Palmerston was a fellow Irishman, and 

 therefore a fellow countryman, of the Duke of "Wellington. 

 As we have seen, out of the relation of inclusion three 

 others arise. We express the four as follows : — 



A = LB, A is an enclosure of B. 



A=L~^B, A is an includent of B. 



A = L°B, A is a co-enclosure of B. 



A= {L-')°B, A is a co-includent of B. 

 It must be remembered that when we speak of co-inclusion 

 or co-includence, we mean, throughout, inclusion in the 

 same includent, or includence of the same enclosure. 

 This is different from the usage of the common logic. 

 Where the old logicians say 



Some A is M, 

 Some B is M, 

 we express this by 



_= fL-'P)° or A and M are co-includents of P ; 



M ^ ' ' 



_ = fL-'Q")° or B and M are co-includents of Q, 



M ^ ^ ' 



where P and Q are or may be different ; and from these 

 premises no conclusion can be drawn. 



By combining the four forms of proposition stated 

 above, we get sixteen syllogisms, which constitute as 

 many syllogistic canons. Fourteen of these are conclu- 

 sive ; that is to say, in fourteen cases the relations ex- 

 pressed in the two premises combine in the conclusion into 

 a simple relation, which is always of the same kind with 

 one of the four forms given in the premises ; in the re- 

 maining two cases they do not so combine. These sixteen 

 are given in the following tabular statement. As the 

 equations 



r = L and {L~'Y = L-' 



SER. III. VOL. VII. H 



