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I would like to hear some good arguments for moral realism. Most that I find online is based on "If you don't believe in objective values, then murder is okay". While this might seem frightening, I don't think it proves anything. Believing in objective moral values might be a good strategy to maximize happiness, but this does not make them true. Also lets assume that the defender of moral realism is an atheist.
So what arguments exists that are not based on shaming or comfort?
Most arguments are kind-of semantic. We use moral talk everyday, we often discuss moral issues and try hard to convince each others of our moral judgements by appeal to reason and facts, just as if something objective is at stake. A good meta-ethical theory must account for this aspect of common language. Perhaps the best and simplest explanation is moral realism: there are indeed moral facts, there are things one objectively ought to do in such or such situation, and that's exactly what we are talking about when discussing moral issues.
Alternative accounts of moral talk, such as expressivism (the idea that moral judgments are mere expression of feelings, emotions or desires rather than fact statements) or relativism/subjectivism (the idea that moral facts are relative to communities or to individuals) can be demanding. One challenge for expressivism is the Frege-Geach problem. If really moral judgements are only expressions, or attitudes, how is it that they can be combined into logical structures such as "If it is wrong to tell lies, then it is wrong to get your little brother to lie" ?
Another alternative to moral realism is an error-theory: we do pretend to make objective, factual judgments about what one ought to do in some situations, but we are actually plain wrong, there is no such fact of the matter. This position is against our common-sense intuitions, and does not by itself provide an explanation to why we keep on having moral discussions.
Note that moral realism does not mean that moral facts (things one ought to do) do not reduce to something else, such as social acceptability or utility. It only means that moral judgments express potentially objectively true facts rather than nonsense or mere attitudes.
There are primarily three non-theistic routes to try to defend moral realism.
First, there's Mill. In your question, you seem to allude utilitarianism in stating "Believing in objective moral values might be a good strategy to maximize happiness" but then you kind of depart in suggesting that this would not make them true.
For Mill, the word good means pleasure-causing, and the word bad means painful. If there are objective things that would increase or decrease pain or pleasure, then it seems there's an objective account of good and bad along this definitions. This could be called "moral realism." Admittedly, there's a grounding objection ready at hand which is why would what makes these ideas (pleasure and pain) equivalent to ideas we call "good" and "bad." (I will return to this problem shortly). But for Mill, the only keep assumption is that we should relate pain/pleasure to good/bad.
Second, there's Aristotle. I read him as a type of moral realist. On his configuration, what is good is that which accords with the kind that something is. I.e., what makes a dog an excellent dog. This becomes ethical "good" when used in reference to what makes a human an excellent human and enables their flourishing. If there are any facts about human flourishing, there's a reason to view these things as real and thus what this theories declares good or bad to be real. Again, this view might leave us wondering what is different between saying "a good human being" and "a well-functioning human being." In which case, it seems like we could drop the predicate. For a contemporary reference look at "Modern Moral Theories" by G.E.M. Anscombe.
Aristotle actually has a nice objection to crude readings of Mill (anachronistically) -- which is that some people have thoroughly wrong understandings of pleasure and pain due to warped upbringings, etc.
Third, there's Kant and similar theories. Here, "good" means in accordance with objective reason and bad means done subjectively rather than for objective reasons. (I'm sketching quickly here because the details are not relevant to your question).
To put it another way, your question involves a semantic problem as well as a metaphysical one. On the semantic level, it matters greatly what we mean by "good" to answer whether or not, such considerations of the good can actually exist. It seems pretty obvious that there are at least some aspects of pain/pleasure that do exist in the world and actions can occur relative to these. Similarly, it seems pretty obvious that there are animals with certain arrangements that are better or worse for them -- e.g., just ask the cats of vegans.
What often seems to be at work in this sort of question is the rejection of a separate metaphysical category of moral properties that are real. And this would be a deep objection to Kant where such properties do seem rampant.
I'm a nihilist, but I'll bite.
Let us say that the current state of the entire human conscience is independent of individual thought. That is to say, the way humanity perceives anything is based upon our history, our culture, our position in the evolutionary tree, of countless factors in which we have little control. Where the populous as a whole is today has nothing to do with individual thought.
