I shall slightly depart from the order in which Rawls sets things out, to explain his distinction between the "concept" of justice, and "conceptions" of justice. The concept of justice is precisely that: justice. A conception of justice is a particular interpretation of justice, a set of principles which a person believes to define justice.
Rawls begins by setting out what he takes to be the concept of justice. He sees it as being a way of distributing the gains which arise from co-operation between different individuals within a society.
In Rawls' view, a society must not only be just - that is, governed by a conception of justice - but it must be "well-ordered": the members of the society should agree upon this conception of justice, and should for the most part follow it. Furthermore, this agreement should be a matter of common knowledge: everyone not only agrees to this conception, but is aware that everyone else does. The point of being well-ordered is that conflicts between members will inevitably occur over precisely how the benefits of cooperation ought to be in a particular instance. By having a commonly agreed and enforced conception of justice, there is a rulebook which can be consulted in order to resolve such conflicts.
While being well-ordered is a goal of the first importance for a society, it ought to achieve other things besides this. Rawls singles out the issues of coordination, efficiency, and stability. People ought to be able to achieve their plans without coming into conflict; the people in the society ought achieve their individual goals as far as is possible; and when society is successful regarding these goals, it ought to maintain the institutions which allow for this success.
"Justice is the first virtue of social institutions, as truth is of systems of thought." pp.3
"Each person possesses an inviolability founded on justice that even the welfare of society as a whole cannot override." pp.3
"The rights secured by justice are not subject to political bargaining or to the calculus of social interests." pp.4
"Let as assume... that a society is a more or less self-sufficient association of persons who in their relations to one another recognise certain rules of conduct as binding and who for the most part act in accordance with them." pp.4
"Although a society is a cooperative venture for mutual advantage, it is typically marked by a conflict as well as by an identity of interests. There is an identity of interests since social cooperation makes possible a better life for all than any would have if each were to live solely by his own efforts. There is a conflict of interests since persons are not indifferent as to how the greater benefits produced by their collaboration are distributed, for in order to pursue their ends they each prefer a larger to a lesser share," pp.4
"Those who hold different conceptions of justice can, then, still agree that institutions are just when no arbitrary distinctions are made between persons in the assigning of basic rights and duties and when the rules determine a proper balance between competing claims to the advantages of social life." pp.5
"The plans of individuals need to be fitted together so that their activities are compatible with each other and they can all be carried through without anyone's legitimate expectations being severely disappointed." pp.5
Rawls' account of the nature of justice is rich, and he describes it in great detail to the point of tortuousness. Questions worthy of consideration include:
-Are there any moral claims prior to entering into society? If there are, what happens to them when one joins a society?
-How relevant are the different features of society that he mentions?
- Self sufficiency seems more like a way of defining the scope of society than as being of moral relevance. But if this is so, can he resist the claim that we live in a global, rather than local or national, society?
-See Heath, J. "The Benefits of Co-operation." Should different benefits be governed by different principles of justice?
-Hayekian thoughts about spontaneous order. How important is coordination as a concern of political relevance?
-"Legitimate expectations". Is there a way to define "legitimate" expectations without presupposing moral answers that Rawls is trying to provide?
-We might expect the society to revise its conception of justice over time. Even if the conception of justice does not change, the institutions required in order to achieve justice almost certainly will. How does this mesh with stability?
-Is the requirement to know, let alone accept, a particular conception of justice rather demanding upon the average person? I believe Rawls is following Bernard Williams' criticism of "Government House utilitarianism", in which a small elite know the rules by which society is run but most people are given a different justification. Perhaps Williams' argument has some force, but there is also something to be said for being able to get on with your life without having to wonder whether you are complicit in injustice. We outsource questions like "what should the interest rate be" to experts, so why not moral questions?
-Usual questions regarding contractualist morality: is there any morality prior to the contract, and does the duty to obey the contract presuppose pre-contractual duties to follow agreements?
-Surely it is massively unrealistic to expect agreement upon one conception? (Of course, Rawls realised this; hence Political Liberalism).