I've been wanting to say why I think Aristotle's Doctrine of the Mean is interesting and even profound. Being aware that this is a blog, I'll be brief.
I can perhaps best make my points through a contrast. There's a passage in NE 3.1, not about the mean, which helps to explain what Aristotle means by the 'parameters' of action. This is where he gives examples of various ways an act can be contravoluntary through ignorance of a particular. In the Ross translation:
Perhaps it is just as well, therefore, to determine their nature and number. A man may be ignorant, then, of who he is, what he is doing, what or whom he is acting on, and sometimes also what (e.g. what instrument) he is doing it with, and to what end (e.g. he may think his act will conduce to some one's safety), and how he is doing it (e.g. whether gently or violently). Now of all of these no one could be ignorant unless he were mad, and evidently also he could not be ignorant of the agent; for how could he not know himself? But of what he is doing a man might be ignorant, as for instance people say 'it slipped out of their mouths as they were speaking', or 'they did not know it was a secret', as Aeschylus said of the mysteries, or a man might say he 'let it go off when he merely wanted to show its working', as the man did with the catapult. Again, one might think one's son was an enemy, as Merope did, or that a pointed spear had a button on it, or that a stone was pumicestone; or one might give a man a draught to save him, and really kill him; or one might want to touch a man, as people do in sparring, and really wound him. The ignorance may relate, then, to any of these things, i.e. of the circumstances of the action, and the man who was ignorant of any of these is thought to have acted involuntarily, and especially if he was ignorant on the most important points; and these are thought to be the circumstances of the action and its end. Further, the doing of an act that is called involuntary in virtue of ignorance of this sort must be painful and involve repentance.Now, briefly, three points about this.
1. There is another class of ways in which we can go wrong as regards these parameters, which we wouldn't confuse with errors in particular fact, and the reason why we wouldn't confuse them, is that other class somehow is a matter of being off by 'too much' or 'too little'. E.g. The exchange, "There was no button on his sabre.--Did he let his anger get the best of him again?" makes little sense, but "He seemed to get up abruptly just now and slam the door as he left.--Did he let his anger get the best of him again?" does make sense. That is: the doctrine of the mean can be used as a marker of this way of going wrong. Roughly, we can go wrong through failure to control a material process which we should have been able to control.
2. Among errors in that other class, we correctly connect together errors in different parameters, whereas we don't do so with errors in particular fact. We take his getting up abruptly, his slamming the door, his speaking in a loud voice--as all expressions or indications of the same thing. (This is odd: Why should a raised voice and a slammed door have much in common? Cp. why should an agitated dog both jump about more often and bark more frequently?)
3. More than this, when we connect errors in this way, we often take them all to be expressions or indications that go in the same direction, that are off in the same way. We don't regard a raised voice as 'too little modulation of pitch' but rather too high a pitch. We describe slamming the door as too much force, not too little modulation of its closing.
Something is very interesting about all this. It has to do, roughly, with how rational control is 'corrupted' in a certain way, when it in some sense could have been exercised. And this is the sort of thing, I believe, Aristotle aims to get at with his Doctrine of the Mean. It's not a criterion of right and wrong, but a marker of a certain way of our going astray.