It isn't a matter of opinion. Morality starts with a few metaphysical claims about the nature of morality, which need to be defended by reason. For example the claim "It's moral because in the bible" would not be a very defensible claim.
But science has very much to do with our understanding of how people function. Most moral systems have something to do with the idea of 'wellbeing' or happiness. So what makes a good life? You don't think science has anything to say about what does or does not lead to happiness?
The analogy used in the video is of the rule for chess: "don't let them take your queen". Objectively this is a good rule, even though there are situations where you want your queen to be taken. We don't need "always true" rules.
We don't need one universal morality. We need to be able to say that some moral systems are better than others. Societies can reach a high level individually and in different ways (because culture has a large effect on personality), but they can fail in many more ways.
The best moral system for our time might not be the best for a future time. That is not to say that there isn't a best for our time worth striving for. For example, you (CA) might argue that it is wrong for a certain amount of society to be in desperate poverty while a small fraction of a percent are hugely rich. This view may be outdated in a future society that doesn't have poverty problems.So, ultimately, the search for an objective morality would suffer from general human advancement and would find itself quickly outdated and vaunted, a relic of a Modern age.
2 cents.
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What I'm saying applies to many areas, but particularly morality, because that's where people are most likely to say "this is my opinion, not up for argument". It absolutely is up for argument. And to argue you need reasoning and facts (which we get from science).
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