Obverses

Obverses are a type of formal transformation in the traditional (Aristotelian) syllogistic. An obverse is formed by keeping the subject term the same and replacing the predicate term with its complement, while preserving the proposition’s quantity (universal or particular) and quality (affirmative or negative). In other words, each categorical proposition has a corresponding obverse.

The standard conversions are:

- All S are P becomes All S are not-P.

- No S are P becomes No S are not-P.

- Some S are P becomes Some S are not-P.

- Some S are not-P becomes Some S are not not-P, which is equivalent to Some S are P.

Thus, the obverse yields a second proposition about the same subject class, with the predicate negated. Obversion is one of the four traditional immediate inferences in Aristotelian logic and is typically used alongside other techniques such as conversion and contraposition in syllogistic reasoning. The operation relies on interpreting the predicate as having a definite complement within the same domain.

In modern logic, obversion is less central; negation is usually handled at the level of predicates and quantifiers in a more systematic way. Nevertheless, obverses remain a useful historical concept for understanding how old syllogistic form relates to the broader idea of negating the predicate while keeping the subject fixed. Obversion dates back to Aristotle and was developed further in medieval and early modern logic as part of the study of categorical propositions.