(I) "Some A is B."
(E) "No A is B."
(O) "Some A is not B."
These four forms of propositions bear certain logical relations to each other, as follows:
A and E are styled contraries. I and O are sub-contraries; A and I and also E and O are called subalterns; A and O and also I and E are styled contradictories.
A close study of these relations, and the symbols expressing them, is necessary for a clear comprehension of the Laws of Opposition stated a little further back, as well as the principles of Conversion which we shall mention a little further on. The following chart, called the Square of Opposition, is also employed by logicians to illustrate the relations between the four classes of propositions:
Conversion is the process of immediate reasoning by which we infer from a given proposition another proposition having the predicate of the original for its subject and the subject of the original for its predicate; or stated in a few words: Conversion is the transposition of the subject and predicate of a proposition. As Brooks states it: "Propositions or judgments are converted when the subject and predicate change places in such a manner that the resulting judgment is an inference from the given judgment." The new proposition, resulting from the operation or Conversion, is called the Converse; the original proposition is called the Convertend.
The Law of Conversion is that: "No term must be distributed in the Converse that is not distributed in the Convertend." This arises from the obvious fact that nothing should be affirmed in the derived proposition than there is in the original proposition.
There are three kinds of Conversion; viz: (1) Simple Conversion; (2) Conversion by Limitation; (3) Conversion by Contraposition.