A Class Room Logic / Deductive and Inductive, with Special Application to the Science and Art of Teaching

by George Hastings McNair

(4) INFERENCE BY CONTRAVERSION. (Contraposition).

This mode of inference is usually referred to as inference by contraposition, but contraversion, indicating more definitely the nature of the process, is a better term. Contraversion involves two steps: First, obversion; second, conversion. The same principles and rules evident in these two processes obtain in inference by contraversion. The following scheme, therefore, ought to be sufficient to make the matter clear:

Inference by Contraversion.

1.	The Given Proposition.	2.	Obverted.
A.	All men are mortal.		No men are immortal.
	All trees are plants.		No trees are not-plants.
E.	No men are infallible.		All men are fallible.
	No men are trees.		All men are not-trees.
I.	Some men are wise.		Some men are not not-wise.
O.	Some water is not pure.		Some water is impure.
	Some houses are not white.		Some houses are not-white.

3. Converted; giving the contraverse of the original proposition.

No immortals are men.

No not-plants are trees.

Some fallible beings are men.

Some not-trees are men.

An O cannot be converted, consequently the contraversion of an I is impossible.