@Quetzl: If you agree that morality can differ between species, you've already admitted there is no singular objective morality.... or are you arguing in favor of relative objective morality? That's not something I see very often, and I've never seen much difference between that and subjective morality.
@Spinner: Logic isn't based on assumptions, at least not in any of the crass ways that would be implied by your statement. "If P then Q, P, therefore Q" isn't based on assumptions, it's simply how reality works. The example you're referencing may have assumptions made as part of the decision, but the application of logic itself is not based on assumptions, but on an overwhelming preponderance of evidence.
Edit: To be more clear, an example of logic itself failing would completely alter and shift the way we look at reality, and be quite possible one of the biggest discoveries of history. Assuming it's an actual failure of logic, and not a failure of humans to properly apply logic.
I have no idea whether there is actually any kind of objective morality, but ultimately I don't think it matters... because if it exists, we have no way of finding it or identifying it, so we just do the best we can with what we have.
(I also categorically reject the circular arguments which assert that it cannot exist without God, but we know that one or the other exists, therefore both exist, because those are statements of faith, not proof. Believe what you like, just don't present your faith-based assumptions as rational arguments which I should be swayed by.)