This letter is addressed to Dionysius the Younger. It is notable for having a particularly vivid statement of the idea that Plato's real teaching is not found in his dialogues. In the course of the letter, Plato remarks that he has been teaching his main doctrines for more than thirty years, which is difficult to reconcile with any plausible dramatic dating.
Plato notes that Dionysius has been complaining about Plato and his associates complaining about Dionysius, and remarks that he has no power to control his friends; however, he has heard nothing of this matter, and recommends that if Dionysius hears such rumors in the future that he simply write Plato and ask about it. The relation between Plato and Dionysius is very public and will be known to future generations, for people like to converse about such relationships, since "wisdom and great power go together" (310e). Thus they should take care to conduct themselves well, since "men of superior virtue do everything in their power to have themselves well spoken of after they are dead" (311c).
He continues by noting that when he went to Syracuse his reputation among philosophers was very good, and that he went in order to show philosophy in a good light to the masses, but failed utterly. The cause is that Dionysius did not trust him. If he has no interest in philosophy, he should leave well enough alone; if he is interested but thinks he has found better doctrines, he should hold to them; but if he agrees with Plato, he should honor both Plato and his doctrines. If he does this, Plato can honor him; but if Plato honors him without being honored in return, Plato looks like a flatterer out for money.
The letter then turns to philosophical matters, talking in deliberately enigmatic terms of "the first":
Upon the king of all do all things turn; he is the end of all things and the cause of all good. Things of the second order turn upon the second principle, and those of the third order upon the third. Now the soul of man longs to understand what sort of things these principles are, and it looks toward the things that are akin to itself, though none of them is adequate; clearly the king and the other principles mentioned are not of that sort. (312e-313a)
Dionysius had said that he had discovered this himself, although Plato had remarked that he had never met anyone who had; but perhaps Dionysius did indeed start on the right track and just "neglected to fix fast the proofs of it" (313b), so that they constantly seemed to shift, which is certainly a common experience. But by conversing with philosophers as he is doing, he will, if his inquiry is sincere, remedy this problem.
Plato warns him not to let his letters be read by the uninitiated; those not instructed properly will only find themselves strange. Those with whom Plato has discussed them have often found that after many years of inquiry the things that initially seemed hardest to understand are now clear and self-evident, while the things that seemed clearest turned out not to be. Thus one should not expose the teachings without due care:
The best precaution is not to write them down, but to commit them to memory; for it is impossible that things written should not become known to others. This is why I have never written on these subjects. There is no writing of Plato's, nor will there ever be; those that are now called so come from an idealized and youthful Socrates. Farewell and heed my warning; read this letter again and again, then burn it. (314b-c)
(The phrase translated 'idealized and youthful' here, kalos kai neos, could also be translated as 'fine and new' or 'beautiful and renovated'.) The letter then ends with comments about mutual acquaintances.
The enigmatic discussion of the first sounds a lot like late Middle Platonism or early Neoplatonism, so it is possible that this is an attempt to give an account of how the philosophical speculations of Platonists in the author's day is related to Plato's dialogues. The answer, which appears to have affinities to ideas in both Phaedrus and the Seventh Letter, is that there was an esoteric teaching by Plato, passed on orally, with respect to which the dialogues were merely introductory, so that the dialogues give not Plato's views but the views of a Platonized Socrates. On the other hand, since this letter is likely one of the sources of these strands in Middle Platonism and Neoplatonism, whether authentic or inauthentic, the origin of its ideas may be something else entirely.
Fourth Letter
This letter is addressed to Dion. Plato says that his good will toward Dion's work has been driven by "no other reason than admiration for noble deeds" (320a), because those who do virtuous deeds deserve recognition. He urges Dion to continue in "truthfulness, justice, high-mindedness, and the grace of conduct which these virtues express" (320b-c), so that they can show themselves to be the men they claim to be. This is especially important because the whole world already knows of Dion; people will be looking for him to fail. He ends by urging Dion to write, since Plato is receiving nothing but rumor, and reminds Dion that it is necessary to please men if one is to do anything with them.
Tenth Letter
This letter, the shortest of the Platonic epistles, is addressed to an otherwise unknown Aristodorus, encouraging him in his support of Dion. Plato says that he hears that Aristodorus manifests the most philosophical virtues, "for to be steadfast, loyal, and dependable,--this, I say, is true philosophy; whereas all other learning, and all cleverness directed to any other end than this, I call--and I think rightly--mere ornaments" (358c).
Thirteenth Letter
This letter is addressed to Dionysius the Younger, and is mostly taken up with money matters. It has a clear reference to Phaedo under the subtitle/description "On the Soul" (363a).
Plato sends some treatises and Helicon, a mathematician, encouraging Dionysius to learn from him. In addition, he is sending some statues, wine, and honey. All of this has been done on credit, and Plato remarks that while he is stewarding it as best he can, but notes that there are problems with the funds and expenditures -- some of Dionysius's contacts are reluctant to supply money on credit because they had difficulty getting money back from Dionysius's father. He insists that Dionysius must make sure that he keeps informed about expenses, despite the reluctance of his men to talk about them:
You must therefore compel them to form the habit of speaking about these things as well as other matters; for it is your duty to know everything, so far as is possible, and pass judgment and not shrink from any facts. This will be the best of all ways of enhancing your authority. To make expenditures rightly and to repay debts properly is a good thing in many ways, and even furthers the acquisition of money, as you yourself will see more and more. then do not allow those who profess to be looking out for your interests to give you a bad name; for there is no advantage nor honor in being known as difficult in money matters. (362d)
There then follows a number of pieces of advice on various particular matters of concern.
Some nineteenth century scholars defended the authenticity of this letter by pointing to Aristotle's curious mention of "sailing to Aegina is necessary to recover one's money" as an example of a sine qua non condition in the Metaphysics; they suggested that the example might be an allusion to this letter. This is a very slim thread, though, and not such as to convince most scholars.