Completing the square of opposition

Abstract

In this paper a set of categorical sentences called an antilogistic tetrad is presented as a perspective on Aristotle's square of opposition. An antilogistic tetrad is formed by collecting the premises of a pair of valid syllogisms the conclusions of which are contradictory categorical sentences. A set of such premises serves to bring together Aristotle's concern with debate and the syllogism, and as such may be seen as a way of “completing” Aristotle's analysis of the square of opposition.

The debate context is characterized by opposing views for which arguments are offered. The square of opposition captures that contending of opposing views; and is also basic to the presentation of categorical sentences, a necessary condition for the syllogism. By using C. S. Peirce's notion of abductive argument to produce the middle term, and hence to construct deductive syllogistic arguments, antilogistic tetrads may be formed on any contended subject. For that reason, the process sketched above for forming antilogistic tetrads is called “completing the square of opposition.”