Presented at the 1996 DIMACS Symposium on Teaching Logic And Reasoning In An Illogical World, 1996 and also at the 11th International Workshop-Conference on Teaching Philosophy, 1996.
Abstract
A large volume of research shows that humans reason poorly about conditional statements and that the formal notion of material implication is difficult to learn. Textbooks on logic have used a variety of approaches to the introduction and justification of a truth-functional definition of material implication. This paper surveys eight such techniques — definition by truth table, definitions based on other logical operators, the use of examples, ways of avoiding the need for a definition, an adaptation of Peirce’s notation, the motivation of universally quantified conditionals, the analogy with contractual reasoning, and finally a new suggestion based on elementary set theory.