Abstract

According to the Principle of Conditional Non-Contradiction (CNC), unless p is impossible, conditionals “If p, then q” and “If p, then not q” are jointly inconsistent. Although intuitively appealing, CNC gives rise to serious problems that semantic theories of conditionals validating it have to face. Most notably, an example of violation of CNC, as presented by Allan Gibbard, may lead to the conclusion that conditionals do not express propositions at all. In the preset paper we propose a new analysis of Gibbard's argument showing that the violation of CNC is only apparent. Subsequently, we suggest a new way of defining truth conditions for conditional sentences.