?Drawing Illusions? ? a case study in the incorrectness of diagrammatic reasoning

Abstract

In ?Something to Reckon With? [6], a system for diagramming syllogistic inferences using straight line segments is presented (see also Englebretsen [5]). In the light of recent research on the representational power of diagrammatic representation systems (Lemon and Pratt [12, 13]) we point out some problems with the proposal, and indeed, with any proposal for representing logically possible situations diagrammatically. We shall first outline the proposed linear diagrammatic system of Englebretsen [5], and then show by means of counterexamples that it is inadequate as a representation scheme for general logical inferences (the task for which the system is intended). We also show that modifications to the system fail to remedy the problems. The considerations we present are not limited to the particular proposals of Englebretsen [5, 6]; we thus draw a more general moral about the use of spatial relations in representation systems.