Influences of Greek Geometrical Analysis on Maimon's Notions of Analysis

It is often claimed that analysis is grounded on the principle of contradiction alone and synthesis is grounded not only on the principle of contradiction but on pure intuition as well. This distinction is inaccurate. In my talk, I discuss the notion of analysis as something that can be grounded on sensibility as well. For this purpose, I present practices of Greek geometrical analysis and discuss how they shaped philosophical and mathematical notions of analysis that are broader than merely logical analysis. I present the case of the philosopher Salomon Maimon (1753-1800) and his work on the different notions of analysis. Maimon's work on analysis is entwined with his work on invention. When writing the outlines of a theory of invention, he turns to Euclidean geometry and practices of Greek geometrical analysis as his main source of influence. This influence is extended not only to his formation of methods of invention but also to his notions of analysis and invention. He presents several notions of analysis, philosophical and mathematical, that are grounded not only on the principle of contradiction but on intuition as well. My discussion of such influences will be accompanied by examples taken from Euclid's Elements and Data. This study of the different forms of analysis is meant to shed light on the less known aspects of the concept and its practices.