INTRODUCTION AND PLAN OF THE CHAPTER

Greek mathematical deduction was shaped by two tools: the lettered diagram and the mathematical language. Having described the first tool, we move on to the second.

Before starting, a few clarifications. First, my subject matter is not exhausted by that part of the mathematical language which is exclusively mathematical. The bulk of Greek mathematical texts is made up of ordinary Greek words. I am interested in those words no less than in ‘technical’ words – because ordinary words, used in a technical way, are no less significant as part of a technical terminology.

Second, I am not interested in specific achievements in the development of the lexicon such as, say, Apollonius' definitions of the conic sections. Such are the fruits of deduction, and as such they interest me only marginally. When one is looking for the prerequisites of deduction, the language is interesting in a different way. It is clear that (a) a language may be more or less transparent, more or less amenable to manipulation in ways helpful from the point of view of deduction. It is also clear that (b) a language is influenced by the communication-situation. The focus of this chapter is on the ways in which (a) the lexicon served deduction; I shall also try to make some remarks here concerning (b) the probable contexts for the shaping of the lexicon.

Third, there is much more to any lexicon than just one-word-long units.