If there were no mathematical truths, would the observable universe be different?
If I'm understanding the question correctly, then probably. Assuming for the sake of an argument that there could be an observable universe at all without mathematical truths, then I'd say we should at least expect things like the same numbers to add up to different sums in different contexts, circles having variable ratios of circumference to radius, etc. The consequences would probably be much more dramatic than we can even imagine if we're bound by our familiarity to our own universe.
If every intelligent entity just passively recorded facts, that would be valid. But agents act, and morality is about acting rightly.
This doesn't imply that any sort of moral objectivity need exist. Agents act, and judge, but they do not all act or judge the same way, and there need not be any objective standard according to which one can determine which agents act rightly.
Taste is about assigning aesthetic preference, and agents assign aesthetic preferences (at least some of them do.) Does that imply that taste must be objective?
If I'm understanding the question correctly, then probably. Assuming for the sake of an argument that there could be an observable universe at all without mathematical truths, then I'd say we should at least expect things like the same numbers to add up to different sums in different contexts, circles having variable ratios of circumference to radius, etc
You think matheMatical truth is causal, SOMEHOW?
This doesn't imply that any sort of moral objectivity need exist.
It wasn't meant to: it was an argument against an argument against a claim, not an ar...
One of the most annoying arguments when discussing AI is the perennial "But if the AI is so smart, why won't it figure out the right thing to do anyway?" It's often the ultimate curiosity stopper.
Nick Bostrom has defined the "Orthogonality thesis" as the principle that motivation and intelligence are essentially unrelated: superintelligences can have nearly any type of motivation (at least, nearly any utility function-bases motivation). We're trying to get some rigorous papers out so that when that question comes up, we can point people to standard, and published, arguments. Nick has had a paper accepted that points out the orthogonality thesis is compatible with a lot of philosophical positions that would seem to contradict it.
I'm hoping to complement this with a paper laying out the positive arguments in favour of the thesis. So I'm asking you for your strongest arguments for (or against) the orthogonality thesis. Think of trying to convince a conservative philosopher who's caught a bad case of moral realism - what would you say to them?
Many thanks! Karma and acknowledgements will shower on the best suggestions, and many puppies will be happy.