First notions of logic (preparatory to the study of geometry)

by Augustus De Morgan

Every X is A, Every X is B, therefore Some A is B

would have been considered as formed by a spurious and unnecessary excess of assertion. The minimum of assertion would be contained in either of the following,

Every X is A, Some X is B, therefore Some A is B

Some X is A, Every X is B, therefore Some A is B

In this tract, syllogisms have been divided into two classes: first, those which prove a universal conclusion; secondly, those which prove a partial conclusion, and which are (all but one) derived from the first by weakening one of the premises, in such manner as to produce a legitimate but weakened conclusion. Those of the first class are placed in the first column, and the other in the second.

	Universal.		Particular.
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