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Ancient writers such as Herodotus pointed out that moral judgments varied in different parts of the known world. This fact, by itself, has not been thought especially important by moral philosophers. It is generally thought to be crucial for the relativist to show that the existing differences are fundamental. Here are some comments by the moral philosopher Richard Brandt. Notice that he makes an attempt to provide a useful definition of what fundamental differences are.

Brandt indicates that the ethical relativist usually accepts several theses. He then says the following:

The first thesis, without which the others would lose interest, is that the values, or ethical principles, of individuals conflict in a fundamental way....

The most important and controversial part of the first thesis is the claim that diversities in values (and ethics) are fundamental. To say that a disagreement is "fundamental" means that it would not be removed even if there were perfect agreement about the properties of the thing being evaluated. (If disagreement is nonfundamental then it may be expected that all ethical diversity can be removed, in principle, by the advance of science, leading to agreement about the properties of things being appraised.) Thus it is not necessarily a case of fundamental disagreement in values if one group approves of children's executing their parents at a certain age or stage of feebleness whereas another group disapproves of this very strongly. It may be that in the first group the act is thought necessary for the welfare of the parent in the afterlife, whereas in the second group it is thought not to be. The disagreement might well be removed by agreement about the facts, and indeed both parties might subscribe, now, to the principle "It is right for a child to treat a parent in whatever way is required for the parent's long-run welfare." The disagreement might be simply about the implications of this common principle, in the light of differing conceptions of the facts.

From "Ethical Relativism" by Richard Brandt, The Encyclopedia of Philosophy, Volume 3. For more of Brandt's views on ethical relativism, see his Ethical Theory. For another discussion of the importance of fundamental and nonfundamental differences, see J. L. Mackie Ethics: Inventing Right and Wrong, p. 36-7.