4. EPITOME OF THE FOUR PROCESSES OF IMMEDIATE INFERENCE IN CONNECTION WITH THE FOUR LOGICAL PROPOSITIONS.
| [*] | Proposition symbolized | Name of Process | Inference symbolized | Principle involved |
| A | All S is P[†] | Opposition | Some S is P (I) | What is said of all may be said of some. |
| Obversion | No S is not-P (E) | Two negatives are equivalent to one affirmative. | ||
| Conversion by Limitation | Some P is S (I) | An undistributed term cannot be distributed. | ||
| Contraversion | No not-P is S (E) | Same principles which obtain in obverting A and converting E. | ||
| E | No S is P | Opposition | Some S is not P (O) | What is said of all may be said of some. |
| Obversion | All S is not-P (A) | Two negatives are equivalent to one affirmative. | ||
| Simple Conversion | No P is S (E) | Distribution not affected. | ||
| Contraversion | Some not-P is S (I) | An undistributed term cannot be distributed. | ||
| I | Some S is P | Opposition | Doubtful | None. |
| Obversion | Some S is not not-P (O) | Two negatives are equivalent to one affirmative. | ||
| Conversion | Some P is S (I) | Distribution not affected. | ||
| Contraversion | Impossible | None. | ||
| O | Some S is not P | Opposition | Doubtful | None. |
| Obversion | Some S is not-P (I) | Two negatives are equivalent to one affirmative. | ||
| Conversion | Impossible | None. | ||
| Contraversion | Some not-P is S (I) | Same as in obversion of O and conversion of I. |
[*] – Name of proposition
[†] – “S” represents any subject and “P” any predicate.
INFERENCE BY INVERSION.
Some logicians treat of a form of immediate inference known as inversion though it is of small importance and of little practical value.
The process can be applied only to propositions A and E. In the one case the contradictory subject is limited by “some” and then denied of the predicate, whereas, in the other case, the contradictory subject is merely affirmed of the predicate.
Illustrations.
| The Given Proposition. | The Inverse. | |
| I. | All S is P. (A) | Some not-S is not P. (O) |
| All planets rotate. | Some not-planets do not rotate. | |
| II. | No S is P. (E) | Some not-S is P. (I) |
| No men are immortal. | Some not-men are immortal. |
From the foregoing we are able to conclude that the inverse of “A” is found by negating the subject and changing to an “O”; while the inverse of “E” is found by negating the subject and changing to an “I.”