Contraposition (LOGIC)
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Contraposition is a logical operation that forms a new proposition from an original one by negating or contradicting terms. There are two types: partial/simple contraposition changes quality between affirmative and negative but not subject and predicate terms, while complete contraposition changes both quality and subject and predicate terms. Partial contraposition changes an affirmative proposition to a negative one and vice versa. Complete contraposition preserves quality but changes subject and predicate terms such that if the original proposition is affirmative, so is the contraposition.
Contraposition (LOGIC)
- 1. This is a kind of education which results from a formulation of a new proposition whose subject term is the contradictory of the predicate term in the original proposition. In principle, contraposition is a product of both conversion and obversion . Thus like conversion , contraposition involves an interchange of the subject and predicate terms, and like obversion , it involves either the use or removal of negatives which affects the copula and the terms.
- 2. We can immediately see that there are two types of Contraposition. They are Partial or Simple and Complete. Partial Contraposition consists the formulation of a new proposition (contraposit) through the following: a. Its (contraposit) subject is the contradictory of the predicate term of the original proposition (contraponend), Ex. (Contraponend) All whales are mammals. (A) to Su Pp (Contraposit) No non-mammals are whales. (E) Su Pu
- 3. b. The quality of the contraponend is changed in the contraposit; and Ex. (Contraponend) No fishes are dogs. (E) to Su Pu (Contraposit) Some non-dogs are fishes. (I) Sp Pp c. The predicate term in the “A” proposition is changed to “E”, while “E” proposition to “I”, and an “O” proposition to “I”. Ex.(Contraponend) Some students are not studios.(O) to Sp Pu (Contraposit) Some non-studious are not non-students.(E) Sp Pp
- 4. Complete Contraposition. a new proposition (contraposit) is formulated through the following steps: a. The subject term in the contraposit is the contradictory of the predicate term in the contraponend , b. The quality of the contraponend is not changed in the contraposit ; and c. The predicate term in the contraposit is the contradictory of the subject term in the contraponend. In complete contraposition, an “A” proposition is changed to A, then E to O, and O to O.
- 5. 1. (Contraponend) All whales are mammals. (A) to Su Pp (Contraposit) All non-mammals are non-whales.(A) Su Pp 2. (Contraponend) No fish is a dog. (E) to Su Pu (Contraposit) Some non-dog is not a non-fish. (O) Sp Pu 3. (Contraponend) Some students are not studious.(O) to Sp Pu (Contraposit) Some non-studious are not students.(O) Sp Pu