Plato’s explanations were transmitted orally, the question does not lie in accepting that these unwritten teachings did in fact exist, but rather in determining what this doctrine corresponded to40.
Whether or not we interpret the doctrine of principles (the principal focus of later indirect testimonies) as part of Plato’s oral teachings or as a subsequent and highly scholastic interpretation of Plato’s doctrine in an Academy impregnated by Pythagoreanism41, we are faced with a very confusing situation indeed regarding Platonic philosophy. It is possible that the doctrines of Plato had been so contaminated by the subsequent developments introduced by his direct disciples42 that by Arcesilaus’ time they had reached a point of no return. In light of the hypothesis of the unwritten theories, it would be reasonable to assume that the views developed in later doctrines would eventually alter Plato’s written doctrine to such a degree that it would be difficult to distinguish genuine Platonic principles from those espoused by his disciples, especially by the members of the Academy who had not had direct access to his teachings.
It seems clear, then, that because there was no written account of these explanations or as a result of later developments, the Platonic principles of Plato’s followers differed to a greater or lesser degree from those espoused by Plato himself. This is not surprising, since from the beginning Plato’s thought presented, due to its investigative generosity, an incomplete, unfinished edifice full of perplexity and doubt, an essential feature of all thought, which after much effort, compelled one towards a non-established truth. This may explain why the dialectical contradictions that fed Plato’s creative
40 This is not the place for a detailed discussion of the scope or value of Plato’s unwritten teachings. It is clear that Plato included passages and texts in his works on the impossibility of putting in writing all knowledge, or transmitting it to another person. For more on this see the monographic issue of the journal Méthexis, Vol. VI, 1993 or Román Alcalá, R., “¿Son los ágrapha dógmata las lecciones no escritas de Platón?”, Anales del Seminario de Historia de la Filosofía, (1999), 16, 85-108.
41 Luc Brisson is one of the staunchest defenders of this interpretation. He explicitly states the suppositions and consequences of opting for the first interpretation. Cf. “Présupposés et conséquences d'une interprétation ésotériste de Platon”, Méthesis, Vol. VI, 1993, pp. 11-35.
42 It is difficult to reconcile Plato’s writings and oral theory with the doctrine of principles espoused by Speusippus and Xenocrates. After Plato’s death, the history of the Academy is inexorably linked to the history of mathematics given the widely used concept of “number”, which some view as the development of the unwritten Platonic doctrine of the Priniciples of Oneness and Infinite Duality, while others view it as a subsequent Pythagorean interpretation of Plato’s dialogues, cf. Napolitano Valditara, L.M., “Riparlare di Platone. Ancora su scrittura, oralità e dialettica”, Méthesis, VII, (1994), pp. 5-25, esp. pp. 22-25.