| Negate the predicate and change |  | (1) A to E |
| (2) E to A | ||
| (3) I to O | ||
| (4) O to I |
(3) IMMEDIATE INFERENCE BY CONVERSION.
Conversion is the process of inferring from a given proposition another which has, as its subject, the predicate of the given proposition, and, as its predicate, the subject of the given proposition. It is simply a matter of transposing subject and predicate. The original proposition is called the convertend while the derived proposition is named the converse.
The process of conversion is limited by two rules. First rule. No term must be distributed in the converse which is not distributed in the convertend. Second rule. The quality of the converse must be the same as that ofthe convertend. More briefly: (1) Do not distribute an undistributed term. (2) Do not change the quality.
We recall that a term is distributed when it is referred to as a definite whole. An undistributed term is referred to only in part. The principle underlying rule “1,” therefore, is the one which forms the basis of inference by opposition; namely, “Whatever may be said of the entire class may be said of a part of that class.” The converse of this is not true, that is, “What is said of part of a class cannot be said of the whole of that class.” When we distribute an undistributed term we are saying of the whole class what was said only of a part of that class. This is fallacious. On the other hand, we may say of a part what was said of the whole, or “undistribute” a distributed term.
We recall that the conclusion of the whole matter of inference by opposition was, that only an I could be inferred from an A and only an O from an E, or to put it in another way: Only an affirmative from an affirmative and only a negative from a negative. This establishes the truth of the second rule in conversion: “Do not change the quality.”
Let us apply the two rules to the four logical propositions.
Converting an A proposition.
Take as a type, “All horses are quadrupeds.” Here the subject “horses” is distributed, but the predicate “quadrupeds” is undistributed. In transposing subject and predicate we cannot distribute the term “quadrupeds,” according to the rule which says, “Do not distribute anundistributed term.” Hence in interchanging subject and predicate we cannot say, “All quadrupeds are horses,” but must limit the assertion to, “Some quadrupeds are horses.” Logicians call this process Conversion by Limitation.
Conversion by Limitation Exemplified Further.