In order to more clearly understand the logical processes involved in Derived Judgment, we should acquaint ourselves with the general relations of Judgments, and with the symbolic letters used by logicians as a means of simplifying the processes of thought. Logicians denote each of the four classes of Judgments or Propositions by a certain letter, the first four vowels—A, E, I and O, being used for the purpose. It has been found very convenient to use these symbols in denoting the various forms of Propositions and Judgments. The following table should be memorized for this purpose:
Universal Affirmative, symbolized by "A."
Universal Negative, symbolized by "E."
Particular Affirmative, symbolized by "I."
Particular Negative, symbolized by "O."
It will be seen that these four forms of Judgments bear certain relations to each other, from which arises what is called opposition. This may be better understood by reference to the following table called the Square of Opposition:
Thus, A and E are contraries; I and O are sub-contraries; A and I, and also E and O are subalterns; A and O, and also E and I are contradictories.
The following will give a symbolic table of each of the four Judgments or Propositions with the logical symbols attached:
(A) "All A is B."
(I) "Some A is B."
(O) "Some A is not B."