II. Do not distribute an undistributed term. No term must be distributed in the converse which is not distributed in the convertend.
The reason of these rules is that it would be contrary to truth and logic to give to a converted judgment a higher degree of quality and quantity than is found in the original judgment. To do so would be to attempt to make “twice 2” more than “2 plus 2.”
There are three methods or kinds of Conversion, as follows: (1) Simple Conversion; (2) Limited Conversion; and (3) Conversion by Contraposition.
_In Simple Conversion_, there is no change in either quality or quantity. For instance, by Simple Conversion we may convert a proposition by changing the places of its subject and predicate, respectively. But as Jevons says: “It does not follow that the new one will always be true if the old one was true. Sometimes this is the case, and sometimes it is not. If I say, ‘some churches are wooden-buildings,’ I may turn it around and get ‘some wooden-buildings are churches;’ the meaning is exactly the same as before. This kind of change is called Simple Conversion, because we need do nothing but simply change the subjects and predicates in order to get a new proposition. We see that the Particular Affirmative proposition can be simply converted. Such is the case also with the Universal Negative proposition. ‘No large flowers are green things’ may be converted simply into ‘no green things are large flowers.'”
_In Limited Conversion_, the quantity is changed from Universal to Particular. Of this, Jevons continues: “But it is a more troublesome matter, however, to convert a Universal Affirmative proposition. The statement that ‘all jelly fish are animals,’ is true; but, if we convert it, getting ‘all animals are jelly fish,’ the result is absurd. This is because the predicate of a universal proposition is really particular. We do not mean that jelly fish are ‘all’ the animals which exist, but only ‘some’ of the animals. The proposition ought really to be ‘all jelly fish are _some_ animals,’ and if we converted this simply, we should get, ‘some animals are all jelly fish.’ But we almost always leave out the little adjectives _some_ and _all_ when they would occur in the predicate, so that the proposition, when converted, becomes ‘_some_ animals are jelly fish.’ This kind of change is called Limited Conversion, and we see that a Universal Affirmative proposition, when so converted, gives a Particular Affirmative one.”
In Conversion by Contraposition, there is a change in the position of the negative copula, which shifts the expression of the quality. As for instance, in the Particular Negative “Some animals are not horses,” we cannot say “Some horses are not animals,” for that would be a violation of the rule that “no term must be distributed in the converse which is not distributed in the convertend,” for as we have seen in the preceding chapter: “In Particular propositions the _subject_ is _not_ distributed.” And in the original proposition, or convertend, “animals” is the _subject_ of a Particular proposition. Avoiding this, and proceeding by Conversion by Contraposition, we convert the Convertend (O) into a Particular Affirmative (I), saying: “Some animals are not-horses;” or “Some animals are things not horses;” and then proceeding by Simple Conversion we get the converse, “Some things not horses are animals,” or “Some not-horses are animals.”
The following gives the application of the appropriate form of Conversion to each of the several four kind of Judgments or Propositions:
(A) _Universal Affirmative_: This form of proposition is converted by Limited Conversion. The predicate not being distributed in the convertend, it cannot be distributed in the converse, by saying “all.” (“In affirmative propositions the _predicate_ is _not_ distributed.”) Thus by this form of Conversion, we convert “All horses are animals” into “Some animals are horses.” The Universal Affirmative (A) is converted by limitation into a Particular Affirmative (I).