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The author of this article writes: "The Law of Peoples examines the state of nature between 'peoples'". This is very misleading. Rawls imagines a hypothetical situation that he calls the Original Position, in which representatives of the various 'peoples' come together to affirm the terms of their association. It is different from the state of nature as found in Hobbes, Locke etc. Furthermore, the original position is not "examined": rather, it is constructed in such a way that it represents a situation of equality which (along with various built-in constraints) will yield principles that 'reasonable peoples' can affirm as governing the terms of their association. Perhaps it is true to say that Rawls examines the constraints that he builds into the original position. But the original position itself is an argumentive device; it is a distinctive feature of Rawls' Constructivist methodology.
The author goes on: "Groups of people forming states should be encouraged to follow the principles from Rawls's earlier A Theory of Justice". This is incredibly confused. First of all, as far as I know, Rawls' argument does not concern 'groups of people forming states': it concerns already-formed 'peoples' (Rawls specifically avoids the term 'states') and the terms of their association with other already-formed 'peoples'. Secondly, these 'peoples' are placed in a position (the original position) in which it is supposed that they decide for themselves the terms of their association: no-one encourages them to do anything. Thirdly, it is against the whole spirit of Rawls' enterprise that peoples or persons should be 'encouraged' to adopt his two principles from the earlier 'A Theory of Justice'. These two principles comprise what the later Rawls would call a 'comprehensive doctrine'. His later works (see esp. 'Political Liberalism') admit that there are many comprehensive doctrines around today (he calls this the 'fact of reasonable pluralism') and that nobody can be expected to give their doctrine up in favour of another. In the later Rawls, peoples and persons are not 'encouraged' to buy into comprehensive doctrines they do not already affirm; indeed, Rawls believes (rightly, I think) that any such endeavour is bound to be fruitless. Instead, the later Rawls seeks a 'political conception of justice' (as opposed to a comprehensive one like his earlier two principles): this is a conception of justice that we can reasonably expect persons with different comprehensive views to buy into, despite their fundamental differences. 'The Law of Peoples' is an extension of this idea from domestic politics to the international arena.
If anyone's wondering why I didn't just write the article, I haven't actually read the 1999 version of Law of Peoples: just the (much shorter) 1993 version. I think I'll have to read it before I go for the article. Any comments would be most welcome.