The Reason Why Antecedent Negation Works

Abstract

In the first-order logic, previous studies demonstrate that the negation of the antecedent is invalid to negate the consequent in sufficient conditionals. This paper justifies some particular cases of it with a concrete example "If I have enough money, I will buy a car." by using the semantic presupposition theory, the pragmatic presupposition theory and the Cooperative Principle. In this example, sufficient conditional can be proven sufficient and necessary so that the denial of the original condition can work effectively. Then this paper discusses that there are limitations to this method. It is demanding and can become unworkable by even only changing one verb. Only if there is a unique and biconditional relationship between the antecedent and the consequence can it be proven that the negation of the antecedent works. In addition, this paper expands on this, using the relevance theory in linguistics to try to eliminate some of the strict constraints of the biconditional relationship. Sometimes the particularly strong cause will exceed the other weak causes so that the case will be temporarily viewed as a biconditional case, which is limited to daily conversations. Therefore, it is able to be applied to the main argument.