Moral Platonism holds that there is an object that exists that is good. As in, we have things like rocks, trees, mountains, and a good. So not something that is described as a good thing (like a cake is good), but a thing that is good ("look at that good roaming the countryside").
I think for most people, the initial reaction to this concept is that it's nonsense. How could it be that good is a thing? It makes no sense. Dr. William Lane Craig calls it unintelligible.
I'd agree that it seems completely crazy on the face of it, but my obligation to be as unbiased as possible reminds me that plenty of scientific discoveries have seemed to fly in the face of common sense. So even if this idea of a good thing seems to be nonsense, it doesn't mean that it actually is. We actually have to find out if it's nonsense. Is a good thing simply difficult to understand, or is it actually unintelligible like a square circle?
The reason Moral Platonism comes up in theological debates is usually as a response to the Moral Argument and a defence of the Problem of Evil. How it usually goes is something like this:
Atheist: "God does not exist because Problem of Evil."
Theist: "The Problem of Evil actually proves God exists because Moral Argument."
Atheist: "Ahah, but P1 of Moral Argument is false if Moral Platonism is true!"
At that point, the atheist somehow feels their work is done, but they haven't actually given any reason to think that Moral Platonism is true. Seeing as most people off the bat feel that Moral Platonism is nonsense, they should probably put some effort in. For the Moral Argument to fail, then Moral Platonism has to be true. They can't just have a 'maybe' hanging over it.
So before they waste their time, let's see why it doesn't work.
As we know, atheists have to be either materialists or naturalists. Any atheist materialist can't have Moral Platonism, because if good is an object, it's an abstract one, which means it's immaterial. Good if it exists isn't something made of matter. You can't get hold of it and put it in a bucket.
So perhaps, a naturalist could have abstract objects in their worldview. However, naturalists need the laws of physics to exist before anything comes into being, so physics and the material realm would exist before any immaterial stuff. Immaterial abstract things would be emergent properties of the material. Platonism would suggest that numbers exist immaterially, but seeing as physical laws rely on numbers, then numbers would have to exist first. So naturalism has a problem in that it holds that physical laws come first, and any immaterial abstracts would arise from their material output, but laws require these immaterial abstracts to work in the first place. Aren't laws immaterial anyway? Seems that the naturalist is in a circular mess.
So let's say that to escape the problem, we allow for immaterial laws, logic, numbers, and such, to exist before matter and the naturalist can go on from there. I don't think you can call that naturalism any more, but at least there's room for a thing called good.
So we've got some realm of immaterial entities which exist as brute fact that somehow give rise to the universe and all material things. At this point, I don't see why God should be such a difficult concept to grasp.
At the beginning of all things we have an abstract object called good. What other abstract objects do we have? Do we have a justice, and a generosity, and a care, and a mercy? If each of these are abstract objects then we should also expect to find things called hate, violence, anger.
Because all of this comes back to trying to refute the Moral Argument, we have to remember that we're looking for an objective source for moral values and duties. Now, if there are a whole bunch of objects like justice, courage, and mercy, that we like and a bunch of objects like hate, revenge, and anger that we don't like, then it goes straight back to being a subjective choice between which group of objects we personally prefer to live our life by.
If good exists in this way, then it isn't a suitable objective standard because we have no obligation to live according to it. We could just as well live by hate and whatever we do in the universe would still be insignificant.
So what if we don't have all these small abstract objects? What if justice, mercy, love, generosity, care, and so on are all part of a parcel which is the object called good? And what if hate, revenge, anger, and violence are simply anything that isn't in the parcel of good?
We still have the subjective option to live according to good, or to not. It still doesn't really matter what we do. It's just an object. It's like choosing to live your life in a similar way to a crab. There's no objective reason that you should or shouldn't. You could come up with several reasons why it might be personally helpful or harmful to live a certain way, but you're still stuck with the problem of there being no ultimate meaning when the human race becomes extinct, the planet burns up, and the universe dies a heat death. It all ends up the same. It's still just a subjective standard.
As an object, it's inanimate, like a rock, or a tree, or a table. It exists but it doesn't try to pass on any wisdom or message or rules to you. It doesn't have any wisdom or rules. It's inanimate. There is no reason whatsoever to align yourself with a rock.
An atheist might suggest that we have evolved to be in line with his object called good. That's pure speculation, and considering the odds of how evolution could have turned out, it seems as though there's no reason why we would evolve to be in line with it. As good is an inanimate object that most creatures don't interact with, there doesn't seem to be much requirement for it in survival. Most of the animal kingdom live amorally (without morality) and get along just fine. Why would we evolve and keep a handicap when our basic goal is survival? Why is it that we (and perhaps a few other more intelligent species) are the only ones who have to pledge allegiance to this inanimate good, while the less intelligent species can carry on as they are? What's the connection between intelligence and good anyway?
There doesn't seem to be any reason at all for any of it from an atheistic perspective.
Here's where I explore why an immaterial inanimate good is a bit like a square circle (i.e. an impossibility). It doesn't seem that good can simply be a thing. Good is tied up with morality, but as we know, inanimate things like rocks, mountains, rivers, and such don't have morality. They just do what they do according to the laws of nature. They don't impose any obligation on anyone. No inanimate object can.
Only a person or a purpose can impose obligation. Good as a platonic object in itself is not a person, and is not a purpose. In an atheistic world, we could be good all our lives and end up exactly the same as someone who was evil. Dead, forgotten, nothing. Platonic good can serve the subjective purpose of extending human survival, but serving a subjective purpose does not make for an objective standard.
This is why God is the only potential objective standard for good. If this good, rather than being an object, is a person, then it can give commands, or explain which rules are the best. It knows because it is the ultimate best thing/person. Those are objective moral duties. God also provides an eternal afterlife, which means our actions are no longer insignificant and meaningless, but are part of a larger thing that will echo on for eternity. That's an objective moral purpose.
Platonic good is a subjective choice which offers subjective duties for a non-existent purpose.
So the Moral Argument stands strong.