AND MULTIPLICATION OF LOGICAL RELATIVES. 211 



the same includent ; and {L~^y means coincludent, or 

 includence of the same enclosure. When A and B are co- 

 includents, the old logic would say merely '^'some A is Bj '' 

 but these expressions are not equivalent. As we shall see 

 further on, I propose for '^ some A is B ^^ to say ^^ A and B 

 are participants of each other." Every pair of coincludeuts 

 are participants ; and every pair of participants are coin- 

 cludeuts ; but we say that coincludeuts are coincludeuts 

 of the common part or enclosure, and participants are par- 

 ticipants of each other. It must also be remembered that 

 every relative with zero index is used transitively, so that 

 when we speak of coinclusion or coincludence we mean, 

 throughout, inclusion in the same includent, or includence 

 of the same enclosure. 



With L meaning inclusion, the interpretations of these 

 sixteen canonical equations are as follows : — 



1. Enclosure of enclosure is enclosure. 



2. Enclosure of coen closure is coenclosure. 



3. Enclosure of coincludent is enclosure. 



4. Enclosure of includent is coenclosure. 



5. Coenclosure of enclosure is enclosure. 



6. Coenclosure of coenclosure is coenclosure. 



7. Coenclosure of coincludent constitutes no relation. 



8. Coenclosure of includent is coenclosure. 



9. Coincludent of enclosure is coincludent. 



10. Coincludent of coenclosure constitutes no relation. 



11. Coincludent of coincludent is coincludent. 



12. Coincludent of includent is includent. 



13. Includent of enclosure is coincludent. 



14. Includent of coenclosure is includent. 



15. Includent of coincludent is coinckulent. 



16. Includent of includent is iucludent. 



p2 



