That's not a philosophical argument, though. Morals are.
All science is based in philosophy. Empiricism is a philosophy, even logic is a branch of philosophy. Science relies on empiricism, but you can reject empiricism on a number of philosophical bases (the subjective nature of the senses by which we gather evidence in support of science being one obvious one).
As a matter of logic, though, a things can be unprovable by humans and yet still true. There is no room in logic for the notion that some statements are objective because they are "science" without a lot of unpacking, nor are all non-empirical statements subjective.
Logically speaking, there may be invisible and incorporeal fairies dancing on your lawn that cannot be detected by science. There is no way to disprove their existence objectively. What we generally do is rely on the unspoken assumption that unless a thing can be empirically demonstrated, we treat it as untrue.
To assert that morality is untrue because people disagree is similar to asserting that religion is untrue because people disagree on it. It is a kind of reverse "appeal to popularity" fallacy. If everyone
agreed on what the moral rules were, that would not make morality necessarily objective, and if the next person born disagreed with the rest of humanity on it, he would not be provably wrong. The same can be said of the reversed argument: that people do not agree does not make a thing subjective.
How do you prove that, though?
Assuming there were an objective morality, the ability to prove the content of it would be a different question. Right now, in this world, I could posit there is a smartest living human. I cannot prove who that person is, and even if I found him or her, I do not really know what test to run to confirm it (even if I tested everyone on Earth, the very
test itself would be subject to critique that renders it useless as an absolute proof). So, even in principle, it is not possible to prove who is the smartest person on Earth; still, I feel reasonably confident in saying that there is such a person.
It is still subjective, just this time around, it is this god that decides what right and wrong is.
Under the view of the Abrahamic religions, God created everything, including logic and science, so would the existence of God render those "subjective" since He made them up?
In fact, if God invented morality, then He could be the objective source by which we determine what it is. If He is not, in your view, then I think it is largely inescapable that *nothing* in the universe is objective since he invented it all. I'd argue that in the case where Giod exists, what we mean by the word "objective" would be "whatever God thinks" since He is infallible.
That's because you cannot prove morality any more than you can prove beauty.
Who says beauty is subjective? Again, that people may disagree on what is beautiful is not evidence of subjectivity. Many of those people may simply be wrong. If a lack of provability were the definition of subjectivity, then the Theory of Evolution would be subjective. Scientific theories are *not* provably true. They are falsifiable, but there is always a possibility that however well your theory accords with reality in terms of experiments, that the next time you run the experiment you will find a result that confound the theory.
Basic Humean philosophy tells is that all deduction based on prior evidence is subject to bias and error. Will the Sun rise tomorrow? I tend to think it is certain because it has risen every day in the last 4.5 billion years, but despite that track record of success for the "Sun will rise tomorrow" model, there is a small non-zero chance that the Earth will be destroyed and that the Sun will therefore not rise.
In evolution too there is the logical possibility that molectular biologists will find a tiny tag inside a cell that reads in English "Yaweh was here, and He designed this. Suck it, biotches!"
So evolution is still not "proven" either. The theory is remarkably predictive, it fits with the evidence we do see and it is falsifiable. That's what makes it a useful and scientific model.