With an O proposition the subject is _undistributed_ while the predicate is distributed. This condition presents a peculiar difficulty. Consider, for example, the O proposition, “Some men are not wise.” Convert this into, “Some wise beings are not men,” and the _undistributed_ subject of the convertend, which is “men,” becomes the _distributed_ predicate of the converse. _Thus the O proposition cannot be converted without violating the rule for distribution._ _A Summary of How the Four Logical Propositions May be Converted._ 1. _A._ The ordinary A proposition may be converted by _limitation_ only. The co-extensive A may be converted _simply_. 2. _E._ The E proposition is converted _simply_. The E may also be converted by _limitation_, but the inference thus obtained is _weakened_. 3. _I._ The I proposition may be converted _simply_ only. 4. _O._ The O proposition _cannot be converted_. (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. Some impure liquids are water. Some not-white buildings are houses. It is indicated in the foregoing scheme that “I” cannot be contraverted. This is due to the fact that the obverse of an I is an O, and it will be remembered that “O” cannot be converted. All the other propositions admit of contraversion. =4. EPITOME OF THE FOUR PROCESSES OF IMMEDIATE INFERENCE IN CONNECTION WITH THE FOUR LOGICAL PROPOSITIONS.=