When Thrasyllus put together his ancient collected works of Plato, he discovered a number of works circulating under Plato's name that he thought were very likely not Plato's, and one of these was a work called the Horoi, or definitions, which is exactly what you would think: it is a list of definitions. The content is obviously connected with Plato's Academy, but Thrasyllus was probably right in taking the work to be spurious. Some ancient authors thought that the list was drawn up by Speusippus, who was Plato's nephew and the head of the Academy after him. This is probably also not right. We have no particular reason to attribute it to anyone we know, or even to regard it in its origins as the work of any single author. But it does give us some indication of Platonic thought and practice in the Academy that Plato left behind. Because the work consists just of a list of definitions without much context, it's usually regarded as a bugbear to translate -- it isn't always clear what is meant, and lists are more easily corrupted in transmission than more complex works which have many things that can help suggest that a word-choice is wrong, so who knows how it has changed and shifted over the many centuries since the Hellenistic period. But it is interesting to consider some of the definitions. I'll be using Dough Hutchinson's translation from the Complete Works, except for stripping out the Greek letters, which are not important to bother with here.
arete, virtue: the best disposition; the state of a mortal creature which is in itself praiseworthy; the state on account of which its possessor is said to be good; the just observance of the laws; the disposition on account of which he who is so disposed is said to be perfectly excellent; the state which produces faithfulness to law.
There is very little surprising about this definition of 'excellence' or 'virtue', but we see here the political character of the Greek understanding of virtue in its clear connection to law.
phronesis, practical wisdom: the ability which by itself is productive of human happiness; the knowledge of what is good and bad; the knowledge that produces happiness; the disposition by which we judge what is to be done and what is not to be done.
We can see that the first three clauses in this definition of prudence or practical wisdom are related: prudence is that which through itself produces human happiness, and it is knowledge of good and bad, so it is knowledge that produces happiness. How does it produce human happiness, though? Through judgment of what is to be done and what is not to be done. The link between prudence and happiness (understood not as pleasure, but as a totality or completeness of good in a life) is essential for understanding its significance in any Platonic (e.g., the deuterocanonical book Wisdom) or Aristotelian (e.g., Aristotle's Nicomachean Ethics) context.
dikaiosune, justice: the unanimity of the soul with itself, and the good discipline of the parts of the soul with respect to each other and concerning each other; the state that distributes to each person according to what is deserved; the state on account of which its possessor chooses what appears to him to be just; the state underlying a law-abiding way of life; social equality; the state of obedience to the laws.
At first glance, these clauses seem to be a jumble of external and internal things, about the state of the soul and the state of the city. But, of course, in Plato's Republic we'll see how the two would probably have been taken to be interrelated. The definition of justice as 'the state that distributes to each person according to what is deserved', or, as it is often put, the disposition of rendering to everyone what is due to them, is the dominate definition of justice in the history of philosophy. In any Platonic system, however, this rendering to others what's due to them presupposes, if it is to be consistent, a state of your own character in which all the parts of your life are rendered what is due to them -- a harmony of the soul with itself arising from the discipline of parts of your soul (which is just whatever it is that makes you a living thing) in relation to each other.
sophrosune, self-control: moderation of the soul concerning the desires and pleasures that normally occur in it; harmony and good discipline in the soul in respect of normal pleasures and pains; concord of the soul in respect of ruling and being ruled; normal personal independence; good discipline in the soul; rational agreement within the soul about what is admirable and contemptible; the state by which tis possessor chooses and is cautious about what he should.
Sophrosyne, or temperance, is a big theme throughout Plato; a significant part of the Gorgias, for instance, is concerned with arguing that it is necessary for justice. It is thus perhaps not surprising that there seem to be connections between the definitions of justice and temperance in this work.
andreia, courage: the state of the soul which is unmoved by fear; military confidence; knowledge of the facts of warfare; self-restraint in the soul about what is fearful and terrible; boldness in obedience to wisdom; being intrepid in the face of death; the state which stands on guard over correct thinking in dangerous situations; force which counterbalances danger; force of fortitude in respect of virtue; calm in the soul about what correct thinking takes to be frightening or encouraging things; the preservation of fearless beliefs about the terrors and experience of warfare; the state which cleaves to the law.
Here we get a rather more complicated tangle; it's unclear how all of these fit together. But courage, and particularly its relation to knowledge play a significant role in the Laches and the Protagoras.
These four, phronesis, dikaiosyne, sophrosyne, and andreia, are, of course, what later generations would call the cardinal virtues. Since this is one of the most influential and lasting elements of the Platonic legacy, it seems appropriate to select them out here as a sort of reminder to ourselves to be on the look-out for the roles they play in the dialogues.
Two other definitions of special note:
philosophia, philosophy: desire for the knowledge of what always exists; the state which contemplates the truth, what makes it true; cultivation of the soul, based on correct reason.
Wisdom itself is defined in the Horoi as knowledge of what always exists (which corresponds to the first clause here) and knowledge that contemplates the cause of beings (which seems to correspond to the second clause here).
sophistes, sophist: paid hunter of rich and distinguished young men.
This comes from Plato's Sophist (223b). The Visitor in the Sophist divides the hunting of men into two kinds: hunting by force and hunting by persuasion; the latter is divided into lovers and money-earners. Of money-earning hunters of men, some only manage to be hangers-on, like people who set honeyed traps and just collect what they can get from them, and these are flatterers. Sophists differ from these only in that they are better at what they do: instead of waiting for men to fall into their traps, they actively seek them out and bag them. This is not the complete account of the Sophist in the the dialogue, since the dialogue also goes on to discuss other aspects of the sophist's trade; so it's interesting that this alone is selected out.
Quotations from Plato, Complete Works, Cooper and Hutchinson, eds., Hackett (1997) pp. 1677-1686.