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"There are sets of objective moral truths such that any rational being that understood them would be compelled to follow them". The arguments seem mainly to be:
1) Playing around with the meaning of rationality until you get something ("any rational being would realise their own pleasure is no more valid than that of others" or "pleasure is the highest principle, and any rational being would agree with this, or else be irrational")
2) Convergence among human values.
3) Moral progress for society: we're better than we used to be, so there needs to be some scale to measure the improvements.
4) Moral progress for individuals: when we think about things a lot, we make better moral decisions than when we were young and naive. Hence we're getting better a moral reasoning, so these is some scale on which to measure this.
5) Playing around with the definition of "truth-apt" (able to have a valid answer) in ways that strike me, uncharitably, as intuition-pumping word games. When confronted with this, I generally end up saying something like "my definitions do not map on exactly to yours, so your logical steps are false dichotomies for me".
6) Realising things like "if you can't be money pumped, you must be an expected utility maximiser", which implies that expected utility maximisation is superior to other reasoning, hence that there are some methods of moral reasoning which are strictly inferior. Hence there must be better ways of moral reasoning and (this is the place where I get off) a single best way (though that argument is generally implicit, never explicit).
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I hate to break it to you, but if setting two things beside two other things didn't yield four things, then number theory would never have contrived to say so.
Numbers were invented to count things, that is their purpose. The first numbers were simple scratches used as tally marks circa 35,000 BC. The way the counts add up was derived from the way physical objects add up when grouped together. The only way to change the way numbers work is to change the way physical objects work when grouped together. Physical reality is the basis for numbers, so to change number theory you must first show that it is inconsistent with reality.
Thus numbers have a definite relation to the physical world. Number theory grew out of this, and if putting two objects next to two other objects only yielded three objects when numbers were invented over forty thousand years ago, then number theory must reflect that fact or it would never have been used. Consequently, suggesting 2+2=4 would be completely absurd, and number theorists would laugh in your face at the suggestion. There would, in fact, be a logical proof that 2+2=3 (much like there is a logical proof that 2+2=4 in number theory now).
All of mathematics are, in reality, nothing more than extremely advanced counting. If it is not related to the physical world, then there is no reason for it to exist. It follows rules first derived from the physical world, even if the current principles of mathematics have been extrapolated far beyond the bounds of the strictly physical. I think people lose sight of this far too easily (or worse, never recognize it in the first place).
Mathematics are so firmly grounded in the physical reality that when observations don't line up with what our math tells us, we must change our understanding of reality, not of math. This is because math is inextricably tied to reality, not because it is separate from it.
On the other hand...
http://en.m.wikipedia.org/wiki/Is_logic_empirical%3F