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contraposition


Subject Philosophy

DOI: 10.1111/b.9781405106795.2004.x


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L ogic In traditional logic, an immediate inference formed by negating both the subject term and the predicate term of a proposition and exchanging their positions. The result is called the contrapositive, in which the predicate of the original proposition becomes the subject. Thus, contraposition is the operation of converting the obverse of a proposition or of obverting its converse. Of the four basic categorical propositions in traditional logic, the contrapositive of SAP (“All s are p”) is “all not p are not s”; that of SEP (“All s are not p”) is “all not p are not not s”; that of SIP (“Some s are p”) is “Some not p are not s,” and that of SOP (“Some s are not p”) is “some not not p are not s.” The contrapositions of SAP and SIP are valid, while that of SEP and SOP are invalid. In modern logic, contraposition is an inference consisting in negating both the antecedent and the consequent of a conditional, and exchanging their positions. For instance, from the premise “If p then q,” contraposition yields “if not q then not p.” This is a valid inference. “Contraposition may be defined as a process of immediate inference in which from a given proposition another proposition is inferred having for its subject the contradictory of the original predicate.” Keynes, Formal Logic ... log in or subscribe to read full text

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