Chapter 2: Wide reflective equilibrium and theory acceptance in ethics
He deals with theory acceptance/justification in ethics. The basis for a justification is coherence (equilibrium) in an ordered triple: moral judgments, principles supporting them and underlying background theories. - moral theory = moral judgments + principles that account for/generate them [p.21]
- Theory acceptance/justification in ethics is intractable unless we grant privileged status to moral judgments (intuitions) or to „self-evident“ principles or unless we also take into account a set of relevant background theories [21/22]
- The method to reach an equil.: start with considered moral judgments; propose various sets of moral principles (don't take the one that fits best – that would be „narrow equil.“) and argue for them based on relevant backgr. theories, back and forth, adjusting one or the other.  (The principles must not be mere generalizations of the judgments.) All 3 parts are considered and reconsidered, tested for plausibility and revised to reach coherence. We want to exclude a bias (self-interest, cultural influence etc.).
- Independence constraint: The backgr. theories should show that a particular set of principles is more acceptable on another ground than its coherence with the moral judgments (we need independent support) otherwise there is no improvement over the narrow equil. => it shall be required the theories have a scope reaching beyond the range of the considered moral judgments  The moral judgments constraining the theories and the principles should be partly different.
- Example: Rawls' theory of justice: backgr. theories (t. of person, social theory, t. of procedural justice, t. of morality) lead to accept the contract and its constraints as basis for selecting among theories of justice; the principles being chosen here must match our considered moral judgments (and yield feasible, stable, well-ordered society). 
- wide equil. (taking into account backgr. theories) may reveal deeper sources of disagreement and help to understand why st. is considered relevant and important 
- Rawls: utilitarians apply a principle acceptable for distributing goods between life-stages of 1 person to a distribution among distinct individuals [mentioned on page 25]
2. The Revisability of Considered Moral Judgments
One objection to W.R.E. argues it's actually a form of moral intuitionism. But there is no basic set of „self-evident“ judgments or st. similar and intuitions have no priority.
Subobjection 1: WRE „merely systematizes some relatively determinate set of moral judgments“  – not, for it permits extensive revision of these judgments based on backgr. theories (in opposition to narrow equil.) Actually, even the theories and the principles are revised.
Subobjection 2: „Considered moral judgments are not a proper foundation for an ethical theory“  for they're but (subjective and biased) beliefs. They have no credibility in opposition to (nonmoral) observations, only credence. 1) Daniels: the analogy between intuitions and observations (of facts) is inappropriate . 2) Only a theory emerging from WRE may help us distinguish moral facts (if there are any) and thus determine judgment's credibility from merely believed intuitions. (The story why observations are credible is also a product of (nonmoral) WRE, relatively recent one.)
There are both variations and disagreement as well as uniformity and agreement on c. m. judgments among persons and cultures . (Moral philosophy should help us to explain both.) => it's shortsighted to deny credibility to intuitions because of the disagreements. (Source of agreement – a widespread accepted backgr. theory.)
4. Objectivity and convergence
Two central senses of „objectivity“ (other senses – free from bias, reliability, replicability - reduce to them): 1) significant degree of intersubjective agreement, 2) a claim is obj. if it expresses truths relevant to the area of inquiry [includes correspondence with reality?].
1 worry: lack of agreement => there're no moral truths (assumes if there were some it'd produce more agreement). But WRE may increase agreement. Note the same argument could conclude there are no scientific truths, at least at some time in history.
2nd worry: WRE could lead to acceptance of moral falsehood, perhaps constituting it as a moral truth, and elimination of any realist notion of objective m. truth. „... though convergence in wide equilibrium is neither a necessary nor a sufficient condition for claiming we have found objective moral truths, such convergence may constitute evidence we have found some“. It depends why we arrived to the convergence (for it's a truth? because an aspect of human psychology? for shared bias? ...).
„wide reflective equilibrium embodies coherence constraints on theory acceptance or justification, not on truth“
If we've reached an equilibrium and there is no way to destabilize it  (no better arguments etc.) it's unnecessary to worry whether we've reached a m. truth.
