Two negatives are equivalent to one affirmative.
{ (1) A to E Negate the predicate { (2) E to A and change { (3) I to O { (4) O to I
_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 of the 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.
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 an undistributed 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_.