Why Care beyond the Square? Classical and Extended Shapes of Oppositions in Their Application to “Introspective Disputes”

Abstract

So called “shapes of opposition”—like the classical square of opposition and its extensions—can be seen as graphical representations of the ways in which types of statements constrain each other in their possible truth values. As such, they can be used as a novel way of analysing the subject matter of disputes. While there have been great refinements and extensions of this logico-topological tool in the last years, the broad range of shapes of opposition are not widely known outside of a circle of specialists. This ignorance may lead to the presumption that the classical square of opposition fits all disputes. A broader view, which takes expanded shapes of opposition into account, may come to a more nuanced appraisal of possible disputes. Once we take other shapes of opposition into account, some alleged disputes may turn out to be Scheindisputes. In order to do the wide range of linguistic expressions justice and to differentiate Scheindisputes from real ones, a broader view is advised. To illustrate this point, I discuss the notion of “introspective disputes”. These are commonly reconstructed as obeying the square, but are more aptly reconstructed with a more complex octagon. If we reconstruct these disputes based on Buridan’s octagon, it becomes obvious that “introspective disputes” are likely Scheindisputes.