The precedent studies on the validity of Modus ponens and Modus tollens have been carried out with most regard to a major type of conditionals in which the conditional clause is a sufficient condition for the main clause. But we sometimes, in natural language arguments, find other types of conditionals in which the conditional clause is a necessary or necessary and sufficient condition for the main clause. In this paper I reappraise, on the basis of new definitions of Modus ponens and Modus tollens, their validity/invalidity in natural language arguments in consideration of all types of conditionals.
Negation is frequently found in every language, and many logicians or linguists have been carrying out research on it. Their investigations are, however, mostly confined to the languages of Europe. Although some of them pay attention to non-European languages, we can hardly find research on negation in Korean. In this paper, we carry out contra-linguistic analysis of four aspects of negation in Korean and English. First, we compare the expressions of negative elements in Korean and English sentences. Second, we contrast the types of negation in Korean with those of English. Third, we draw a distinction between Korean and English in what decides the scope of negation. Finally, we contrast the answers to questions which contain negative elements.