11. Unfortunately, by Buridan's time the principle of contraposition had been advocated by a number of authors. 12. In mathematics, "'proof by contraposition "'is a rule of inference used in proofs. 13. Thus, partial contraposition can be obtained conditionally in an " E " type proposition with a change in quantity. 14. Also, notice that contraposition is a method of inference which may require the use of other rules of inference. 15. The successive applications of conversion and obversion within the process of contraposition may be given by a variety of names. 16. Some writers in the twelfth century and thirteenth centuries adopted a principle called " conversion by contraposition . " It states that 17. These are [ Jean ] Buridan's examples, used in the fourteenth century to show the invalidity of contraposition . 18. Syntactically, ( 1 ) and ( 2 ) are derivable from each other via the rules of contraposition and double negation. 19. Notice that contraposition is a valid form of immediate inference only when applied to " A " and " O " propositions. 20. Popular rules of inference in propositional logic include " modus ponens ", " modus tollens ", and contraposition .
