Applying these rules to the four fundamental forms of proposition, we have the following table:—
| Convertend. | Converse. |
| All S is P. A. | Some P is S. I. |
| Some S is P. I. | Some P is S. I. |
| No S is P. E. | No P is S. E. |
| Some S is not P. O. | (None) |
It is desirable at this stage briefly to call attention to a point which will receive fuller consideration later on in connexion with the reading of propositions in extension and intension, namely, that, generally speaking, in any judgment we have naturally before the mind the objects denoted by the 128 subject, but the qualities connoted by the predicate. In the process of converting a proposition, however, the extensive force of the predicate is made prominent, and an import is given to the predicate similar to that of the subject. At the same time the distribution of the predicate has to be made explicit in thought. It is in passing from the predicative to the class reading (e.g. from all men are mortal to all men are mortals), that the difficulty sometimes found in correctly converting propositions probably consists. We shall at any rate do well to recognise that conversion and other immediate inferences usually involve a distinct mental act of the above nature.
It follows from what has been said above that some propositions lend themselves to the process of conversion much more readily than others. When the predicate of a proposition is a substantive little or no effort is required in order to convert the proposition; more effort is necessary when the predicate is an adjective; and still more when in the original proposition the logical predicate is not expressed separately at all, as in propositions secundi adjacentis. Compare for purposes of conversion the propositions, Whales are mammals, Lions are carnivorous, A stitch in time saves nine. In some cases, in consequence of the awkwardness of changing adjectives and verbal predicates into substantives, the conversion of a proposition appears to be a very artificial production.[125]
[125] Compare Sigwart, Logic, i. p. 340.
97. Simple Conversion and Conversion per accidens.—It will be observed that in the case of I and E, the converse is of the same form as the original proposition; moreover we do not lose any part of the information given us by the convertend, and we can pass back to it by re-conversion of the converse. The convertend and its converse are accordingly equivalent propositions. The conversion under these conditions is said to be simple.
In the case of A, it is different; we cannot pass by immediate inference from All S is P to All P is S, inasmuch as P is distributed in the latter of these propositions but undistributed in the former. Hence, although we start with a universal proposition, we obtain by conversion a particular 129 proposition only,[126] and by no means of operating upon the converse can we regain the original proposition. The convertend and its converse are accordingly non-equivalent propositions. The conversion in this case is called conversion per accidens,[127] or conversion by limitation.[128]
[126] The failure to recognise or to remember that universal affirmative propositions are not simply convertible is a fertile source of fallacy.
[127] The conversion of A is said by Mansel to be called conversion per accidens ‘because it is not a conversion of the universal per se, but by reason of its containing the particular. For the proposition ‘Some B is A’ is primarily the converse of ‘Some A is B,’ secondarily of ‘All A is B’” (Mansel’s Aldrich, p. 61). Professor Baynes seems to deny that this is the correct explanation of the use of the term (New Analytic of Logical Forms, p. 29); but however this may be, we certainly need not regard the converse of A as necessarily obtained through its subaltern. It is possible to proceed directly from All A is B to Some B is A without the intervention of Some A is B.
[128] Simple conversion and conversion per accidens are also called respectively conversio pura and conversio impura. Compare Lotze, Logic, § 79.