Obversion

The obversion of O is the other useful one. A negative particular becomes an affirmative one. "Some agreements are not enforceable" becomes "some agreements are unenforceable", which is the form in which a pleading would put it.

The obversion of A and of I are the awkward ones, because they produce double negatives: "no contract is a non-agreement", "some agreements are not non-contracts". They are perfectly valid and they read badly, and their real use is as a step in a longer chain, which is exactly what sequences 470 to 490 do with them.

Where a lawyer meets it

In statutory drafting, constantly. A drafter chooses between "no person other than a registered practitioner shall practise" and "every person who practises shall be a registered practitioner". Those two are obverses of each other, so they assert exactly the same thing, and the choice between them is a choice about emphasis and about where the burden practically falls, never about content.

In reading a double negative. A provision reading "no order shall be made unless the officer is not satisfied that the ground does not exist" is a chain of negations, and obversion is the tool for unwinding it one negation at a time until it says something a reader can hold.

In understanding "unless". "No suit shall lie unless notice is given" obverts to "every suit that lies is one in which notice is given", which is the form that actually tells a litigant what to do.

A worked example

Section 25 of the Indian Contract Act 1872 begins: "An agreement made without consideration is void, unless..."

Reduce and label. Setting the exceptions aside, the main limb is an A proposition: All agreements made without consideration, other than the three excepted classes, are void agreements.

Obvert. Change the quality and negate the predicate: No agreement made without consideration, other than the three excepted classes, is a non-void agreement.

Is that useful? As it stands, barely, and this is the honest position with the obversion of an A proposition. Its use is as a step.

Take the step. The obverse is an E proposition, and E converts simply, as sequence 450 established. Converting gives: No non-void agreement is an agreement made without consideration other than the three excepted classes. In plainer words: every agreement that is valid either has consideration or falls within one of the three exceptions.

That is a genuinely useful proposition and it is the one a drafter checking a document actually needs. It could not have been reached by conversion alone, because A does not convert simply, and it could not have been reached by obversion alone, because the obverse of A reads as a double negative. The two operations together produce it, and the combination is the partial contrapositive, which is sequence 480.

Distinctions that carry marks

What this does not mean

Obversion does not change the subject. Only the predicate is negated, and a student who negates both has performed something else entirely.

"Non-P" is not the same as "the opposite of P". It is the contradictory, everything in the universe of discourse that is not P, as sequence 190 established. "Non-void" covers valid and voidable agreements alike, and it is not a synonym for "valid".

The double negatives are not errors. "Some agreements are not non-contracts" is a correct obverse and reads badly, and its purpose is to be the next step in a chain.

Quick revision

Obversion: change the quality, replace the predicate by its contradictory. Subject and quantity untouched.

Valid for all four propositions, without limitation, because no term moves position.

Letters: A to E, E to A, I to O, O to I.

The useful directions: E to A turns a prohibition into an affirmative rule; O to I turns a negative particular into an affirmative one.

The awkward directions: A to E and I to O produce double negatives and are used as steps in longer chains.

In drafting: "no person other than X may do Y" and "every person who does Y shall be X" are obverses and say the same thing.

Test yourself

1. Define obversion and state its rules.

Obversion is the immediate inference in which the quality of the given proposition is changed and its predicate is replaced by the contradictory of that predicate, the subject and the quantity remaining unchanged. Its rules are therefore two: change the quality, so that an affirmative gives a negative and a negative an affirmative, and negate the predicate term, leaving everything else exactly as it was.

2. Why is obversion valid for all four propositions when conversion is not?

Because no term changes position. The distribution of the subject is fixed by the quantity, and the quantity is unchanged; the distribution of the predicate is fixed by the quality, and the quality does change, but the predicate is simultaneously replaced by a different term. So no term that was undistributed in the obvertend is distributed in the obverse, and the distribution rule can never be broken.

3. Give the obverse of each of A, E, I and O.

"All S is P" gives "No S is non-P", an E. "No S is P" gives "All S is non-P", an A. "Some S is P" gives "Some S is not non-P", an O. "Some S is not P" gives "Some S is non-P", an I. Quantity is preserved throughout and the letters exchange within each quantity, A with E and I with O.

4. Which obversions are practically useful, and why?

The obversion of E, which turns a prohibition into an affirmative rule with a negative predicate: "no unregistered document is admissible" becomes "every unregistered document is inadmissible", which is the form a court uses. And the obversion of O, which turns a negative particular into an affirmative one: "some agreements are not enforceable" becomes "some agreements are unenforceable". The obversions of A and I produce double negatives and are chiefly useful as steps in longer chains.

5. What does obversion tell a drafter about "no person other than a registered practitioner shall practise"?

That it says exactly the same thing as "every person who practises shall be a registered practitioner", since the two are obverses of one another. The choice between them is therefore a choice about emphasis and about where the burden practically appears to fall, and never about the content of the rule. Nothing can be argued from one form that could not be argued from the other.

6. Why is "non-void" not a synonym for "valid"?

Because a contradictory term covers everything in the universe of discourse that is not the original term, and the universe here contains voidable agreements as well as valid ones. "Non-void" therefore takes in both, while "valid" takes in only one. Treating a contradictory as though it were the contrary is the error at sequence 200, and it changes the reach of a proposition every time it is made.