Do the methods of inquiry in ethics tend to produce convergence because they bring us close to m. truths? Only indirect argument 4 it though highly qualified. A method is successful in an area = it produces convergence and growth of knowledge; the only plausible account of its success is it leads to better approximation of truths relevant to the area => we should adopt a realist account of the relevant objects of inquiry. The argument requires the realist account has some independent plausibility of its own.
He points to some similarity of WRE and methods of science (equ. of observances, laws and theories).
Chapter 6: An argument about the relativity of justice
1. Is justice local? = are principles of justice local to a society? - he wants to oppose Walzer's relativism and communitarian view in Spheres of Justice.
Walzer's theory – 2 central claims: (a) The Sphere Thesis: soc. needs divide into spheres governed by distinct distributive principles that determine allowable inequalities in each sphere; (b) The Non-Domination Thesis: inequ. in 1 sphere shouldn't dominate other spheres.
Walzer doesn't say what makes for distinct spheres (diff. soc. meaning or diff. distrib. principle).
Walzer's methodological stance: (c) The Cultural Relativity Thesis: empirical claim that diff. cultures give diff. soc. meaning to diff. good; (d) The Moral Anthropology Thesis: these meanings can be discovered by st. like moral anthr., not traditional ethical theory; (e) The Incommensurability Thesis: there's no acceptable method for ranking the goodness of cultural products (goods+meanings); (f) the Justification Thesis: we cannot justify assigning a distrib. principle to a sphere if it doesn't fit the soc. meanings ascribed to its goods by people. => W. claims justice is relative to soc. meanings.
„The 'theory' is at best a scheme ... for theories of complex equality“ => W. can't say what makes for distinct spheres. „The content of his scheme can only be provided by finding the principles already embedded in a particular culture, and so moral theory becomes moral anthropology.“
R. Dworkin noted it's difficult to find unified „soc. meaning“ for important soc. goods in many cultures . Authenticity of a shared soc. meaning: it may seem like true consent but be not (thanks to history of class struggle, domination of the ruling class etc.). Walzer claims we are all equal in the sense that we are all culture-producing creatures <=> false authenticity of meanings; => inauth. cult. doesn't deserve the respect required. Is this claim itself relative to soc. meanings? Yes-> doesn't hold in some cultures; no -> where does this universal principle come from? 
People comply with institutions for different reasons (indifference, self-interest), consent isn't necessarily the most important motivation (*) => examining them doesn't discover a commonly shared meaning.  If (*) is true it implies we are able to detach ourselves from our actual commitments and the alleged shared meanings in our everyday reasoning => Walzer's relativist conclusions may rest on assumptions different from our true moral experience.
3. Locality and strong internalism
On Rawls' view we can have no social ranking of conceptions of the good that doesn't do violence to the very ideal of a person we all share and which wouldn't lead to unacceptable results. (What is good for me depends on my rational plan of life.)  Walzer treats soc. meanings as if they were indiv. conceptions of the good.
Accord. to Rawls, reasonable people would accept his way of selecting principles of justice, though it abstracts from their actual preferences, because it's procedurally fair to them and it preserves the „ideal“ of free and equal persons which they share.  Accord. to W., no such conception will adequately respect the soc. meanings shared by actual persons in actual societies.
One's conception of the good (<=> his plan of life) is revisable by himself, i.e. it's a subject of rational assessment => though there is no objective, individual independent, way of ranking conceptions of the good, one does compare and rank them for himself. Accord. to W., shared soc. meanings are not a subject of rational assessment, we cannot detach from them. But since they're an important part of one's plan of life they must be revisable too => challenge to the Justification Thesis (<- an argument is persuasive only if it reflects values/shared meanings/ one does already accept (~ strong individualism) => hypothetical contract is not such an argument for it abstracts from one's actual values). 
„In considering reasons for doing things, we consistently detach ourselves from significant parts of our actual preferences in order to adopt an impartial, rational stance.“ => Walzer's strong form of internalism is untrue to our moral experience.