Abstract

Ancient Platonists and Aristotelians considered the heuristic method of reasoning to first principles as “analysis.” It was derived from Greek geometrical practice. Plato’s theory of first principles, as we reconstruct it following Aristotle, postulated such an “analytic system.” In this system both sensible things and mathematical objects, ideas and eidetic numbers are gradually reduced to the same principles (ἕν – μέγα – μικρόν). In the reversal order, from the principles are genetically elicited eidetic numbers and through them numbers, mathematical objects, and sensible things. This is a great analytical system that in fact has a mathematical structure. It transcends the physical explanation of the Timaios and is a broad translation of the nature of things. Our considerations concern a reconstruction and debatable issues, and they follow the following topics: 1. Testimonia Platonica, 2. Analytic theory of principles and agrapha dogmata, 3. Contextual problem and the field of agrapha dogmata, 4. The construction of a system: a procedure from and toward the principles, 5. The alleged paradox: “Good – One.” Ethics or mathematics? 6. Written and unwritten dogmata: dialogue or system?