210 



MR. JOSEPH JOHN MURPHY ON ADDITION 



then L~^ will mean effect, L° concause (to use a good 

 though obsolete word), and {L-^)° coeffect, and all the 

 syllogisms in the foregoing table will be true. 



But its most important application is to that part of the 

 ordinary logic which deals with the relation of inclusion^. 

 Using L as the symbol for inclusion, the old " syllogism 

 in Barbara,^^ 



becomes 



or, in language, 







AisB, 









BisC, 









A is C, 









A=ZB, 









B = Z,C, 









A=L"C, 









= LC, 





A 



is 



included in 



B, 



B 



is 



included in 



c, 



A 



is 



included in 



c. 



of which syllogism the canonical equation is 



U = L; 



which we may express in language by saying that the en- 

 closure of an enclosure is an enclosure. And, conversely, 



or the includent of an includent is an includent. 



L° in this notation means coenclosure, or enclosure in 



* The problems of the ordinairy logic are generally stated as dealing with 

 the relations of inclusion and exclusion ; but they may easily be generalized 

 so as to deal with coexisteiace and non-coexistence. 



