I have a really hard time understanding moral realism. How does it account for the multitude of moral systems in the world? And if moral statements can be true or false, why isn't there a general consensus as to how exactly determine it?

Wouldn't the moral relativist assert that you have made a basic category error in your M and A in that M is about opinions and A is about facts. Let's change things around to illustrate this.

(M1) If growing up under different circumstances could give you a completely different set of beliefs about who should should win the World Series in 2015 than the ones you have now, then fan bias is correct. M2) Growing up under different circumstances could give you a completely different set of beliefs about who should should win the World Series in 2015 than the ones you have now. (M3) So fan bias is correct. Now consider an analogous argument that I don't think you'll be so keen to accept. (A1) If growing up under different circumstances could give you a completely different set of beliefs about who did win the 2014 World Series than the ones you have now, then fan bias is correct. (A2) Growing up under different circumstances could give you a completely different set of beliefs about who did win the 2014 World Series than the ones you have now. (A3) So fan bias is correct.

The obvious difference being that The San Francisco Giants did win the World Series in 2014, and who should win in 2015 is an opinion. If you had grown up in ancient Greece your beliefs about astronomy would be wrong, your beliefs in the 1940's about gay marriage wouldn't have been proven wrong by anything.

Such a person may agree that, while on the surface many people appear to have conflicting views about what's right, these surface-level disagreements can actually be boiled down to a deeper level consensus.

Can they? If one believes homosexuals are by nature leading a sinful lifestyle that they will impart to their children, no sociological survey is going to convince that person otherwise. Similarly, if a gay rights activist believes that it is a moral imperative that gay couples have the same rights as straight couples, sociological data is unlike to impress them either. Each camps answer to the what is best for children question is a lot more deep seeded then you seem to give it credit for, and in neither case is really an evidence based claim about child welfare. Utility based arguments tend to appeal to people who do not have strong opinions either way. In fact, this really just comes off like a 50 cent version of the No Labels campaign. Besides for being based on the stupendously stupid idea that you could get a five foot nothing nebbishy authoritarian elected President if you could just get rid of labels, No labels failed because people really do have different values.

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