For our universe to run on mathematical laws, there have to be some.
Laws may be causal. I was asking about truths.
Not every mathematical truth need apply directly to the real world, but if none of them did, then we'd have rather less reason to suspect that they were actually truths.
The vast majority of them do not apply to the real world. For every inverse square law that applies, there is an inverse cube law (etc) that does not. However, that is physics. (Pure) mathematicians aren't concerned about that.
Can you give any examples of things we would mutually recognize as truths for which we cannot observe evidence? Math, as we have already covered, I do not acknowledge as an example,
OTOH, I have never seen a mathematical proof that used observation of experiment.
We don't use empirical verification for individual proofs, but the edifice of mathematics as a whole is subject to evidence with respect to whether or not it works.
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.