Habermas's moral theory is meant to address a particular historical situation in which morality may appear to be on shaky ground. Broadly speaking, the situation in question is a modern, liberal society in which the older, metaphysical understanding (that could, for instance, assume that natural rights were moral absolutes) has collapsed and given way to a more historical and sociologically sophisticated understanding that all our categories, including the moral ones, are social constructs. To the post-metaphysical self-understanding that is not uncommon in modern, pluralistic societies there are no absolutes, and it can then appear that the prevailing morality is groundless.
The task Habermas sets himself is to reassure the post-metaphysical pluralist that there is a foundation for morality in the pragmatic presuppositions of discourse itself. Morality doesn't need a metaphysical ground because one is provided by the nature of language itself.
The morality in question is characterised by the concern to accord everyone equal respect - and this is treated as an uncontentious principle that virtually everyone in a post-traditional society accepts. It is fair to call this morality Kantian, and it is fair to say that Habermas has been trying to bring Kant's moral philosophy up to date in a way that ditches Kant's solipsism.
Habermas first reinterprets Kantian morality so that it ceases to assume that moral agents can judge for themselves with an autonomy that implies a historical vacuum. The new Kantian moralists recognise that their deliberations can only get going because of a background of inherited values that are part and parcel of their particular culture, and they accept that partly because of their own fallibility the truth about moral rightness is something that can only be established through dialogue. Instead of the Kantian moral subject trying to work out in a solipsistic way which policies would meet with universal agreement, the concern for universality is played out through a dialogue which is open to everyone. The dialogue upholds the Kantian concern for universal respect as long as no voice is excluded and the norms that come out of it are those that everyone can agree to.
In Habermas's words: Kant's principle of universal respect - known as the categorical imperative - "receives a discourse-theoretical interpretation in which its place is taken by the discourse principle (D), according to which only those norms can claim validity that could meet with the agreement of all those concerned in their capacity as participants in a practical discourse."
In addition to this reinterpretation, Habermas wants to come up with a better justification as to why we ought to uphold the principle of universality that is at the core of our morality in a pluralistic society.
The justification begins from the idea that anyone who says anything about what is moral or immoral participates in a form of (discursive) action that has a particular set of pragmatic presuppositions. It is worth clarifying that this is a not a discussion in which people express what they want and try to come to a compromise - it is a discussion in which people try to establish what norms it is right for society to follow. To put the crux of Habermas's argument as simply as possible: Anyone who claims to say something true about morality implicitly raises an issue that can be criticised and in order for this claim to win out it must meet with the rational assent of those who join the discussion. Whether the speaker realizes it or not, if truth is the issue here, the speaker is obliged to appeal equally to the rational assent of everyone else. In this way the discourse ethic is uncovered by identifying what debates about moral norms presuppose, and Habermas's claim is that something very similar to Kant's categorical imperative is presupposed by the discursive act of saying what is or is not moral. Speakers concerned to establish the truth about morality are inevitably obliged to accord equal respect to all those whose assent must be relied on in the collective endeavour to establish what the truth of the matter is.
(Note: the use of "truth" in this reconstruction of Habermas's argument is misleading since Habermas draws a distinction between the truth of claims that refer to an independent objective reality - as is the case in science - and the validity of moral claims that do not refer to some reality indpendent of our history and culture. However, in the context of the critique we want to develop here the distinction is irrelevant. The important point is that the morality of the discourse ethic is all about debating moral norms with all the impartiality and the concern for the strongest arguments that characterise the endeavour to establish the truth of the matter.)
Having found a ground for the principle of universal respect in the pragmatic presuppositions of discourse, Habermas restates how significant this discourse ethic ought to be in our current historical situation:
"The discourse principle provides an answer to the predicament in which the members of any moral community find themselves when, in making the transition to a modern, pluralistic society, they find themselves faced with the dilemma that though they still argue with reasons about moral judgments and beliefs, their substantive background consensus on the underlying moral norms has been shattered. They find themselves embroiled in global and domestic practical conflicts in need of regulation that they continue to regard as moral, and hence as rationally resolvable, conflicts; but their shared ethos has disintegrated."
Habermas also acknowledges that it is possible for the pluralist to give up on morality, accepting perhaps that man is a wolf to man and believing that within the framework provided by liberal society pretty much anything goes. He also acknowledges that people can resolve their differences without recourse to moral discussion. It is still not uncommon for those who are not expected to agree with us to get shot or bombed before being given a chance to participate in the kind of discussion Habermas describes. Interestingly, the discourse ethic does not call this into question because it implies nothing about what ought to be discussed or what ought to be seen as a moral issue. We can quite consistently observe the principle of universal respect when trying to establish the truth about morality on Monday and then resume shooting on Tuesday because, apparently, national interests are at stake, not moral principles. He assumes that people want to resolve their differences through a discussion of what is the morally right thing to do, and with his discourse ethic he wants to say that participants in that discussion are bound by a principle of universal respect because this is something that their discursive activity presupposes.
Interestingly, Habermas envisages the possibility that some unworlded individuals in this pluralistic society might want to collectively work out a shared ethical framework as rich as the older one but now with a secular basis. Quite bluntly he says that "such an effort is doomed to fail." The problem is that without an old-fashioned ethical life it seems inconceivable that there could be agreement about what constitutes a good life or what ought to be our highest aims.
Although the members of the pluralistic society cannot agree on whether football is a sin (because they can't agree whether the word "sin" has a meaning any longer) they can agree on the morality of keeping the discussion open and respecting everyone's point of view.
Habermas wants to go beyond this because anyone wanting to participate in this discussion will soon face the question of how people are to judge what, in reference to any particular practice, is the right thing to do. Okay, they must keep the discussion open so as not to sacrifice the search for truth/validity, but how are they to come to any agreement in a pluralistic society in which agreements are so hard to reach?
Habermas proposes the principle of universalisation: "A norm is valid when the foreseeable consequences and side effects of its general observance for the interests and value-orientations of each individual could be jointly accepted by all concerned without coercion." Presumably this is derived from an interpretation of what is required by genuine respect for the other parties to the moral debate. From his clarification of the reference to coercion here, it is clear that any kind of emotive language or rhetorical arm-twisting or spin is prohibited to ensure that it is the truth (or validity based on the strongest argument) that holds sway, not, for instance, the charisma of personalities or the power of images. As he puts it, if this principle is followed, "nothing but reasons can tip the balance in favor of the acceptance of a controversial norm."
Habermas is not adamant about that particular formulation of the principle of universalisation, but he insists that some such principle will have to be adopted in order to ensure that norms capable of commanding universal agreement are selected.
Footnote: There is an excellent section from: The inclusion of the Other. Studies in Political Theory. Jürgen Habermas. MIT Press, 1998 available on the marxists.org website. It sums up perfectly the point of Habermas's communicative ethics.