'Moral Realism' is defined as the claim that some moral 'entities' (this term being construed in a broad sense: states, properties, facts, objects) exist. 'Objectivist' Moral Realism' is defined as the claim that moral entities exist objectively. (The term "objectivist" is meant to separate the position here under consideration from what may be called "subjectivist" moral realism, the view that moral entities can 'exist non-objectively' (subjectively or intersubjectively), and that some moral entities do. (I think that this position collapses into Non-Realism anyway—which would make the objectivist/subjectivist distinction dispensable—but some disagree.)
The 'Swabian Defence' of Moral Realism is a particular strategy of defending the objective existence of (some) moral entities. Here is an outline of the major steps it suggests taking.
1. We know that psychic states like pleasure and suffering exist.
2. Some psychic states are (objectively) either valuable or dis-valuable: This can be demonstrated by 'hypothetical world-part' tests. Thus, suffering is dis-valuable, and pleasure is valuable.
3. Doubts about the objectivity of the existence of suffering and pleasure (etc.) or about the objectivity of the valuability and dis-valuability of these states, respectively, usually go back to confusions, due to the lack of keeping separate different senses of the 'objective'/'subjective' dichotomy.
4. Value and dis-value do not only exist objectively but, indeed, they are widespread—at least as widespread as valuable and dis-valuable psychic states.
5. That someone can choose either to create value or to prevent dis-value for non-egoistic motives is sufficient that he or she morally ought to do it, and hence is sufficient for the existence of a 'moral ought' (and an 'ought' in the sense at issue with 'Hume's law').
6. An intention which is non-egoistically directed at the creation of a valuable state is a 'moral intention', and the success of such an intention results in a 'moral action'. The existence of a moral intention, or of a moral action, or of a 'moral ought', is a moral fact. Quite apparently, such intentions and such actions exist. Hence, moral facts exist.
7. Moral Non-Realism is true only if no single moral entity exists. Correspondingly, Moral Realism is true as soon as but one moral entitiy exists. (Moral Non-Realists usually overlook the radicality of their position, or fail to take it seriously.)
8. Given that the existence of some moral entities (moral oughts, moral intentions, moral actions) cannot plausibly be denied, Moral Non-Realism is unworldly. It is thus unworldly to deny that Moral Realism is true.
To review what I think are the sticking points of the argument click here. To see the full argument (in its present state of elaboration) click here.
The meta-ethical discourse of the last century was dominated by a number of prominent debates, referring, for example, to the 'natural'/'non-natural' distinction (Moore), the Argument from 'Relativity' (e.g., Mackie), the Argument from 'Queerness' (e.g., Mackie), the 'Internalism'/'Externalism' opposition (e.g., Smith, Brink), and the 'Is'/'Ought' divide (e.g., Hume). It is characteristic of these debates that they access the Moral Realism issue indirectly, by discussing and trying to reject objections against Moral Realism. The Swabian Defence is motivated in part by the idea that a very convincing case for can be made for Moral Realism by a direct argument, showing how plausible Moral Realism is, and how comparatively implausible its denial is.
Apart from the direct/indirect aspect, there are additional reasons to devote to those traditional issues much less attention than they are given. One very important reason is that they all suffer from one rather pivotal defect: All of them turn out, by closer inspection, to be rather unclear, and they are all subject to different kinds of vagueness. For example, there is no common agreement about what the predicate 'non-natural' actually refers to. The sense applied by Moore seems actually to aim at the lack of a plausible reduction (to 'natural' entities, but in fact also to any non-'natural' entities) of the notion 'good'; so what Moore aimed at would probably better be captured by the word "unanalysable". Today, people mean other things by "non-natural", including 'non-non-normative' [sic], 'non-scientific', 'non-epmirical' (etc.). Now notice that the significance of 'non-naturalist' objections to Moral Realism is clearly based on the assumption that Moore's argument was worth taking very seriously; yet Moore's argument seems actually not to be a "non-naturalist" argument. So the high reputation of of "non-naturalist" arguments against Moral Realism seems to be based upon a misinterpretation provoked by an unhappy terminological choice on part of Moore.
For reasons like this, those traditional, established debates seem to be much less significant than is commonly assumed. It does not seem reasonable to devote much space and labour to the consideration of arguments, even if they are prominent, or propagated by prominent people, or otherwise well established, if they are not clear, or if their value depends on misinterpretations. Yet those who still prefer to know how the Swabian Defence is related to these prominent debates, some particular remarks on each of them are offered here.