However, it can be argued that what is taken to be moral truth is dictated by the human population as a whole. We think murder is wrong, because we have learned from history that allowing ourselves to be callous, means others might be forgiven for doing the same. There have been massive movements in support of homosexuality, but this only occurred after secularism took hold and society developed to the point that tradition had less of an impact on what we deem wrong.
At the end of the day, no individual has the ability to control the collective human conscience. So it is not possible to have objective values. What is considered moral is not a personal affair. We do develop personal opinions about what is moral, but even that development happens in an environment that encourages you toward commonly held beliefs about morality.
So there could be realism, but in a sense that allows for continuous change.
That is about the only explanation I have come up with. It will be interesting to see what other people have to say.
From biology.
One does not have to be a total moral relativist to believe that morality is an aspect of a species, and not of some deeper aspect of rationality that transcends biology. Ants don't seem to fear death, so if we somehow grafted intelligence onto them, they would probably never develop a compunction against killing individuals.
To me this suggests that no moral principle is 'infinitely deep' in the way our restriction on murder seems to be. So all arguments that derive moral principles straight from rationality, or from anything more abstract, seem questionable. We need to look within the species, and the only reality these things can have would necessarily be evolutionary.
Fortunately among other things, humans in general do seem to have evolved two forms of moral sense, and it is clear how those support our survival. We have a sort of shared mind that allows us to enjoy one another's happiness, and a power of projection that gives us a clear understanding of our own limited interchangeability. We can see aspects of both of these in animals like dogs or monkeys, that have hierarchical social structures with clear obligations.
We know that whatever happens to another human can also happen to us. So we want protection from those events. In fact, as a species, we are given to irrational paranoia. It seems that we need reassurance of protection in order to not continually degrade our own ability to behave rationally.
We also know that pleasure is often a group effect, and we like to be around it. So one of the events we want protection from is the limitation of our own autonomy to find pleasure idiosyncratically, and therefore we fear the excessive control of others' behavior.
It is not far from that impulse to a full-blown Lockean social contract. Humans have not just never been found without any such device, but we can easily see how it destroys them to be deprived of it. These two impulses suggest that that fact is not accidental, but part of the way we frame our thinking. Beyond that, it suggests that it is not incidental that these contracts always involve aspects of both Utilitarianism and the Golden Rule, no matter how far they evolve away from their roots.
Therefore moral claims may not have an existence independent of humanity, or be derivable from anything but the overall patterns these contracts take, but to the same extent 'shelter' is a real category of things, 'morality' is real.
More immediately, from psychology.
The human capacity for self-destructive and outright masochistic behavior is widespread. It is one of our primary psychological problems alongside excessive fear and uncontrollable competitive impulses. (Ruling out things that we generally end up attributing almost completely to physiological variation, like schizophrenia.)
While it is easy for us to see the purpose in survival of fear and aggression, and their internal logic, it is harder to imagine a real use for guilt, if morality is not something real that transcends individual thought. It is possible, to see guilt as self-aggression or self-fear and elaborate a working theory based on some theory about surviving development or reconciling behavioral codes with one's group.
But we do not, in general find guilt more common in children. And we do not find it is truly decreased by being fully justified, or even compelled into violations by one's society. Military men since the dawn of civilization have descended into self-destruction later in life, attempting to deal with survival guilt or other forms of self-hatred from moral injury under a long succession of names.
We know that fear results from the reality of danger, and aggression results from the reality of competition. It is hard to imagine there is not a genuine reality behind the phenomenon of guilt that would not be better served by other machinery already present in people. Altruism, empathy, etc. all redundantly serve the goals we find guilt pursuing, but it is hard to imagine how they would cause widespread self-destruction.
That suggests guilt is the more basic form of those more productive impulses, and that the phenomena it seems to directly serve are real at a level that mere social order would not require.
Kantian categorical imperative
‘I ought never to act except in such a way that I could also will that my maxim should become a universal law’
refers to something like a universal moral principle, so one is tempted to assert that such a principle somehow exists. However, any objective location of moral values and laws (God, world harmony or like) is very difficult to concord with the condition that morality arises from personal convictions of people that translate them in judgments and acts. These convictions are its ultimate source, and people assume their responsibility for them as well as for what follow from them. If one puts the source of morality somewhere beyond human consciousness, it would mean that some part of the responsibility could be transferred to this moral authority. By the way, this is why many atheists seriously opposed to religious vision of moral - people can through off their responsibility to the God, which undermines moral; I would say that this objection is no less important than those contra atheist position, that you mention.
