  One answer often offered is that, at a suitably abstract level, there are premises or principles that everyone in fact accepts.  Perhaps 'Murder is wrong', or 'pain is bad', or 'everyone should be treated equally', would qualify. But of course such claims hardly do much work since questions immediately arise about which killings constitute murder and about how different pains should be compared and about which way of treating people counts as treating them equally in the relevant way. No moral claim that is plausibly offered as actually accepted by all, or nearly all, people can possibly be substantive enough to help settle on one view rather than another as better justified. 