In The Sources of Normativity Korsgaard provides a dialectical examination of different conceptions of the sources of normativity or reasons -- conceptions that appeal to voluntarism, realism, and reflective endorsement -- that culminates in her own Kantian or neo-Kantian conception of normativity that is grounded in autonomy.  Her method is dialectical (or really Dialectical) inasmuch as her neo-Kantian conception is supposed to reveal the truth or grain of truth in each of the three prior conceptions.

Korsgaard begins Lecture 1 with a statement of the main problems that arise in connection with the normativity of ethics: the explanatory problem is how moral considerations can influence us, and the normative or justificatory problem is why we should care about conforming to moral demands (12-13).  The rest of Lecture 1 probes voluntarist and realist conceptions of the sources of normativity.

VOLUNTARISM
According to the voluntarist, obligation derives from command or perhaps agreement.  You must do X because God commands it or because a political sovereign whom you have agreed to obey commands it.  On this view, normativity is grounded in authority.  Authorities can have reasons for what they command (their commands need not be arbitrary), but it is the fact of their command that creates the obligation.

Pace Korsgaard, if the command can only obligate if its content tracks independent reasons (= is not arbitrary), then the obligation depends on normative reasons that are prior to an independent of the command.  In any case, as Korsgaard does argue, the obligation does depend upon commandment-independent principle about the existence of reasons to obey commands -- a principle recognizing filial duties or the duty to keep one's covenants.

REALISM
The realist says that these normative principles or considerations that underlie the obligations created or imposed by commands are prior to and independent of the commands.  They do not derive from command.  More generally, the realist posits ultimate or unconditioned normative truths.  We can ask of any consideration X why we should care about it.  Often we can answer by relating consideration X to another type of consideration Y.  But if either X or Y is to have normative significance, its derived or extrinsic normative significance must ultimately be grounded in something intrinsically normatively significant, whose normative significance does not depend on anything else.  If a consideration is of ultimate normative significance, we cannot justify its significance in terms of anything else, for then its significance would not be ultimate.  Hence, our normative knowledge must rest on self-evident normative truths.

Korsgaard describes this sort of normative realism as substantive normative realism and contrasts it with procedural normative realism (35).  She accepts procedural realism but has problems with substantive realism.

Korsgaard raises two problems for substantive normative realism.  (1) Are there any ultimate normative truths that are self-evident?  (2) Even if there are, why suppose that they support the normative discriminations most of us make?  If an assertion of ultimate normative truths is not to be a mere expression of confidence in our own normative judgments, we must be able to explain the normative authority of factors that we take to be normatively significant.  But, claims Korsgaard, the realist cannot do that since that would show that the factors in question did not enjoy ultimate normative significance.

We might wonder whether the realist is barred from a discursive justification of her ultimate normative factors.  We should distinguish between metaphysical and epistemic dependence.  Derived normative truths are asymmetrically metaphysically dependent on ultimate normative factors.  But the epistemic dependence among normative judgments need not be asymmetrical; epistemic dependence can be bi-directional.  The epistemology of ultimate normative truths need not be one of self-evidence.  A first principle identifies an ultimate normative factor.  Consequently, it makes no sense to ask of a first principle that we take to be true "In virtue of what further property is F an ultimate normative factor?"  For F to be an ultimate normative factor is precisely for its normative not to depend upon some further property.  But we can still sensibly ask whether F is an ultimate normative factor.  "Is F really a first principle?"  But we can answer these questions by showing how treating F as an ultimate normative factor would sustain and explain our independent beliefs about what we have reason to do.

REFLECTIVE ENDORSEMENT
Korsgaard thinks we can avoid the problems of substantive realism if we ask not whether our actions, projects, and commitments track objective normative facts but rather whether they can be reflectively sustained (Lecture 2).  To appeal to reflective endorsement, she thinks, is to appeal to human nature (19).  It also appears to be a form of procedural realism inasmuch as it implies that moral considerations have rational authority just in case moral commitments would survive a process of reflective endorsement.  Korsgaard's main examples of figures in the tradition of reflective endorsement are Hume, Williams, and Mill.  This tradition appears to put reflective endorsement within a broadly sentimentalist framework inasmuch reflective endorsement appears to be a matter of what commitments and ways of living we are prepared, upon clear-eyed reflection, to endorse or live with.  Korsgaard's discussion of Hume is instructive (51-66).

Hume thinks that moral judgments are based on sentiments of approval and disapproval that we feel when we contemplate someone's character from a general or common point of view that aims at public accord rather than private interest (Treatise 581-82; Enquiry sect. ix, pt. 1).  While we can explain the basis of moral judgments in this way, Hume seems to think that we can still ask how they obligate, by which he seems to mean what their authority consists in.  In the Enquiry he writes

Having explained the moral approbation attending merit or virtue, there remains nothing but briefly to consider our interested obligation to it, and to inquire whether every man, who has any regard to his own happiness and welfare, will not find his account in the practice of every moral virtue [ix 2].

