A Every A is X Some A is X I A Every X is B ────── Every X is B A ———————————— ————————————— A Every A is B Some A is B I Some A is X I No X is B E ┌ ——————————————— A Every A is X │ Some A is not B O E No X is B ─────┼ Every A is X A ———————————— │ E No A is B │ Some B is not X O └ ——————————————— Some B is not A O Every X is A A ...... Some X is not B O ——————————————— Some A is not B O In all works on logic, it is customary to write that premiss first which contains the predicate of the conclusion. Thus, Every X is B Every A is X Every A is X would be written, and not Every X is B ———————————— ———————————— Every A is B Every A is B The premises thus arranged are called major and minor; the predicate of the conclusion being called the major term, and its subject the minor. Again, in the preceding case we see the various subjects coming in the order X, B; A, X; A, B: and the number of different orders which can appear is four, namely— XB BX XB BX AX AX XA XA —— —— —— —— AB AB AB AB which are called the four figures, and every kind of syllogism in each figure is called a mood. I now put down the various moods of each figure, the letters of which will be a guide to find out those of the preceding list from which they are derived. Co means that a premiss of the preceding list has been converted; + that it has been strengthened; Co +, that both changes have taken place. Thus, A Every X is B A Every X is B I Some A is X becomes A Every X is A: (Co +) ———————————— ———————————— I Some A is B I Some A is B And Co + abbreviates the following: If some A be X, then some X is A (Co); and all that is true when Some X is A, is true when Every X is A (+); therefore the second is legitimate, if the first be so. _First Figure._ A Every X is B A Every X is B A Every A is X I Some A is X ———————————— —————————————— A Every A is B I Some A is B