Categorical Logic (The Mechanics of Conversion, Obversion, and Contraposition)

Contraposition

A proposition is contraposed when its subject and predicate terms are switched, and a complement is added to each: - All "S are P," becomes "All non-P are non-S." - No "S are P," becomes "No non-P are non-S." - Some "S are P," becomes "Some non-P are non-S." - Some "S are not P," becomes "Some non-P are not non-S." The contrapositive is a valid inference for A- and O-propositions on both the traditional and modern interpretations. The contrapositive is a valid inference by limitation for E- and I-propositions on the traditional interpretation only. (See the image for the problem with the E- and I-proposition inferences on the modern square.)

Conversion

A proposition is converted when its subject and predicate terms are switched: - All "S are P," becomes "All P are S." - No "S are P," becomes "No P are S." - Some "S are P," becomes "Some P are S." - Some "S are not P," becomes "Some P are not S." Conversion is a valid inference for E- and I-propositions on both the traditional and modern interpretations. Conversion is valid by limitation on the traditional interpretation only. (See the image for the problem with the A- and O-proposition inferences on the modern square.)

Obversion

A proposition is obverted when the quality is changed, and a complement is added to the predicate term: - All "S are P," becomes "No S are non-P." - No "S are P," becomes "All S are non-P." - Some "S are P," becomes "Some S are not non-P." - Some "S are not P," becomes "Some S are non-P." Conversion is valid for all four proposition types on both the traditional and modern interpretations.