I've heard explanations by Sam Harris and Michael Schermer, but I'm not super convinced on this one. People like Harris and Schermer seem to be trying to get an ought from an is.
They all seem to be trying to get an ought from an is.
Who are "they all"?
Anyway, I'll provide two things. Firstly, a taxonomy of theories that argue for "objective morality" (or something close enough). Secondly, I'll point to one argument that is compatible with pretty much all "Moral Realist" positions I describe beforehand.
In order to say that there is "objective morality", we'll need to argue for three things:
- Moral statements are truth-apt. (That is, at least some are.)
- Some of those moral statements are true.
- The truth of at least one statement is not relative to something.
Let's call theories that argue for all three things Moral Realism. The term gets sometimes used more specifically. Also, for some theories it's not clear whether they really fulfill all three things. Pretty much all the popular theories in metaethics are secular.
In anglophone analytic philosophy, Moral Realism (as a vague label and not what I've defined) is held by a slim majority. In the last 20 years or so a number of defenses have been made.
1 is important because moral statement could function differently. Non-cognitivists hold that when we make a moral statement like "Murder is bad." we're not saying "It is true that murder is bad." but instead something like "Boo murder." or "Don't murder." Both examples have no truth value, so if non-cognitivsts are correct then we can't really talk about Objective Morality. The arguments here usually require a background in philosophy of language, so I'll just mention that cognitivism (and therefore affirming 1) is more popular (look under "Moral Judgment").
2 is probably the most contested. "Truth" is ofc a problematic term itself. I'll just ignore that here and use some vague correspondence theory. In order for moral statements to be true, there have to "moral facts". There has to be something that makes them true.
But how can moral facts exist? When we believe that the world could theoretically fully described by physics then existence of such facts would be strange. This idea is the short description for one of the stronger arguments for Error Theory. It's also called the "argument from queerness" because moral facts would be "queer" (in the sense of strange) entities whose existence has ontological problems. Error Theory holds that no moral statements are true. When Moral Realists can convincingly argue for the possiblity of the existence of moral facts then this clears one of the highest hurdles for "objective morality".
There are a number of approaches to do so:
a) argue that moral facts come from natural facts. This position is called Moral Naturalism. Defenders try to address the is-ought-problem in various ways.
b) argue that moral facts are abstract facts. What the hell are "abstract facts"? An easy analogy is mathematics. Number and proofs aren't found in the world. When we know the basic rules then everything else that follows follows. Because mathematical facts aren't just out there in the world, we could think that they are "abstract". (There's roughly an even split between people that defend something like that about mathematics and people that attack it.) Moral Non-Naturalists argue that moral facts are such timeless and placeless entities.
c) I'd say that another direction falls under Moral Realism. That is Kantian constructivism. The idea is roughly this: when we possess reason then when thought through there's only one kind of behaviour we could rationally will which is moral behaviour. Such a position would say that this moral behaviour is universal. The idea is that moral facts aren't out in the world, but mind-dependent. But because there's nothing else we could rationally will, we could say that morality is then universal or "objective".
(I'll leave aside 3 for now, mainly because Moral Relativism isn't all that popular in contemporary philosophical literature, from what I've seen.)
This is just taxonomy. The SEP can provide some short discussion. For approach a: see here. For approach b: see here. I also want to mention that there are many more issues like Moral Motivation and Free Will. Moral Realists think that those can also be dealt with, in the end.
I'll also describe one imo fairly strong argument for Moral Realism. You can find it in Cuneo's The Normative Web (2007). It is sometimes called the "Partners in Crime"-argument. Here, I'll just describe a less demanding variation of it (for the sake of simplicity):
(P1) If moral facts aren't possibly existing entities, then epistemic facts aren't possibly existing entities.
(P2) But epistemic facts are existing entities. (And therefore also possible.)
(C) So moral facts possibly existing entities.
This argument is supposed to refute scepticism of the existence of moral facts. If they are possibly existing entities then this means that they have no ontological problems, so the "argument from queerness" wouldn't be an issue anymore. It can also be used against more arguments from Error Theorists and even against Moral Relativists.
So how does this work? Premise 1 works by making a comparison. Epistemic facts are facts about rational behaviour when it comes to knowledge or belief. They are normative. For example: when people ignore evidence then they aren't rational, they behave wrong when it comes to their beliefs. Premise 2 is usually said to be the prerequisite for any sort of argumentation. When we argue about what we should believe then we appeal to epistemic facts. If there were no epistemic facts then we'd have no reason to f.e. not ignore evidence. There are a number of formulations that accuse someone that denies premise 2 of holding a self-defeating position.