EXTENSION OF THE ORDINARY LOGIC. 99 



of the relation; and if L is understood to mean any 

 transitive relation whatever^ all the syllogisms as stated 

 above remain true, but with changed interpretations. 

 Let L, for instance, mean cause, then L~^ will mean effect, 

 L° concause (to use a good though obsolete word), and 

 (Z/~')° co-effect; and let us assume that the cause of a 

 cause is a cause ; or let 



L mean superior, 

 Z/~' „ inferior, 

 L° „ co-superior, 

 (Z/~')° „ co-inferior; 



with either of these interpretations of our symbols, all 

 the sixteen syllogisms will remain true. 



The interpretations of the foregoing sixteen equations 

 ai'e as follows : — 



1 . Enclosure of enclosure is enclosure. 



2. Enclosure of includent is co-enclosure. 



3. Enclosure of co-enclosure is co-enclosure. 



4. Enclosure of co-includent is enclosure. 



5. Includent of enclosure is co-includent. 



6. Includent of includent is includent. 



7. Includent of co-enclosure is includent. 



8. Includent of co-includent is co-includent. 



9. Co-enclosure of enclosure is enclosure. 



10. Co-enclosure of includent is co-enclosure. 



1 1 . Co-enclosure of co-enclosure is co-enclosure. 



12. Co-enclosure of co-includcnt constitutes no relation. 



13. Co-includent of enclosure is co-includent. 



14. Co-includent of includent is includent. 



1 5. Co-includent of co-enclosure constitutes no relation. 



16. Co-includent of co-includent is co-includent. 



H 2 



