Distinctions with Differences: Comparing Criteria for Distinguishing Diagrammatic from Sentential Systems

Abstract

A number of criteria for discriminating diagrammatic from sentential systems of representation by their manner of semantic interpretation have been proposed. Often some sort of spatial homomorphism between diagram and its referent is said to distinguish diagrammatic from sentential systems (e.g. Barwise & Etchemendy 1990). Or the distinction is analysed in terms of Peirce’s distinctions between symbol, icon and index (see Shin (forthcoming)). Shimojima (1999) has proposed that the sharing of ‘nomic’ constraints between representing and represented relations is what distinguishes diagrams. We have proposed that the fundamental distinction is between direct and indirect systems of representation, where indirect systems have an abstract syntax interposed between representation and represented entities (Stenning & Inder 1994; Gurr, Lee & Stenning 1999; Stenning & Lemon (in press).

The purpose of the present paper is to relate the distinction between directness and indirectness to the other criteria, and to further develop the approach through a comparison Peirce’s Existential Graphs both with sentential logics and with diagrammatics ones. Peirce’s system is a particularly interesting case because its semantics can be viewed as either direct or indirect according to the level of interpretation. The paper concludes with some remarks on the consequences of sentential vs. diagrammatic modalities for the conduct of proof.