On Diagram Tokens and Types

Rejecting the temptation to make up a list of necessary and sufficient conditions for diagrammatic and sentential systems, we present an important distinction which arises from sentential and diagrammatic features of systems. Importantly, the distinction we will explore in the paper lies at a meta-level. That is, we argue for a major difference in metatheory between diagrammatic and sentential systems, by showing the necessity of a more fine-grained syntax for a diagrammatic system than for a sentential system. Unlike with sentential systems, a diagrammatic system requires two levels of syntax—token and type. Token-syntax is about particular diagrams instantiated on some physical medium, and type-syntax provides a formal definition with which a concrete representation of a diagram must comply. While these two levels of syntax are closely related, the domains of type-syntax and token-syntax are distinct from each other. Euler diagrams are chosen as a case study to illustrate the following major points of the paper: (i) What kinds of diagrammatic features (as opposed to sentential features) require two different levels of syntax? (ii) What is the relation between these two levels of syntax? (iii) What is the advantage of having a two-tiered syntax?