§ 512. From A again an inference can be drawn in the reverse order of conversion per accidens followed by permutation-- All A is B. .'. Some B is not not-A. All ingenuous persons are agreeable. .'. Some agreeable persons are not disingenuous. § 513. The intermediate link between the above two propositions is the converse per accidens of the first--'Some B is A.' This inference, however, coincides with that from 1 (§ 508), as the similar inference from E (§ 510) coincides with that from 0 (§ 506). § 514. All these inferences agree in the essential feature of combining permutation with conversion, and should therefore be classed under a common name. § 515. Adopting then this slight extension of the term, we define conversion by negation as--A form of conversion in which the converse differs in quality from the convertend, and has the contradictory of one of the original terms. § 516. A still more complex form of immediate inference is known as _Conversion by Contraposition._ This mode of inference assumes the following form-- All A is B. .'. All not-B is not-A. All human beings are fallible. .'. All infallible beings are not-human. § 517. This will be found to resolve itself on analysis into three steps of inference in the following order-- (1) Permutation. (2) Simple Conversion. (3) Permutation. § 518. Let us verify this statement by performing the three steps. All A is B. .'. No A is not-B (by permutation). .'. No not-B is A (by simple conversion). .'. All not-B is not-A (by permutation). All Englishmen are Aryans. .'. No Englishmen are non-Aryans. .'. No non-Aryans are Englishmen. .'. All non-Aryans are non-Englishmen. § 519. Conversion by contraposition may be complicated in appearance by the occurrence of a negative term in the subject or predicate or both, e.g. All not-A is B. .'. All not-B is A. Again, All A is not-B. .'. All B is not-A. Lastly, All not-A is not-B. .'. All B is A. § 520. The following practical rule will be found of use for the right performing of the process-- Transpose the subject and predicate, and substitute for each its contradictory term. § 521. As concrete illustrations of the above forms of inference we may take the following-- All the men on this board that are not white are red. .'. All the men On this board that are not red are white. Again, All compulsory labour is inefficient. .'. All efficient labour is free (=non-compulsory). Lastly, All inexpedient acts are unjust. .'. All just acts are expedient. § 522. Conversion by contraposition may be said to rest on the following principle-- If one class be wholly contained in another, whatever is external to the containing class is external also to the class contained. [Illustration] § 523. The same principle may be expressed intensively as follows:--