INTRODUCTION AND PLAN OF THE CHAPTER

The question before us is ‘What made Greek mathematicians write the way they did?’. This is related to the question ‘What made Greek mathematicians begin to write the way they did?’, but the two are not identical. Since what I study is not some verbalised ‘discovery’ (say, ‘Mathematics is axiomatic!’), but a non-verbalised set of practices, explaining the emergence is not the same as explaining the persistence. Assertions, perhaps, simply stay put once they are propounded. The persistence of practices must represent some deeper stability in the context.

We are therefore obliged to adopt the perspective of the long duration. The question about the ‘critical moment’, the moment at which the cognitive mode started, is not ‘What happened then?’ but ‘What is true of the entire period from then onwards, and is not true of the entire period before that?’ – which does not rob the critical moment of its interest. Something has happened there – and therefore I will raise the chronological question. When did Greek mathematics begin? When was the style described in this study fixed? Section 1 discusses such questions. (But I must warn the reader: I deliberately avoid the temptation of rich chronological detail, which can easily lead us astray. The chronological argument is briefly argued, and is more dogmatic – also for the reason explained above, that this is not after all the main issue.)

More central are the questions of the long-duration historical background.