Material Obversion
Chapter Fifty
Syllabus topic 3.4, "Other immediate inferences- material obversion, Inference by Added Determinants, Inference by Complex Conception & Inference by Converse Relation."
Pages 236 to 239 of 334
In one line
Material obversion replaces both the subject and the predicate of a proposition by their contraries, and it is not a formal inference.
In the wording a student can write in an examination: material obversion is the so-called inference in which the contrary of the subject is taken as the new subject and the contrary of the predicate as the new predicate. It is called material because its correctness depends on knowledge of the subject matter and not on the form of the proposition, and it is not valid as an immediate inference.
What it looks like
"All wise men are respected" yields, by material obversion, "All foolish men are despised."
"Virtue is praiseworthy" yields "Vice is blameworthy."
"All diligent students pass" yields "All idle students fail."
Each of the three has a certain rhetorical satisfaction, and each is a different proposition about a different class, arrived at by replacing both terms with their contraries.
Why it is not formally valid
Because the original says nothing about the contrary class. "All wise men are respected" is about wise men. It leaves the foolish entirely alone, and whether they are despised, ignored, pitied or elected is a matter it does not touch. To conclude anything about them is to go beyond the premise.
Because contraries leave a middle. As sequence 200 established, "wise" and "foolish" are contraries and not contradictories: a man may be neither. So the two propositions are not even about complementary classes, and the middle is unaccounted for by both.
And because the contrary of a predicate is not fixed by logic. Is the contrary of "respected" the term "despised", or "ignored", or "not respected"? Only knowledge of ordinary usage decides, and that knowledge is not part of the form of the proposition. A step that needs to be told what the words mean is not a formal step.
Compare ordinary obversion at sequence 460. There the predicate is replaced by its contradictory, which is fixed by logic alone, and the subject is untouched. Both differences are what make obversion valid and material obversion not.
When it does hold, and why that is not a rescue
Material obversion sometimes reaches a true conclusion, and the cases where it does are instructive.
It holds where the two pairs of contraries happen to divide the field between them and to correspond. If in a given context everyone is either wise or foolish and everyone is either respected or despised, and if the connection between wisdom and respect is a real one, then the conclusion may follow. But every one of those is a fact about the subject matter, not a feature of the proposition.
So the inference, where it holds, is not an immediate inference at all. It is a mediate inference with the extra facts as suppressed premises, which is to say it is an enthymeme, as sequence 40 described. Completing it exposes exactly what it was resting on.
Material Obversion
That is the honest description, and it is what an examination answer should say. Material obversion is not a rule of logic. It is a rhetorical figure that sometimes coincides with a sound argument.
Where it does damage in law
It does a great deal, and under a different name. The argument from the converse of a rule is material obversion in a wig.
"The Act protects tenants in occupation, so it leaves tenants out of occupation unprotected." The premise concerns tenants in occupation. Nothing follows about the others, who may be protected by another provision, by the general law, or by a proviso.
"Since a registered document is admissible, an unregistered one is inadmissible." This is the fallacy of denying the antecedent from sequence 290, dressed as an inference about contrary classes, and it is wrong for the same reason: registration is one route to admissibility and the provision never said it was the only one.
"The section penalises wilful default, so negligent default is innocent." Again nothing follows: negligent default may be penalised elsewhere, or may attract a civil consequence, or may be caught by a different limb.
The maxim that looks like an exception. Expressio unius est exclusio alterius, the expression of one thing is the exclusion of another, appears to license exactly this move. It does not. It is a canon of construction, applied where the structure of a provision shows that the omission was deliberate, and every book on interpretation warns that it is a weak canon to be used with care. It is not a rule of logic, and it operates only because a court has decided that in this statute the list was meant to be exhaustive. That is a decisional implication, at sequence 120, and not a formal inference.
A worked example
A rule provides: "An advocate who appears without a vakalatnama shall not be heard."
Apply material obversion. Contrary of the subject: an advocate who appears with a vakalatnama. Contrary of the predicate: shall be heard. Conclusion: "An advocate who appears with a vakalatnama shall be heard."
Is it true? Very likely, as a matter of practice.
Does it follow? No. The rule states a disqualification. It does not state that filing a vakalatnama is sufficient to be heard, and it plainly is not: an advocate may be unheard because the matter is not listed, because the party is unrepresented in that capacity, because leave is required, or for any number of other reasons.
