Circles Disturbed: The Interplay of Mathematics and Narrative by Doxiadis Apostolos

Author:Doxiadis, Apostolos [Doxiadis, Apostolos]
Language: eng
Format: epub
Tags: Mathematics, History & Philosophy, Writing, Science, History, Philosophy
ISBN: 9780691149042
Google: X9Uoug4lNWkC
Amazon: 0691149046
Goodreads: 13555737
Publisher: Princeton University Press
Published: 2012-01-01T08:00:00+00:00

antipodes of logic, has blocked the investigations of rhetorical practice from becoming

essential to the cognitive history of logico-deductive proof.

In the view I adopt here, the two practices have a large area of overlap, as shown in

simple diagrammatic form in figure 10.1. When the older, internalist historians of mathematics mentioned rhetoric at all, they did so while placing themselves squarely in

the right-hand side of figure 10.1, casting their glance leftward only to highlight the differences of mathematics from rhetoric. However, we shall begin on the opposite side, first examining rhetoric in order to understand the similarities of the two practices, similarities it would take a gross leap of faith to consider accidental. After all, though early forms of rhetoric have older roots, both practices blossom at about the same time,

in the latter part of the fifth century and on into the fourth century BCE, in circles of intellectually sophisticated citizens, living in a handful of Greek poleis, that is, in the Greek adversarial cultural context, which promoted “the ambition to secure a

demonstration that would silence the opposition once and for all” (Lloyd 2002, 66).

Identifying similarities between any two contemporaneous practices A and B begs the

question of influence: did A beget B, did B beget A, or are both the offspring of a common ancestor, C? Based on the available textual evidence, in the case of Greek rhetoric (A) and mathematics (B) I would opt for a combination of the first and the third

answers. However, as most of my arguments here are structural, they are really

independent of the question of influence, and thus stay mostly clear of it.2

Figure 10.1. A diagrammatic depiction of the relationship of rhetoric and mathematics.

I shall begin my investigation slightly outside the area mapped in figure 10.1, on the left side. For before examining how certain rhetorical concepts, methods, and patterns

were instrumental to mathematical proof, I want to examine out how they entered the

domain of rhetoric in the first place: to say that mathematics took a large part of its logico-deductive, apodictic tools from rhetoric but leave the origin of these tools in rhetoric unexplained would simply relocate rather than answer the original question.

I shall use the streetcar-named-Desire metaphor to guide us through various

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