On the evening of 11/10, we're discussing John Rawls. What is justice? Rawls interpreted this question as asking what basic social rules and structures would result in a society that we'd consider fair. Justice is fairness, on a social level.
Fairness, of course, is an intuitive notion, and begs for a philosophical definition, but instead of doing some sort of old fashioned search for a definition (as in Plato's Republic) which we can then use to deductively ground this general social framework, he wants to translate our intuitions straight into these social rules. Rawls came up the the name "reflective equilibrium" to talk about the considered opinion we reach on something when we carefully evaluate and make consistent our current set of beliefs.
This is an important element of modern philosophical method to understand, way beyond the context of Rawls: it signals an abandonment of any pretense at a foundationalist picture of knowledge, where a la Descartes we we're supposed to start with unassailable foundations and build on them. Instead, acknowledging that there are no such foundations, you start where you are, with the complex network of beliefs that you've inherited from history, and tweak those only insofar as you need to to make them consistent (so it's also called "methodological conservatism"). If you find that one of your theories implies something deeply intuitively unacceptable like that murder is great, you modify that theory. (The Stanford Encylopedia attributes this method, though not the name reflective equilibrium, to Nelson Goodman, incidentally.)
Despite this rejection of foundationalism, Rawls gives us a method for testing our intuitions that involves us coming up with basic principles of justice based on what sounds foundationalist in the manner of social contract theory; Rawls is self-consciously continuing and modernizing the enterprise of Hobbes, Locke, and Rousseau. To figure out the basic principles of justice to use to set up your social institutions, imagine that you're making a deal with the other citizens about what society to have, before you know whether you're going to end up rich or poor in that society, smart or dumb, of any particular race or social class. He calls this imaginary starting point the "original position" and characterizes it as being behind a "veil of ignorance," where we not only don't know those things I mentioned, but we don't know what our particular life goals, religious beliefs, or attitudes toward risk are. We do know some basic things about human psychology, e.g. that people do have rational life goals and that they will be frustrated if these are not achieved. Even though we don't know what every person will consider to be a good, we can know that there are basic goods, such as opportunity and money, that in general allow anyone increased power to achieve his or her goals, even if, e.g. the person ends up being a monk who wants to give away all his money.
Rawls then argues that from this original position, we will all choose (again, if we really think about it) these principles of justice:
1. "Each person is to have an equal right to the most extensive basic liberty compatible with a similar liberty for others."
2. Social and economic inequalities are to be arranged so that "they are to be of the greatest benefit of the least-advantaged members of society, consistent with the just savings principle (the difference principle)" and "offices and positions must be open to everyone under conditions of fair equality of opportunity."
He spends a lot of time explaining and arguing for the particulars of this original position and considering the alternatives principles such as various versions of the utility principle, explaining why they don't capture our intuitions as well has his principles. He argues that he's giving an articulation compatible with and descended from Kant's views of morality: these principles capture what it means at a societal level to treat people as ends and not merely as means.