People keep asking for an example for objective morality…and I keep giving one, and honestly I don’t think people are quite understanding the answer. It is based upon the same line of reasoning that Harris or Carrier uses to ground objective morality. This bizarre notion some atheist have that objective morality can not exist is merely a kneejerk reaction to theist sometimes asserting that to have objective morality you must have a God, or that objective morality exist then God must exist. Neither of which are true.
Objective morality is merely a metaethical position that propositions express moral facts, same as subjective morality…the difference being that an objective moral fact is akin to a objective ontological fact (putting aside any argument from queerness here) in that it makes *no* difference to the framework if the axioms or bases for the framework is subjective or even arbitrary (this is the trap of subjective reductionism). In math we have axioms which are subjective in that they are unsupported assumptions, and not objectively true. However, 1+1=2 is true by analytical definitions based upon those axioms and therefore objectively true. It makes no difference whatsoever if someone disagrees and thinks 1+1=3 to the objective fact that 1+1=2. Using this same analogous relationship we can apply it to morals and say if we formulate axioms (grounding) we can then build an objective moral framework from it. So when people ask for an example of objective morality here is my answer:
Moral grounding in harms/benefits by a society by mutual compact allows a hypothetical imperative case of having an an objective moral framework to allow for such moral facts such as “it is morally impermissible to be wantonly cruel to someone for the sake of being cruel.” would be an example of objective morality.
The one thing to remember is that when philosophers speak of objective morals is that basically they are saying that there is a fact of the matter to be had which is accessible to anyone. A toothache for example is subjective as in only you can experience or have access to it…but the rules of chess are objective as anyone can go read them. So a person who accepts moral realism is saying there are moral facts which anyone can discover or have access to, while a moral subjectivist believes moral facts exist but are not accessible to anyone but an individual. (not to be confused with “objective” as in scientifically objective)