You know my argument does look a little like circular reasoning. However, I think we're just dealing with obvious subject matter, which becomes clear when analyzed logically, and thus the proof I gave was so simple and flowed so directly it almost appeared circular. I'm actually not sure if it would be circular to be honest. Let me give an example of another proof that is so obvious it appears circular.
The surface of the sun is 5800k.
If the surface of the sun is more than 350k, it is hot.
The surface of the sun is hot.
Now, it seems this is circular, because one could argue that I "started with my conclusion". But we didn't start with "the sun is hot", we started with "the sun is X degrees" and then demonstrated that this made it hot.
I believe my proof is the same. I didn't start with "morality is subjective", I started with where morality comes from, and then demonstrated that this made it subjective. Maybe both proofs are circular reasoning, but if they're circular then the argument wasn't even necessary - I need only assert that morality is a description of our desires. If that automatically makes it subjective, then morality is obviously subjective.
And yes, virtually all people do agree on the basics. But I don't think this has anything to do with absolute morality, I think this has to do with society. I have already explained this causal link extensively in this thread, so I won't revisit my previous arguments. Suffice to say, it's not more indicitive of objective morality that nearly everyone in society values socially conducive action than it is indicitive of objective taste that nearly everyone thinks dog poop is disgusting. Some things are common sense, this needn't be evidence or proof of transcendent metaphysical, absolute moral laws. If you give someone a pair of pants, they're not going to try and put it on like a shirt. Even if they've never seen pants before. So is everyone spiritually in tune with a metaphysical absolute standard of clothing? Or do people just have a degree of common sense? If everyone killed everyone, we'd all be dead or soon to be dead. So seeing murder as a bad thing is common sense. If everyone stole from everyone, pretty soon it'd be pointless trying to acquire property and goods. So seeing theft as a bad thing is common sense. But just as tastes vary the more you get away from the extremes, so does morality vary the more you get away from the extremes.
To answer ae, so maybe Fledge will see what he's asking:
I think logic is objective. It is based on a system of axioms that are self-evident and undeniable, such as the law of noncontradiction, law of identity, law of excluded middle, modus ponens, modus tollens, and others. Anyone who rationally approaches logic and is taught it sufficiently will immediately see the truth to it and you're not going to find people who disagree (In their right mind) with it. The most laws of logic are true by definition, which is about as objective as you can get.
Also math would qualify, since math is a deductive axiomatic system very much like logic, just a more specific application of logical principles and deduction to specific mathematical axioms.