Another difficulty with the objective view of the morality is the fact that it is impossible to fix its content. The life is changing all the time and old and established meanings become sometimes useless or do not work. We can see many moral problems - euthanasia, gay marriages, abortion etc - and, apparently, this objective law cannot resolve them.
I do not find the idea of moral realism convincing. My understanding is that it suggests ethical principles are objective features of the world, which we may discover over time as if we were to approach a single, fixed goal.
For those inclined towards Platonic idealism the fact that many cultures in the world history have "discovered" versions of the Golden Rule ("One should treat others as one would like others to treat oneself") may point to an objective feature whose existence is being revealed. Perhaps Kant's categorical imperative (as mentioned in a previous answer) can also be counted here. This is the (relatively) most convincing argument in favor of moral realism that I am aware of.
For my own inclination, what is more important is that moral realism is not the opposite of Nihilism, but that those two sit at opposite ends of a broader spectrum. I am interested in "pragmatic" arguments for ethical principles that occupy the middle ground: "good strategies to maximize happiness" (as mentioned by the OP) and the basis for cohesion in societies, which is key to survival.
I often find myself exploring the part of the spectrum where it approaches Nihilism. Perhaps one could argue that ethical principles from Buddhism fit here. If I were to explore the part of the spectrum where it approaches moral realism, I would look e.g. towards Confucianism for (perhaps) convincing arguments that fit there. I am referring to Asian philosophies, because for them the distinction between philosophy (within the scope of this question) and religion ("for comfort", and therefore out of the scope of this question) is less clear than for Western ideas.
Your question makes some false assumptions that get in the way of you finding the answer.
The first problem is that you're asking for proof, but proving any statement is true or probably true is impossible, unnecessary and undesirable. This is true whether the statement is deemed to be philosophical or not. If you assess ideas using argument then the arguments have premises and rules of inference and the result of the argument may not be true (or probably true) if the premises and rules of inference are false. You might try to solve this by coming up with a new argument that proves the premises and rules of inference but then you have the same problem with those premises and rules of inference. You might say that some stuff is indubitably true (or probably true), and you can use that as a foundation. But that just means you have cut off a possible avenue of intellectual progress since the foundation can't be explained in terms of anything deeper. And in any case there is nothing that can fill that role. Sense experience won't work since you can misinterpret information from your sense organs, e.g. - optical illusions. Sense organs also fail to record lots of stuff that does exist, e.g. - neutrinos. Scientific instruments aren't infallible either since you can make mistakes in setting them up, in interpreting information from them and so on.
Rather, knowledge is created by noticing problems, guessing solutions to those problems and criticising the solutions until there is only one left and you don't know how to find or invent any criticisms of it.
So the standard by which to judge objective morality is whether it solves problems. Objective moral standards are institutions that help make it easier for people to deal with one another. They are invented by human beings, but that doesn't mean they are arbitrary. Nor does it mean that different ideas about what standards people should hold are all equally good. For example, if the government can steal from people at will and are totally unaccountable for their plundering this makes it very difficult for anybody to deal with other people. You can't say that you will deliver some grain to market because the government might decide to steal the grain. Also, it will not be in your interest to advertise that you have grain for fear of the government stealing it. You can't make long range plans with respect to grain growing because the government might steal the seed you intend to plant for next year's harvest. Such a system was tried in the Ukraine when it was occupied by the Soviets and led to famine.
You write:
Believing in objective moral values might be a good strategy to maximize happiness, but this does not make them true.
They are not a standard for maximising happiness. First, happiness can't be measured. Happiness is some kind of subjective sensation and there is no particular reason to think different people mean the same thing by that term. So there is no standardised happiness that can be measured. Second, whatever subjective sensation it happens to be it is not the be all and end all of making decisions that make sense, so it's not particularly useful.
For more see,
"The Beginning of Infinity" by David Deutsch, especially chapter 10,
The answer is: There are no valid arguments whose correctness we can be sure of. My research? My research builds upon the absence of any other valid researches on this topic.
Could be answered if you brought in "outer" intention (God, Simulation theory, etc.). Then by how coherent a moral obligation is with this intention, its value could be defined, otherwise: bollocks.
nihilism?