Transposition (Logic)

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<!--, blanked the info box again and referenced set theory section to Transposition -->In the methods of deductive reasoning in classical logic, **transposition** is the rule of inference that permits one to infer from the truth of "A implies B" the truth of "Not-B implies not-A", and conversely.Brody, Bobuch A. "Glossary of Logical Terms". *Encyclopedia of Philosophy*. Vol. 5-6, p. 76. Macmillan, 1973. Its symbolic expression is:

The "→" is the symbol for material implication and the doubleheaded arrow "↔" indicates a biconditional relationship. The symbol "~" indicates negation. "P" and "Q" are components representing statements that form a truth functional compound proposition, where in a hypothetic proposition the first statement will be the antecedent and the last statement will be the consequent. The expression "truth function" has distinctive applications in philosophical logic and mathematical logic. This article concerns its philosophical application. (See also Transposition .)

## Traditional logic

### Form of transposition

In the inferred proposition, the consequent is the contradictory of the antecedent in the original proposition, and the antecedent of the inferred proposition is the contradictory...

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- (P → Q) ↔ (~Q → ~P)Copi, Irving M.
*Symbolic Logic*. 5th ed. Macmillan, 1979. See the Rules of Replacement, pp. 39-40.

The "→" is the symbol for material implication and the doubleheaded arrow "↔" indicates a biconditional relationship. The symbol "~" indicates negation. "P" and "Q" are components representing statements that form a truth functional compound proposition, where in a hypothetic proposition the first statement will be the antecedent and the last statement will be the consequent. The expression "truth function" has distinctive applications in philosophical logic and mathematical logic. This article concerns its philosophical application. (See also Transposition .)

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