The final three sections of the first chapter of A Theory of Justice all concern, in one way or another, the question of how to establish rules of priority between distinct principles of justice. It is in this context that Rawls discusses intuitionism, which is treated exclusively as a sceptical doctrine asserting the impossibility of arriving at any such priority rules and appealing only to an ill-defined notion of "intuition" when confronted with such problems.
There are two points to make about these final sections of the first chapter. The first point is that this is a very odd view of intuitionism, the second concerns the constructive case Rawls gives here for responding to the putative sceptical challenge posed by intuitionism. It is in the seventh section of the first chapter that Rawls discusses intuitionism. However, whilst the view of utilitarianism presented in the previous two sections drew essentially on Henry Sidgwick's account of utilitarianism, it is not the case that there is a parallel source for Rawls' view of intuitionism. In a footnote Rawls refers to a series of sources for his conception of intuitionism as basically a sceptical view of priority rules but none of these are classic intuitionist texts. The latter are also mentioned by Rawls but only as sources for the epistemic view of intuitionism that he basically leaves aside. The view that the right or the good is unanalyzable, questions of self-evidence, the status of prima facie duties as a specific class of duties, all these issues are left aside so Rawls gives instead a "broad sense" of the doctrine that becomes equivalent to pluralism in the sense that it recognises a plurality of first principles (but fails to offer a means of setting them in priority formations).
In presenting intuitionism in this way Rawls certainly does the doctrine a disservice. Interestingly, Sidgwick, by contrast, effectively conflated intuitionism with common sense morality and then argued for the need for a higher principle than common sense morality in the form of the principle of utility. If Rawls had adopted a similar stance towards intuitionism then his treatment of it could have echoed Kant's reply to the common view of morality as presented in the first section of the Groundwork. There are traces of an approach of this sort as when Rawls considers the example of fair wages and relates this to everyday ideas of justice concluding: "To reach some measure of understanding and agreement which goes beyond a mere de facto resolution of competing interests and a reliance on existing conventions and established expectations, it is necessary to move to a more general scheme for determining the balance of precepts, or at least for confining it within narrower limits". Here we have a clear echo of the Sidgwick approach which does bear a close relation to Kant's response in Groundwork I.
However, despite this echo, the main point of Rawls' response to intuitionism is in terms of the sceptical challenge it is alleged to pose. In relation to such a challenge the key point is to present the criteria that enable priority rules to be given. So, in treating intuitionism primarily as a sceptical doctrine Rawls simply sets it up as a foil that enables the constructive case to get going. In doing this Rawls indicates the key point is how to limit the appeal to intuition, just as, in his setting out of the priority of the right over the good, he aimed at undercutting the appeal to given desires as valuable in themselves.
There are three ways that Rawls aims to limit the appeal to intuition. The first point relates to the choice situation that is the "original position". In the "original position" part of the point is to abstract away from principles that may seem intuitively plausible given a certain place in society so here the appeal to intuition is treated as a kind of social prejudice (echoes again here of Sidgwick). Rather than rest on appeals to self-evidence we take a choice situation in which the abstraction involved prevents us from being able to make assumptions grounded in a social "common sense" that may be variable given different roles. So the first way of limiting intuition is through utilisation of the "original position" and this utilisation has precisely the same kind of point as the priority of the right over the good, namely, it eliminates the ability to appeal to something currently existent as a value.
The second way of appealing to intuition is to present a case for treating principles in order, to present a response, that is, to the priority problem of a sort that the sceptic has deemed impossible. If the principles really can be shown to have a lexical ordering then one would only invoke some of them in situations where the others are sufficiently satisfied (again, a structural point comparable to the priority of the right over the good). Clearly this assumes, at this stage, something that the sceptical intuitionist has called into doubt and so does not reply to this doubt but does indicate a way we can expect the priority problem to be tackled by means of showing the grounds for lexical priority of some principles at the cost of others.
Thirdly, dependence on intuition can be reduced by introducing prudential considerations in place of moral ones. This appears an odd way of limiting appeal to intuition. However, what Rawls means by it is less peculiar than his formulation might suggest. This concerns the appeal to the standard of the "representative person" and asking whether it is more rational to prefer one type of arrangement or another. This appeal does not eliminate intuition but it does re-describe its scope since the standard of such a person is adopted in a generic way and this is what leads to the diminution of simple moral points being made.
The final section of the chapter reverts to making some general remarks about moral theory, remarks that re-treat in part the initial paper Rawls wrote on decision procedures in ethics. This involves appealing to the notion that each person develops a sense of justice with relation to intellectual maturity and then describes a conception of justice as something that characterizes our moral sensibility. Given that this is the role of the conception of justice there is a basic claim that common sense morality, by virtue of its lack of systematic character, does not really comprehend the sense of justice that it displays. (So here again we have a parallel to Sidgwick's response to intuitionism and Kant's to common morality.)
After making this negative comment Rawls introduces, for the first time in the book, the notion of "reflective equilibrium". The point of introducing it is related to the previous description of the reason for moral theory: "From the standpoint of moral theory, the best account of a person's sense of justice is not the one which fits his judgments prior to his examining any conception of justice, but rather the one which matches his judgments in reflective equilibrium". What goes on in reflective equilibrium is the consideration of one's basic principles in relation to an account of them that leads to their systematisation.
However, after this first pass at the notion of "reflective equilibrium" has been made Rawls goes on to look at other interpretations of it as an idea. The idea varies depending upon whether one is presented with descriptions (or theories) that vary from one's practice in only minor detail or whether there is instead a much more comprehensive and wide-ranging consideration of theories and descriptions of one's moral sense. The latter is clearly what is generally at work in moral theory. What this shows for Rawls is that the theory that needs to be considered is "a theory of the moral sentiments", a key point that will be returned to in detail in subsequent parts of the book. However such an account has to use "contingent assumptions and general facts", not merely definitions and references to logic (which latter is treated by Rawls as if it were exhaustive of the "a priori"). Again, in adopting this standard Rawls aligns his enquiry with that of Sidgwick.