Treating vice with the greatest candour, and making it all possible concessions, we must acknowledge, that there is not, in any instance, the smallest pretext for giving it the preference above virtue, with a view to self-interest; except, perhaps, in the case of justice, where a man, taking things in a certain light, may often seem to be a loser by his integrity.  And though it is allowed, that, without a regard to property, no society could subsist; yet, according to the imperfect way in which human affairs are conducted, a sensible knave, in particular incidents, may think, that an act of iniquity or infidelity will make a considerable addition to his fortune, without causing any considerable breach in the social union and confederacy.  That honesty is the best policy, may be a good general rule; but is liable to many exceptions: And he, it may, perhaps, be thought, conducts himself with most wisdom, who observes the general rule, and takes advantage of all the exceptions [ix 2].

I must confess, that, if a man think, that this reasoning much requires an answer, it will be a little difficult to find any, which will to him appear satisfactory and convincing.  If his heart rebel not against such pernicious maxims, if he feel no reluctance to the thoughts of villany or baseness, he has indeed lost a considerable motive to virtue ....  But in all ingenuous natures, the antipathy to treachery and roguery is too strong to be counterbalanced by any views of profit or pecuniary advantage.  Inward peace of mind, consciousness of integrity, a satisfactory review of our own conduct; these are circumstances very requisite to happiness, and will be cherished and cultivated by every honest man, who feels the importance of them.
     Such a one has, besides, the frequent satisfaction of seeing knaves, with all their pretended cunning and abilities, betrayed by their own maxims; and while they purpose to cheat with moderation and secrecy, a tempting incident occurs, nature is frail, and they give into the snare; whence they can never extricate themselves, without a total loss of reputation, and the forfeiture of all future trust and confidence with mankind [ix 2].

The first response appears to be that honest people will not on reflection approve duplicity.  But that's very close to saying that honesty approves of honesty or that honesty approves of itself.  At points, Korsgaard suggests that this sort of reflexivity test is integral to reflective endorsement.  Later, in discussing Hume's standard of taste, she writes

The faculty of taste gives rise to verdicts of beauty.  According to this theory a faculty's verdicts are normative if the faculty meets the following test: when the faculty takes itself and its own operations for its object, it gives a positive verdict [62].

Hume's last response in this passage does address the Knave's appeal to self-interest.  It appears to argue that it is hard to practice injustice in all and only those occasions when it will go undetected.  The Knave who practices injustice selectively and engages in deception to exploit others with impunity is likely eventually to miscalculate and get caught out.  The penalty for this will be exclusion from the benefits of society (i.e. the forbearance and cooperation of others).  But this seems not to be an argument against Knavery, but against incompetent knavery.  The Competent Knave will disapprove incompetent knavery, but why should she approve justice or honesty per se?  Why not approve instead selective injustice and dishonesty?

At one point, Korsgaard suggests that Hume is claiming not that just acts are always more beneficial than unjust acts but rather that it is always more beneficial to be the sort of person who practices justice for its own sake than to be the sort of person who practices justice iff it is the most beneficial option available (60).  Korsgaard offers fairly little by way of textual support for this interpretive proposal, though one might note that Hume introduces the challenge of the Sensible Knave in the context of a discussion of what sort of "disposition ... he would choose for the foundation of his happiness and enjoyment" (ix 2).  The suggestion has actually been explored more fully by David Gauthier (Morals by Agreement and "Three Against Justice: the Foole, the Sensible Knave, and the Lydian Shepherd").  This view deserves fuller discussion, but it faces a problem.  It may be hard to be the second sort of person -- to be a genuinely Competent Knave.  If so, our actual choice may be between being a Just Person and an Incompetent Knave.  We may well be better-off choosing justice over incompetent knavery.  But that provides no reason for thinking that we shouldn't prefer competent knavery to justice.  Justice remains, as Glaucon and Adeimantus worry, a second-best option behind undetected injustice.  If so, it's hard to see how the Sensible Knave can give her whole-hearted approval of justice or other artifical virtues.

It was a little hard for me to find a general assessment of reflective endorsement in Korsgaard amidst the details of the Humean, Williamesque, and Millian exemplars of that tradition.  Here's one reaction that would fit with some of Korsgaard's dialectical picture.  The proponent of reflective endorsement imagines an agent reflecting on the authority of an action or disposition to act and asking herself whether she can endorse that disposition or action.  Either she appeals to the very same disposition, as in the reflexivity conception of reflective endorsment, or she appeals to a distinct disposition, as the Knave appeals to self-interest in assessing a commitment to justice.  If it's the same disposition, it provides an impermissibly circular justification.  But if it's a different disposition, we still don't have a justifaction of the original disposition unless this second disposition is suitably grounded.  But now we've just pushed the question of authority or justification back to another level.  An appeal to self-love or any other disposition will not ground the authority of other dispositions or commitments unless its authority can be grounded.  One might regard substantive realism as an antidote to this threat of regress.  But Korsgaard thinks that reflective endorsement can be developed in a Kantian direction.