Material Obversion
What does follow. By ordinary obversion, "every advocate who appears without a vakalatnama is a person not to be heard". By the full contrapositive, at sequence 480, "every advocate who is heard is one who did not appear without a vakalatnama", that is, one who filed it. That last proposition is the true one and it is much weaker than the material obverse: it says filing is necessary, not that it is sufficient.
The difference in one line. Material obversion turns a necessary condition into a sufficient one. That is precisely the error, and it is why the chapter belongs on a law syllabus.
Distinctions that carry marks
| Obversion | Material obversion | |
|---|---|---|
| Subject | Unchanged | Replaced by its contrary |
| Predicate | Replaced by its contradictory | Replaced by its contrary |
| Fixed by | Logic alone | Knowledge of the subject matter |
| Valid | Always, for all four propositions | Not formally valid at all |
| Nature | An immediate inference | A rhetorical figure, or an enthymeme |
| The error it commits | The proposition it produces |
|---|---|
| Says something about a class the premise never mentioned | About the contrary of the subject |
| Assumes contraries exhaust the field | They do not; there is a middle |
| Turns a necessary condition into a sufficient one | This is its practical damage |
What this does not mean
Its conclusions are not always false. They are often true, and that is what makes the figure persuasive. What is wrong is the claim that they follow.
Material obversion is not the same as denying the antecedent, though the two produce the same bad conclusions in law. One replaces terms by contraries; the other misuses a conditional. Both turn a necessary condition into a sufficient one.
Expressio unius is not material obversion made respectable. It is a canon of construction, applied on evidence that the list was meant to be exhaustive, and it is a weak canon even then.
Quick revision
Material obversion: replace subject and predicate each by its contrary, keeping the quality.
Not formally valid. Three reasons: the premise says nothing about the contrary class; contraries leave a middle; and what counts as the contrary of a term is settled by usage and not by logic.
Where it seems to work it is an enthymeme with the extra facts suppressed, not an immediate inference.
In law it appears as the argument from the converse of a rule: "the Act protects X, so it leaves non-X unprotected".
Its characteristic damage: it turns a necessary condition into a sufficient one.
The valid alternative is the full contrapositive, which yields only that the condition is necessary.
Test yourself
1. What is material obversion, and how does it differ from obversion?
Material Obversion
Material obversion replaces both the subject and the predicate of a proposition by their contraries, keeping the quality, as in inferring from "all wise men are respected" to "all foolish men are despised". Obversion, by contrast, leaves the subject untouched, changes the quality, and replaces the predicate by its contradictory rather than its contrary. Obversion is valid for all four propositions; material obversion is not a formal inference at all.
2. Give three reasons why material obversion is not valid.
First, the original proposition says nothing about the contrary of its subject, so any conclusion about that class goes beyond the premise. Second, contraries do not exhaust the field, so the two propositions are not even about complementary classes and the middle is unaccounted for. Third, what counts as the contrary of a given term is settled by ordinary usage and not by logic, so the step requires knowledge of the subject matter and is therefore material rather than formal.
3. If its conclusions are often true, what exactly is the objection?
That they do not follow. The truth of the conclusion is not in question; the claim that the premise establishes it is. Where the conclusion is true, it is true because of further facts about the subject matter, and those facts are suppressed premises. Completing the enthymeme shows that the argument is mediate and rests on material the speaker did not state.
4. How does material obversion appear in legal argument?
As the argument from the converse of a rule: "the Act protects tenants in occupation, so tenants out of occupation are unprotected"; "a registered document is admissible, so an unregistered one is inadmissible"; "the section penalises wilful default, so negligent default is innocent". In each the premise concerns one class and the conclusion concerns its contrary, and in each the omitted class may be provided for elsewhere.
5. Is the maxim expressio unius est exclusio alterius an exception?
No. It is a canon of construction, not a rule of logic, and it applies only where the structure of the provision shows that the omission from a list was deliberate. Even then it is treated as a weak canon to be used with care. It operates because a court has decided that in this statute the enumeration was meant to be exhaustive, which is a decision about the instrument and not an inference from its form.
6. What is the characteristic damage material obversion does, and what is the valid alternative?
It turns a necessary condition into a sufficient one: from "an advocate without a vakalatnama shall not be heard" it produces "an advocate with a vakalatnama shall be heard", which does not follow. The valid alternative is the full contrapositive, which yields only that every advocate who is heard filed a vakalatnama, that is, that filing is necessary. Necessity is what such a rule states, and sufficiency is what material obversion invents.
The rest of this subject
These notes are cut from the University's printed syllabus. Open the syllabus itself, or the past papers, for the same subject.