268 



PROCEEDINGS OF THE AMERICAN ACADEMY 



Any 



Some 

 Any 



Some 

 Any 



It is customary to enumerate six moods of the third figure instead 

 of four, and the moods Darapti and Felapton appear to be omitted. 

 But a particular proposition is asserted (actually and not merely 

 virtually) by the universal proposition which does not otherwise differ 

 from it; and therefore Darapti is included both under Disamis and 

 Datisi, and Felapton both under Bocardo and Ferison. (De Morgan.) 



The second figure, from the assertion of the rule and the denial of 

 the result, infers the denial of the case ; the third figure, from the 

 denial of the result and assertion of the case, infers the denial of the 

 rule. Hence we write the moods as follows, by allowing inferences 

 only on the straight lines : — 



Fig. 1. 



Assertion of Rule, 

 Assertion of Case ; 

 Assertion of Result. 



Fig. 2. 



Assertion of Rule, 

 Denial of Result ; 

 Denial of Case. 



Fig. 3. 

 Denial of Result, 



Assertion of Case ; 



Denial of Rule. 



The symmetry of the system of moods of the three figures is also 

 exhibited in the following table. 



