PLAN OF THE CHAPTER

Much has already been said on letters representing objects in the diagram. The interest has so far focused on the light which such letters throw upon the use of diagrams. Here we concentrate on the letters themselves as they occur in the text. This is a convenient object: a definite, small set, and the combinatorial possibilities are limited. The results can therefore obtain an almost quantitative precision. The practices described here are interesting, then, mainly as a case-study for Greek mathematical pragmatics in general. It is clear that Greek mathematics follows many conventions of presentation, some of which we have noticed already. What can the origin of these conventions be? I will take the conventions regarding letters as a first case-study.

Following an explanation of the nature of the practices involved, I offer a hypothesis concerning the origins of those practices (section 1). Then, in section 2, a few cognitive implications of the practices will be spelled out. These implications are generally a development of points raised in the preceding chapter, but they already suggest the issues concerning the use of language, to be developed in chapters 3–4.

THE ORIGINS OF THE PRACTICES

A preliminary description

The practices with regard to letters fall into two kinds. The first is what I call ‘baptism’ – the process of attaching individual letters to individual objects.