AUTONOMY, IDENTITY, AND HUMANITY
Korsgaard sees Kant as addressing this kind of worry about reflective endorsement by reminding us that the test of reflective endorsement is a test to see if there is a reason to act (89).

If the problem springs from reflection then the solution must do so as well.  If the problem is that our perceptions and desires might not withstand reflective scrutiny, then the solution is that they might.  We need reasons because our impulses must be able to withstand reflective scrutiny.  We have reasons if they do.  The normative word 'reason' refers to a kind of reflective success [93].

Central to Korsgaard's conception of practical reason is her idea of a practical identity (101).  This seems to involve the idea that reflective endorsement will both be guided by and yield (perhaps inchoate) conceptions or descriptions of oneself under which one values oneself.  Often this will take the form of embracing certain roles -- teacher, father, husband, friend, teammate -- as valuable.  Things like rules and commitments can then be assessed for normative significance in terms of their contribution to one's practical identities.

There are at least two worries about this neo-Kantian appeal to practical identities as so far described.

• One worry is that we seem not to have been given any basis for distinguishing between good and bad practical identities.  My identity as philosophy professor, nurturing parent, or decent recreational hockey player may well provide me with reasons to care about and do things.  But does the practical identity of the committed (non-self-loathing) serial killer also give her reasons for action?  Rationalists should want to say that they do not or that, if they do, they are very weak reasons that are easily swamped by her reasons not to so act.
• Another worry is that we have many conflicting identities.  How do we resolve such conflicts?  For instance, how can we show that my practical identity to be a good member of my moral community trumps my practical identity to be a successful scientist when I could advance my career by claiming credit for my lab assistant's discoveries?

Some commitments or identities are valuable only contingently.  They are not intrinsically valuable or valuable independently of being the object of choice.  Value is conferred on them by rational endorsement.  What is not contingently valuable is one's identity as an agent, since adopting this identity is a condition of undertaking reflective endorsement.  Autonomous agency is what confers value on these contingently valuable identities.  Like Kant, Korsgaard understands agency as humanity. (This is potentially misleading, since agency or personhood and humanity are, as we have seen, different categories.  It's better to eschew focus on humanity and keep the focus on agency or moral personality.)  However, to value humanity or agency as such is to care about rational agents as ends in themselves.  This reasoning appears to suggest that Kant's Humanity Formula of the Categorical Imperative has necessary normative authority and conditions the authority of one's other practical identities.  This conclusion would apparently imply not just that moral demands have supreme authority but that contra-moral demands and identities have no authority whatsoever (113-22, 129-30).

One question about Korsgaard's favored conception of normativity, which grounds other-regarding duties in considerations of agency or autonomy, is how it differs from substantive realism.  Why isn't her view representable as a form of realism in which autonomy figures as the ultimate value?  Perhaps she will claim that autonomy is a procedural, rather than substantive, value.  But in this context I don't know what that distinction would amount to.

FROM HUMANITY TO MORALITY
As Korsgard herself recognizes, there is a concern about this defense of the authority of other-regarding morality (121, 130, 132-45).  It is perhaps clear how autonomy or agency is a value that is presupposed by rational endorsement and so is rationally compulsory.  We might even concede that autonomy, so conceived, conditions the value of other projects and identities.  What is unclear is why it is agency or autonomy as such, as opposed to his own agency or autonomy, that has this transcendental value.  Perhaps every agent must be concerned with his own rational agency.  Why should must he be concerned with other rational agents as such?

Korsgaard wants to argue that one cannot value one's own humanity (agency) without valuing the humanity (agency) of others (132-45).  She treats the challenge as one which grants the existence of private reasons but denies that you can get from private reasons to public reasons (134).  Her response is to deny that there are private reasons and to insist that all reasons are essentially public (134-36).  She defends the essentially public character of reasons by analogy with Wittgenstein's private language argument (136-38).  As I understand Wittgenstein, or at least Korsgaard's Wittgenstein, the central idea is something like this.

1. Meaning is a normative notion.
2. Hence, linguistic meaning presupposes correctness conditions.
3. The correctness conditions must be independent of a particular speaker's utterances.
4. Hence, correctness conditions must be established by the usage conventions of a community of speakers.
5. Hence, a private language is not possible.

Korsgaard elaborates on the lessons of the private language argument for practical reason by returning to voluntarist themes.  Practical laws requires two parties a legislator and a legislatee.

Since it is a relation, and indeed a relation in which one gives a law to another, it takes two to make a reason [138].

Korsgaard's failure here parallels Kant's own.  Rational agency is a potentially ambiguous commitment.  Kant explains well why each must regard his rational self as superior to his empirical self but he provides no good explanation of why one rational self should be intrinsically and unconditionally concerned with other rational selves.  If we are to address this gap in the authority of other-regarding concern, we must either find a more cogent defense of impartial practical reason or look to traditions outside Kantian ethics, such as the Greek eudaimonist tradition or the ethics of self-realization found later British idealism, that attempt to show why someone concerned with his own rational agency should be non-instrumentally interested in the rational agency of others.