AND MULTIPLICATION OF LOGICAL RELATIVES. 



From the four relatives 



207 



L or north, 

 L~^ or south, 



L° or fellow-northern, 

 (L~')° or fellow-southern. 



we obtain sixteen syllogisms, as set forth in the following 

 table, which is a multiplication table, and is arranged as 

 such. (In what follows we shall speak of logical premises 

 as factors and logical conclusions as products.) The mul- 

 tipliers, corresponding to the minors of the ordinary logic, 

 occupy the left-hand column ; the multiplicands, corre- 

 sponding to the majors of the ordinary logic, occupy the 

 top line ; any product is found on the line with the mul- 

 tiplier and under the multiplicand *. It will be observed 

 that in half the places the product is zero ; this indicates 

 that in the universe and with the relatives under conside- 

 ration such products do not exist. In the other eight 

 places the products are what we may call affirmative 

 results. 





L 



Zo 



(i-x)o 



Z- 



L 



' 



^ 



3 L 



4 



io 



L° 



5 L 



' LO 



7 



8 







(i-.)o 



9 n 



lO y 



" ^L-r 



12 



L-' 



L-' 



'3 (Z-)o 



'4 L- 



^5 



.6 







The interpretations of these syllogisms are the follow- 

 ing t ; A, B, and C being houses on the north side of the 



* We owe to De Morgan the improvement of writing the minor premise 

 of a syllogism before instead of after the major. 



t This table is the same as that given on p. 45 of Prof. Pierce's " Notation 



