Material Obversion

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.