Socrates-the soul is simple (no parts) and it is rational (directed at knowledge, comprehension of the whole and the parts, wisdom). Virtue is the excellence of the rational part of us = virtue is a kind of knowledge. Vice is a kind of ignorance.
Plato-the soul is a unity composed of three parts (sensitive, spirited, rational). Virtue is the excellence of the whole soul, which is harmony of these parts—our feelings, our motivations, and our thinking—under the direction of the rational part. Virtue = ideal mental health, and the state of ideal mental health is best state to be in = Happiness. The virtuous life is the happy life—the life directed at sensible pleasures as the most important goods is an imbalanced, unhealthy, and unhappy life—the happy life will be pleasant, that part of us needs to be fulfilled as well if we are to function maximally—but we don’t get to happiness simply by pursuing pleasure.
The mistaken view of happiness that Glaucon is talking about rests on a mistaken view of human nature—we naturally pursue the good, but we mistakenly identify pleasure as the highest of the goods that we pursue; our natural drives get out of whack and we head down the wrong path.
Aristotle—accepts Plato’s view of the soul, and accepts a view of happiness that is much like it. That’s why we get the claim that Happiness is the activity of the soul in accordance with virtue—virtue requires that our appetites and our spirited pursuit of them be checked in ways that allow these parts of us to harmonize with what our reason comprehends as the good that comes from pursuing certain things that bring us pleasure—they are not good because they are pleasant; they are pleasant because pleasure is the natural reaction to the good, when it is experienced by someone who is functioning properly, or is healthy, in body and in mind.
The activity of the soul is living and what accords with virtue is good, so the Aristotelian view comes down to the claim that Happiness = The Good Life
We are complicated beings with narratives, developmental stories, successes, failures, lessons learned, etc. that are all a part of who we are—Each state of mind along the way (no matter how pleasant, or how long it lasts) is only one slice of a life story, that exists within the narrative structure of that life—Happiness is not something that characterizes this slice or that slice of the story; it is an ideal standard against which to compare the story as a whole; it is the ideal state of being towards which we strive in all our activities; our representation of it is the guiding thread through all of these various activities; the details of this representation change as we grow and mature, but we are always representing it as what it is that we are aiming at and striving to attain.
How does this relate to modern, subjective conceptions of happiness?
Epicureans-philosophical (rather than common sense) view of pleasure as the good
Stoics– closer continuation of the Platonic, Aristotelian tradition, with the exception of a return to the Socratic view of the soul as simple (no parts), and rational (directed at knowledge, comprehension of the whole and the parts, wisdom). Virtue is the excellence of the rational part of us = virtue is a kind of knowledge.