The Square of Opposition

(Traditional)
  U  Affirmative   Negative   U 
 n 
 i 
 v 
 e 
 r 
 s 
 a 
l 
A
All S are P
E
No S are P		  n 
 i 
 v 
 e 
 r 
 s 
 a 
l 
 P   P 
 a 
 r 
 t 
 i 
 c 
 u 
 l 
 a 
I
Some S are P
O
Some S are not P		  a 
 r 
 t 
 i 
 c 
 u 
 l 
 a 
 r  Affirmative   Negative  r 

Warning: Web Page Notes are not intended as a substitute for attending lectures.


Contradictories (Diagonals): If the one is true the other is false. If the one is false the other is true.
Contraries (Across the Top): If the one is true the other is false. If the one is false the other is indeterminate.
Subcontraries (Across the Bottom): If the one is false the other is true. If the one is true the other is indeterminate.
Subalternates (Both Sides): If the Universal is true the Particular is true. If the Particular is false the Universal is false. Everything else is indeterminate.

For more information see Garth Kemerling's Web Page on Categorical Propositions