The key controversy in meta-ethics today is between cognitivists holding that moral judgements are beliefs, and non-cognitivists holding that they are desires or feelings. Pivotal to this dispute is the practicality argument, currently regarded as the most serious obstacle to any coherent cognitivism.1 Even cognitivists tend to assume that the argument – which they typically describe as ‘Humean’, or as an argument of ‘Humeans’ or of ‘Humean non-cognitivists’ – is formally valid.2 Hence they frequently take it that all they can do in defending their position is to try to refute one of its premisses. It might be thought therefore that, whatever the difficulties and uncertainties surrounding Hume’s original exposition of the argument, a standard or agreed formulation must by now have been arrived at. Certainly many of the participants in the debate talk as though this is so. But it is not: contemporary formulations diverge markedly both from Hume’s original ones and from each other. Thus we find a range of reinterpretations of the first premiss which are best explained as different solutions to the attempt to ensure that the argument is valid when the second premiss is read ‘moderately’. But we also find independent appeals to the second premiss, relying on the ‘extreme’ reading.