Reduction Trees

Abstract

While truth tables allow us to determine the validity or invalidity of arguments by searching for counter-examples, they are limited because as they grow in size, the chance of error increases and the time required to construct and read them becomes increasingly prohibitive. Reduction trees give us a more efficient way of exploring the possible substitution instances of an argument form. They also provide a different and more comprehensible picture of the structure of the argument. Reduction tree construction begins by listing the premises of the argument. The denial of the conclusion is then added as the last item in the list. If the argument is valid, then it is impossible to assert the premises along with the denial of the conclusion without contradiction. The process of developing the rest of the tree involves uncovering the contradictions that must occur if the argument is valid. Let's first consider a simple argument, one whose premises and conclusion consist only of truth functionally simple statements.