Obversion

In one line

To obvert a proposition is to change its quality and to replace its predicate by the contradictory of that predicate.

In the wording a student can write in an examination: obversion is the immediate inference in which the quality of the given proposition, called the obvertend, is changed, and the predicate is replaced by its contradictory term, the subject and the quantity remaining unchanged, the result being called the obverse.

The two rules

Rule one: change the quality. An affirmative obvertend gives a negative obverse, and a negative gives an affirmative.

Rule two: replace the predicate by its contradictory. "Enforceable" becomes "non-enforceable"; "void" becomes "non-void".

And nothing else changes. The subject stays where it is. The quantity stays as it was. That is why obversion, unlike conversion, works on all four propositions and never limits anything: no term moves, so no term can become distributed that was not.

Why it always works

Take the two changes together. Changing the quality of a proposition alters which terms are distributed, but it alters them only for the predicate, since by the rules at sequence 310 quality governs the predicate and quantity governs the subject. And the predicate is simultaneously replaced by a different term.

So the term whose distribution changes is not the same term. The original predicate P leaves; the new predicate non-P arrives; and the subject, whose distribution is fixed by quantity, is untouched because quantity is untouched. No term is ever distributed in the obverse that was undistributed in the obvertend.

That is the proof, and it explains why obversion has no exceptions where conversion has three.

The four propositions

Worked in words.

"All contracts are agreements" gives "No contract is a non-agreement."

"No minor's agreement is enforceable" gives "Every minor's agreement is non-enforceable."

"Some agreements are contracts" gives "Some agreements are not non-contracts."

"Some agreements are not contracts" gives "Some agreements are non-contracts."

Notice the pattern in the letters: A and E swap, I and O swap. Quantity is preserved throughout and only quality moves, which is the whole of the operation.

Where it earns its keep

Two of those four look like empty restatements and two are genuinely useful, and knowing which is which is what makes the operation worth having.

The obversion of E is the useful one. A negative provision becomes an affirmative one with a negative predicate. "No suit shall be entertained without notice" becomes "every suit is a suit not entertainable without notice", and more usefully in the E-to-A direction, "no unregistered document is admissible" becomes "every unregistered document is inadmissible". The second form is what a court writes in an order.