A Streetcar Named (among Other Things) Proof

This chapter traces the origins of deductive mathematical proof in classical Greece by drawing on the tradition of Jean-Pierre Vernant and G. E. R. Lloyd. It first considers how certain rhetorical concepts, methods, and patterns were instrumental to mathematical proof before discussing various cognitive modes, or stations, in historical development. The streetcar-named-Desire metaphor is used to examine certain cognitive aspects of the narrative, along with the linearity and nonlinearity of the narrative surface. The chapter then explores the role of narrative and poetic storytelling in the process of demonstration in Greek forensic rhetoric, along with the use of chiasmus and ring-composition as cognitive tools. Finally, it shows how both the macrostructure and the microstructure of the first proofs in Greek deductive mathematics were affected by forensic rhetoric, as this was shaped under the influence of the cognitive mechanisms of narrativity and the forms of poetic storytelling.

Aesthetics · Art · Cognition · Cognitive science · Composition (language) · Epistemology · Linguistics · Literature · Mathematical proof · Metaphor · Narrative · Narrativity · Rhetoric · Rhetorical question · Storytelling · Classical Antiquity Studies · Historical and Literary Studies · Mathematics · Philosophy · Psychology