Inversion, Partial and Full

In one line

The inverse of a proposition has the contradictory of the original subject as its subject.

In the wording a student can write in an examination: inversion is the immediate inference in which the subject of the inferred proposition is the contradictory of the subject of the original. In the partial inverse the predicate is the original predicate; in the full inverse the predicate is the contradictory of the original predicate.

The shape

Partial inverse: non-S as subject, P as predicate.

Full inverse: non-S as subject, non-P as predicate.

Set that beside the shapes already learned and the whole family is visible at once.

Every combination of the four terms is now accounted for, which is why the list of eductions ends here and why MU's bracket contains exactly these.

Inverting A, step by step

Original: All S is P.

Step one, obvert. No S is non-P. E.

Step two, convert simply. No non-P is S. E.

Step three, obvert. All non-P is non-S. A.

Step four, convert by limitation. Some non-S is non-P. I. This is the full inverse of A.

Step five, obvert. Some non-S is not P. O. This is the partial inverse of A.

In words. "All contracts are agreements" gives, fully, "some non-contracts are non-agreements", and partially, "some non-contracts are not agreements".

Notice which comes out first. The full inverse arrives at step four and the partial at step five, which is the reverse of the order in contraposition. Students expect "partial" to come first because it did there, and writing the chain out is what prevents the mistake.

Inverting E, step by step

Original: No S is P.

Step one, convert simply. No P is S. E.

Step two, obvert. All P is non-S. A.

Step three, convert by limitation. Some non-S is P. I. This is the partial inverse of E.

Step four, obvert. Some non-S is not non-P. O. This is the full inverse of E.

In words. "No minor's agreement is enforceable" gives, partially, "some agreements not made by minors are enforceable".

Notice that the chain begins differently. For A the first step is an obversion; for E it is a conversion. Beginning E with an obversion leads to "all S is non-P", then a conversion by limitation to "some non-P is S", then an obversion to "some non-P is not non-S", which is an O and cannot be converted: a dead end. Choosing the first step correctly is the whole difficulty of inversion, and the rule is: obvert first for A, convert first for E.