Modus Ponens, Modus Tollens, and Likeness

Abstract

Modus Ponens (MP) and Modus Tollens (MT) are taught as basic rules of inference related to conditional statements in introductory logic courses. In ordinary reasoning, MP and MT can have important roles in modes of argumentation. However, one can also distinguish counter-examples to such reasoning patterns when considered as ‘strictly’ valid rules (i.e., McGee’s counterattacks for MP, and Adams’ criticisms of MT). I suggest that this problem can be resolved if we revise MP and MT as basic tools of logic, assuming the above-mentioned counter-cases are valid, on the basis of nonmonotonicity. If the only thing that we know is ‘Tweety is a bird,’ we say ‘Tweety flies.’ But, after learning ‘Tweety is an ostrich,’ we (change our minds and) say, ‘Tweety does not fly.’ In actual life, we use ‘rules of logic’ in a limited sense; when we learn new facts, we change some of our beliefs sometimes. The question arises, ‘In which situation, which exception does not violate which rule?’ When reasoning about something, we use some semantic patterns in order to make inferences, or for the sake of argumentation. Two reasoning patterns employed in ordinary life scenes concerning conditional statements will be identified as MP-like and MT-like. These will be exemplified and discussed. The general idea guiding this tableau will be stated as likeness.